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# المراجعة النهائية فى الماث للشهادة الابتدائية الترم الأول لمدرسة الكمال

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### المراجعة النهائية فى الماث للشهادة الابتدائية الترم الأول لمدرسة الكمال

1. 1. 1 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Revision on Simplifying the fraction and divisibility Example (1): Write a number formed from two digits and divisible by two ………………………………………………………………… Example (2): Put a circle around the number that divisible by two and underline on the number divisible by 3 1324 , 231 , 324 , 380 ………………………………………………………………… Drill: Write three whole number divisible by 5 ……………… , ……………… , ……………… Example (3): Simplify into simplest form: a) = b) = = c) = d) = Remember 1) The numbers that divisible by 2 is the numbers that its unite is (0, 2, 4, 6, 8). 2) The numbers that divisible by 5 is the numbers that unite is (0 , 5) 3) The numbers that divisible by 3 is the numbers that its sum is divisible by 3 (from the multiples of 3) 18 27 ….. ….. 420 490 ….. ….. 13 12 ….. ….. 41 205 ….. ….. Remembe r The prime numbers that numbers have two factors 288 120
2. 2. 2 Math Student's Copy Book AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Write the prime numbers between 1 , 50 The prime numbers is: .................................................................................................................................................................................................. .................................................................................................................................................................................................. .................................................................................................................................................................................................. .................................................................................................................................................................................................. ..................................................................................................................................................................................................  Evaluation: 1) Simplify: a) = b) = 2) Write 5 numbers divisible by 2 of 5 together: ………… , ………… , ………… , ………… , ………… Drill: 1) Write 3 number divisible by 2 of 3 together: ……………… , ……………… , ……………… 2) Write number divisible by 2 of 3 together: ………………………… 3) Simplify: a) = b) = a) = Think 72 84 ….. ….. 5 10 ….. ….. 7 21 ….. ….. 16 32 ….. ….. 18 27 ….. ….. 150 450 ….. …..
3. 3. 3 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Unit (1) Lesson (1) The meaning of ratio Ratio: Is comparing between two quantities or numbers as the same type and same unite. Example (1): Huda has 20 pound and Yasmin has 40 pounds compare between them. Solution: = = = and we write it 1 : 2 and we read it 1 to Z Example (2): Find the ration between two numbers in simplest form 64 , 48 Solution: 1st number : 2nd number 48 : 64 ( 2) 24 : 32 ( 4) 6 : 8 ( 2) 3 : 4 another solution: = = = = = and we write it 1 : 2 and we read it 1 to Z Example: Complete: The ration between two numbers = Drill: Find the ratio between two numbers of the following: a) 16 , 32 b) 150 , 450 c) 34 , 102 : ............: 2nd number1st number:2nd number1st number : ............: ............: 3216 : ............: ............: ............ : ............: ............: ............ H.W: P.B P.5 no. 1 , 2 , 3 Definitions: What with Huda What with Yasmin 205 20 40 2 4 1 2 Simplest form 1st number 2nd number What with Yasmin 205 48 64 24 32 6 8 3 4 1st term (antecedent) (consequent) ….... …....
4. 4. 4 Math Student's Copy Book AL KAMAL AZHARIAN INSTITUTES Primary Six First Term -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
5. 5. 5 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Exercises on The meaning of ratio Example: Find the ratio between two numbers 16 , 40 then determine antecedent and the consequent. Solution: ............................................................................................................................................................................................................. ............................................................................................................................................................................................................. ............................................................................................................................................................................................................. Example (1): In one of the classes of the first grade primary the number of boys is 15 pupils and the number of girls is 20 pupils. Calculate: 1) The ratio between the number of boys and the number of girls. 2) The ratio between the number of girls and the number of all pupils in the class. Solution: - Number of girls = 25 girl - Number of boy = 15 boy - The number of pupils = 25 + 15 = 40 pupils 1) Number of boys : number of girls .................................................:............................................. .................................................:............................................. 2) Number of boys : number of pupils .................................................:............................................. .................................................:............................................. Example (2): Find the ration between 2.3 , 5.75 Solution: 1st number : 2nd number 2.3 : 5.75 ……………. : ..…………… ……………. : ..…………… ……………. : ..…………… ……………. : ..…………… Example (3): If the number of sum pupils in school is 540 pupil, the number of boys is 405 pupil. Find: 1) The ratio between the number of boys 2) The ratio between number of boys and the number of girls in two ways: and the number of pupils: …………………………………………..…. ……………………………..…………… …………………………………………..…. ……………………………..…………… …………………………………………..…. ……………………………..…………… H.W: P.B P.5 no. 4 , 5 , 6 , 7
6. 6. 6 Math Student's Copy Book AL KAMAL AZHARIAN INSTITUTES Primary Six First Term -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
7. 7. 7 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Lesson (2) The properties of ratio - Ton = 1000 kgm - Pound = 100 piasters - Kg = 1000 gm - metre = 100 cm - (feddan – kirate – sahm) are units of cultivated lands. feddan = 24 Kirat kirat = 24 sahm Properties of ratio: - Property 1: The ratio has the same properties of the fraction as reduction, simplifying and comparison. - Property 2: in its simplest form, the two terms of the ratio should be two whole numbers. - Property 3: At comparing two quantities of the same type to form the ratio between them, they must have the same unit. - Property 4: The ratio between two quantities of the same kind doesn't have any units. - Property 5: The ratio keeps the order. Example (1) : Find the ratio between: a) 1 : 2.2 (convert into decimal number) 1.6 : 2.2 ( × 10 the two terms) 16 : 22 ( ) …….. : ……… b) Two areas 0.75 kirats, 16 sahm convert  0.75 kirats = 0.75 × 24 = 18 sahm 1st area : 2nd area 18 : 16 (2) 9 : 8 c) : 3 5 Definitions: Remember 1 2 3 4
8. 8. 8 Math Student's Copy Book AL KAMAL AZHARIAN INSTITUTES Primary Six First Term 4 : 6 (2) 2 : 3 Example (2) A rectangle its length 30 cm and width is 18 cm. Find the ratio between perimeter of rectangle and its length. Solution: Perimeter of rectangle = (length + width) × 2 = (30 + 18) × 2 = 48 × 2 = 96 cm Perimeter of rectangle : length 96 : 30 ……... : …….. ……... : …….. Drill: Find the ratio between two amounts: 250 P.T : 7 pounds Solution: ………….…. : …………….. ………….…. : …………….. ………….…. : …………….. ………….…. : …………….. H.W: P.B P.9 no. 1 , 2 , 3 1 2
9. 9. 9 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
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11. 11. 11 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Exercises on Properties of ratio 1) Circumference of the circle = 2r 2) Perimeter of equilateral triangle = side length. Complete: a) Perimeter of square = ……………… b) The diameter of circle = …………… Example 1: Find the ratio between the perimeter of square and its length. Solution: perimeter : side length side length × 4 : side length 4 : 1 Drill 1:Find the ratio between the perimeter of equilateral triangle and its side length. Solution: ............................................................................................................................................................................................ .............................................................................................................................................................................................................................. .............................................................................................................................................................................................................................. Example 2: Find the ratio between the circumference of the circle and its radius. Solution: ............................................................................................................................................................................................ .............................................................................................................................................................................................................................. .............................................................................................................................................................................................................................. Drill 2: Find the ratio between the circumference of the circle and its diameter. Solution: ............................................................................................................................................................................................ .............................................................................................................................................................................................................................. .............................................................................................................................................................................................................................. Example 3: A rectangle its area is 32 cm2 and its width is 4cm find: 1) Length of rectangle. 2) The ratio between the length and width of rectangle. Solution: ............................................................................................................................................................................................ .............................................................................................................................................................................................................................. .............................................................................................................................................................................................................................. Drill 3: Complete: 1) The ratio between side length of square and its perimeter = …….... : …....… 2) The ratio between the two side lengths of square = ………. : ………. 3) The ratio between the radius of circle and its circumference = …….. : ….... H.W: P.B P.9 no. 4 , 5 / P.10 no. 6 , 7 , 8 Remember
12. 12. 12 Math Student's Copy Book AL KAMAL AZHARIAN INSTITUTES Primary Six First Term -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
13. 13. 13 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Lesson (3) Miscellaneous exercises on ratio and its properties Example (1): Find the ratio between 1 , 3 Solution: 1 : 3 : =  = × = = = 1 : 2 Example (2): If the ratio between the weight of Hani to the weight of Ahmed is 5 : 6 and the weight of Ahmed is 72 kgm. Find the weight of Hani. Solution: Hani weight : Ahmed weight 5 : 6 parts ……. : 72 real value The value of one part = 72  6 = 12 kg. The weight of Hani = 12 × 5 = 50 kg. Example (2): A primary school has 540 pupils, if the ration between the number of boys to the number of girls is 4 : 5 Calculate the number of each boys and girls. Solution: Number of boys : number of girls : sum 4 : 5 : 9 ……. : ……… : 540 The value of one part = 540  9 = 60 pupils The number of boys = 4 × 60 = 240 boys. The number of boys = 5 × 60 = 300 girls Chick the solution: Sum = 240 + 300 = 540 pupils. Drill (2): If the ratio between the weight of (Samia) to the weight of (Seham) is 7 : 5 and the difference between the weights is 9.6 kg. Find the weight of each of them. Solution: Samia weight : Seham weight : ………………. …………….. : ……………... : ……………..... …………….. : ……………... : ……………..... …………….. : ……………... : ……………..... H.W: P.B P.14 no. 1 , 2 , 5 To convert the mixed number into improper fraction 1 = (1×4)+3= 4+3= 7 7 4 3 4 3 4 1 2 3 4 1 2 7 4 7 2 7 4 7 2 7 4 7 2 14 28 1 2
14. 14. 14 Math Student's Copy Book AL KAMAL AZHARIAN INSTITUTES Primary Six First Term -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
15. 15. 15 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Exercises on The ratio and its proprrties Complete: a) One hour = …………... minutes. b) One day = ……………. hours. c) Perimeter of rectangle = ………….. Drill (1): Find the ratio between: a) 8 hours , 2 days b) 18 : 6.3 Solution Solution ............................................................................................................................................................................................ ............................................... ............................................................................................................................................. ....................................................................................................................................... ..................................................... ............................................................................................................................................................................................ ............................................... ............................................................................................................................................. Drill (2): A piece of land is a shape of rectangle the ratio between its dimension 4 : 7 and its perimeter is 44 meter. Find the area of land. Solution: ............................................................................................................................................................................................ .............................................................................................................................................................................................................................. .............................................................................................................................................................................................................................. .............................................................................................................................................................................................................................. .............................................................................................................................................................................................................................. Drill (3): The ration between the heights of two buildings in a town is 4 : 7 if the difference between their in 9 meters. Find the height of each of them. Solution: ............................................................................................................................................................................................ .............................................................................................................................................................................................................................. .............................................................................................................................................................................................................................. .............................................................................................................................................................................................................................. .............................................................................................................................................................................................................................. H.W: P.B P.14 no. 3 , 4 , 6
16. 16. 16 Math Student's Copy Book AL KAMAL AZHARIAN INSTITUTES Primary Six First Term -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
17. 17. 17 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Lesson (4) Ratio among three numbers Complete: 1) If A is half B then A : B = ……… : ……….. 2) If A is double B then A : B = ……… : ……….. Example (1): Three persons start commerce the first paid 400 pounds, the second paid 600 pounds and the third paid 1000 pounds. Find the ration between them. Solution 1st : 2nd : 3rd 400 : 600 : 1000 (100) 4 : 6 : 10 (100) 2 : 3 : 5 Example (2): a , b and c are three numbers such that the ration a : b = 4 : 3 and the ratio b : c = 2 : 3 Find the ratio among the three numbers a , b and c. Solution: A : B : C 4 : 3 : ….. …. : 2 : 3 …. : ….. : …… Drill (1): Find the ratio between 0.5 , , 0.125 Solution: 0.5 : : 0.125 0.5 : 0.25 : 0.125 ……………………………………………… ……………………………………………… ……………………………………………… ……………………………………………… Drill (2): If A : B = 2 : 3 , B : C = 6 : 5 , Find A : B : C Solution: A : B : C ……………………………………………… ……………………………………………… ……………………………………………… ……………………………………………… H.W: P.B P.18 no. 2 , 5 1 4
18. 18. 18 Math Student's Copy Book AL KAMAL AZHARIAN INSTITUTES Primary Six First Term -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
19. 19. 19 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Exercises on The ratio among three numbers Complete: a) If A is third B then A : B = ……… : ……….. b) If A : B = 5 : 6 , B : C = 8 : 9 then A : B : C = ……….. : ……… : …….. Solution ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… Drill (1): Amount of money distributes between (Ahmed) , (Ali) and (Tarek) as the ratio 2 : 5 : 3 if the money with Ali more than the money with (Ahmed) by 45 pounds. Find the money with each of them and the total money. Solution ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….…………
20. 20. 20 Math Student's Copy Book AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Remember The sum of interior angles of triangle is 180 Drill (2): If the ratio between the measures of the angles of triangle is 5 : 6 : 7 and the measure. Find the measure of each of angle and find the type of triangle according to its angles. Solution …………………………………………………… …………….……………………………………… …………………………………….……………… …………………………………………………… ……….………………………………………….. ……….………………………………………….. Drill (3): If A, B , C are three numbers if A = B , and A = C Find the ratio between A : B : C. Solution: A : B : C ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… Drill (4): The ratio between the side lengths of triangle is 2 : 3 : 4 if the perimeter is 54 cm. Find the lengths of each of side. Solution ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… ………………………………………………………………….………… 5 3 10 7
21. 21. 21 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term H.W: P.B P.18 no. 1 , 3 , 4 , 6 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
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23. 23. 23 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Lesson (5) Ratio Applications (Rates) The rate is: The ratio between two quantities of different kinds and the unit of rate is the unit of the first quantity per each unit of the second quantity. Example (1): A factory produces 3000 lamps in 4 hours. Find the rate of production. Solution Rate = = 750 lamp / hour (we read it 750 lamps per hour) Drill (1): A car consumes 20 liters of petrol to cover a distance 350 km. Calculate: the rate of consumption of the car to benzene. Solution ………………………………………………………………….………… ………………………………………………………………….………… Drill (2): Two machines the first produces 3000 meters of cloth in 4 hours and the second produces 2520 meter in three hours and half. What is more efficient? Solution ………………………………………………………………….………… ………………………………………………………………….………… Drill (3): A factory produces 5000 cans in 8 hours. Find the rate. Solution ………………………………………………………………….………… ………………………………………………………………….………… Drill (4): A car covers a distance 250 km in 5 hours. Find the velocity (speed) Solution ………………………………………………………………….………… ………………………………………………………………….………… 3000 lamp 4 hours 3
24. 24. 24 Math Student's Copy Book AL KAMAL AZHARIAN INSTITUTES Primary Six First Term H.W: P.B P.20 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
25. 25. 25 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term General Revision on Unit (1) Drill (1): Find the ration between: a) 1 : 2.2 b) 0.75 kirat , 16 sahm, ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ c) 250 p.t : 7 pounds d) 5 : 14.5 ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ Drill (2): Find the ration between: Divide 150 pounds between two persons such that the share of the first = the share of the second. Find the share of each of them. ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... Drill (3): Find the ration between: If the weight of (Aya) = (Mona) weight, and (Mona) weight = (Arwa) weight. Find the weight of each of them If Arwa weight more than (Aya) weight by 24.1 kgm. ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... .............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. Drill (4): A piece of land in a shape of rectangle the ration between its length to width is 5 : 3, If the perimeter is 64 meter. Find the area of land. ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... 3 5 9 4 2 3 4 3 4 4 2 3 4
26. 26. 26 Math Student's Copy Book AL KAMAL AZHARIAN INSTITUTES Primary Six First Term H.W: P.B P.24 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
27. 27. 27 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Unit (2) Lesson (1) The meaning of proportion The proportion is: The equality of two ratios or more. Complete: 1) = = 2) = = Example (1): Complete the table: a) × = = 6 b) 8  = 8 × = = 12 From the table we deduce = = We consider the number 3 , 2 , 9 , 16 , 12 , 8 proportional numbers Drill (1): a) = = = b) = = 27 ….. 3 2 …. 6 16 ….. 4 3 …. 21 2 3 1 9 1 1 18 3 2 3 1 3 2 24 2 ….. 8 9 ….. 3 2 18 4 3 12 9 ….. 3 12 …. 4 20 39...15... 2...8...12 ÷ 2 3 × 2 3
28. 28. 28 Math Student's Copy Book AL KAMAL AZHARIAN INSTITUTES Primary Six First Term H.W: P.B P.28 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
29. 29. 29 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Lesson (2) The properties of proportion Properties of proportion: Property (1): If we multiply (or divide) each of the two terms of ratio by the same non-zero number, then resultant ratio is equal to the first ratio and they together form a proportion. Property (2): The product of extremes = the product of means. Example (1): Complete: 1) = 2) = Solution 1) = 2) = Example (2): Complete: = Notice that: 3 , 5 , 12 , 20 3 × 20 = 60 (the product of extremes) 5 × 12 = 60 (the product of means) Example (3): Find the value of X in the following proportion: a) = b) X , 7 , 24 , 56 = X = X = = 3 X = 120 Example (4): Find the 3rd proportion of the following 1.8 , 1.5 , 3 1.8 , 1.5 , X , 3 = X = = = 3.6 means Extremes 12 ….. 3 5 3 21 1 ….. 4× 3 5 12 20 114× 3 3 21 1 7 11 3 12 20 3 5 3 24 15 X X 7 24 56 7 × 24 56 24 × 15 3 1.8 1.5 X 3 1.8 × 3 1.5 5.4 1.5
30. 30. 30 Math Student's Copy Book AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Drill (1): Find the fourth proportion for the following 6 , 4 , 8 , 15 Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- H.W: P.B P.33 no.1 , 2 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
31. 31. 31 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term (Follow) Lesson (2) The properties of proportion Example (1): Find the value of X in the following proportion: 1) = 0.8 Solution = X + 3 = X + 3 = 4 X = 4 – 3 X = 1 Example (2): To make fig jam we need 4.8 kgm from sugar to 6 kgm from fig. Find: 1) How many kilograms of sugar added to 15 kgm of fig? 2) How many kilograms of fig added to 14.4 kgm of sugar? 1) Solution 2) The weight of sugar X = = 12 kgm The weight of fig = X = = 18 kgm Drill (1): A car needs 14 liter of benzene to cover a distance 175 km. How many kilometers a care covered if it uses 20 liters? Solution Drill (2): Find the value of X in the following proportion = Solution: ------------------------------------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------------------------------------------------- Weight of fig 6 15 Weight of sugar 4.8 X Weight of fig 6 X Weight of sugar 4.8 14.4 distance 175 ……….. liters ………. ………. 8 10 X + 3 5 4.8 × 15 6 X + 3 5 5 × 8 10 14.4 × 6 4.8 2 X 12 5 2 The distance = …………………… ………………………………………
32. 32. 32 Math Student's Copy Book AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Drill (3): A primary school, its building height is 14 meter and the shade of this building at a certain moment is 5 m length. What is the height of a tree in the same moment if its shade length is 3 meters? Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- H.W: P.B P.33 no.3 , 4 -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
33. 33. 33 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Lesson (3) Drawing Scale Drawing Scale = Kilometer = 1000 meter Meter = 100 cm Kilometer = 100000 cm Example (1): The height of Cairo tower in image 12 cm and the real height 180 meter. Find the ratio between the height of tower in image and the real height Solution Convert = 180 × 100 = 18000 cm The height in image: The height in real 12 : 18000 ( 6) 2 : 3000 ( 2) 1 : 1500 Then = and this is drawing scale  The case of drawing scale: 1) If the drawing scale > 1 this expresses enlargement – (magnification) 2) If the drawing scale < 1 this expresses (minimization) – (reduction). Example (2): If the distance between two cities is 75 km and the distance between them on a map is 15 cm. Find the drawing scale and what is mean? Solution Remember Drawing length Real length 5 The height in image The real height Real length 5 1 1500
34. 34. 34 Math Student's Copy Book AL KAMAL AZHARIAN INSTITUTES Primary Six First Term The real length in cm = 75 × 100 000 = 7500 000 cm Drawing scale = = = and this mean that every 1 cm in drawing represent 500 000 cm real.  Note that: The important converts in drawing scale: km cm m cm m cm Drill (1): If the distance between Aswan and Comompo 40 km, and the distance between them on a map is 10 cm. Find the drawing scale to this map and what is mean? Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Complete: a) 3.5 km = ………….. m b) Drawing scale = ………… Drawing length Real length 5 15 7500 000 1500 1 500 000 1500 × 100 000 × 100  10
35. 35. 35 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term (Follow) Lesson (3) Drawing Scale Complete: 1) If drawing scale < this express ----------------------------------------------------------------- 2) If drawing scale > 1 this express ------------------------------------------------------------------ 3) 15 km = --------------------------------------------- cm Drill (1): A road its length 2.5 km, appear on a map with length 14 cm. Find the drawing scale and its mean what. Solution Real length = ------------------------------------------------------------------------ Drawing scale = ------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Example (1): Adel took a magnified picture with a camera if the length of an insect in the picture is 6 cm and its real length is 4 mm. Find the ratio of magnification (Drawing scale) Solution The real length in cm = 4  10 = 0.4 cm Drawing scale = = = = 15 : 1 Drill (2): If the distance between Cairo and Alex on a map is 3.5 cm. Find the drawing scale if the distance between them 210 km. Drawing length Real length 5 6 0.4 1500 60 4 15 00 15 1
36. 36. 36 Math Student's Copy Book AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------  H.W: 1) A magnified of an insect its real length 5 mm and its length after enlargement 10 cm. Find the ratio of magnification. Solution --------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------- 2) A map drawn to Suize Qanal and its length on a map is 8.6 cm, and real length 172 km. Find the drawing scale. Solution --------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------------------------------------------------
37. 37. 37 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Finding the real length Drill: If the distance between two cities 45 km and if the distance between them on a map 3 cm. Find the drawing scale. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Example (1): A map with drawing scale 1 : 1000 000 and the distance between two cities on this map is 35 cm. Find the real length by kilometer. Solution Drawing scale = Drawing length : Real length 1 : 1000 000 35 cm : ………… Real length = = 35000 000 cm Real length in km = 35000 000  100 000 = 350 km Drill (1): A map was drawn for Suiz Qanal in drawing scale 1 : 500 000, if the drawing length is 34.6 cm. Find the real length by kilometer. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Drill (2): 35 × 1000 000 1
38. 38. 38 Math Student's Copy Book AL KAMAL AZHARIAN INSTITUTES Primary Six First Term A drawing scale of a building was 1 : 1000 , if the height of a building in a picture is 3 cm. Then what's the real length. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------  H.W: 1) Area department drawn by drawing scale 1 : 20 000 if a street appears in Minia on one of maps by 7 cm. Find the length of this street by meters. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- 2) A map was drawing scale 3 : 800000 If the distance between them on a map is 12 cm. Find the real distance by kilometer between this cities. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
39. 39. 39 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term Finding the drawing length Example (1): A magnified picture of an insect was taken with enlargement ratio 50 : 1. If the length of the insect on the picture is 30 cm. What is real length of the insect? Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Example (2): If the drawing scale on a map 1 : 5000000 and the real length between two cities 150 km. Find the length between this cities on a map. Solution The real length in cm = 150 × 100 000 = 15000 000 D.S = D.L : R.L 1 : 5000 000 ……… : 1500 000 D.L = = 3 cm Drill (1): 1 × 15000 000 5000 000
40. 40. 40 Math Student's Copy Book AL KAMAL AZHARIAN INSTITUTES Primary Six First Term If the distance between Cairo and Tanta is 85 Km and the drawing scale is 3 : 5000000. Find the distance between them on this map. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- Drill (2): Ahmed draw a picture for his brother Osama in drawing scale 1 : 40 If the real length of Osama is 150 cm. What his drawing length. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------  H.W: The distance between Ismailia and Eltal Elkebeer is 45 km and the drawing scale is 1 : 3000 000. Find the distance between them ob this map. Solution -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------
41. 41. 41 Math Student's Copy Book Date: -- / -- / 20-- Day: ……………… Date: -- / -- / 14-- AL KAMAL AZHARIAN INSTITUTES Primary Six First Term General Exercises on drawing scale  From the opposite figure: 1- Drawing scale = ………………………….. 2- Drawing length = ………………………… 3- Real length = …………………………….. Drill (1): If the distance between two cities on a map is 5 cm and the drawing scale is 1 : 1000 000 Find: 1- The real length between cities in km. 2- The distance between them on another map it drawing scale 1 : 500 000 Solution 1- Drawing scale = D.L : R.L 1 : 1000 000 5 : ………… R.L = = 5000 000 cm R.L by km = 5000 000  100 000 = 50 km 2- D.S = D.L : R.L 1 : 500 000 ..………. : 5000 000 D.L = = 10 cm Drill (2): 5 × 1000 000 1 D.L R.LD.S ÷ ÷ × 5000 000 × 1 500 000