المراجعة النهائية فى الماث للشهادة الابتدائية الترم الأول لمدرسة الكمال

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
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
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
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
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5
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
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
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7
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
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
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
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
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10
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11
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
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
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13
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
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
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15
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
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

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17
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
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
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19
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
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
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
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
H.W: P.B P.18 no. 1 , 3 , 4 , 6
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23
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
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
H.W: P.B P.20
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25
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
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
............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
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.
.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
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
H.W: P.B P.24
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27
Date: -- / -- / 20--
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Date: -- / -- / 14--
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
H.W: P.B P.28
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29
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
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
Drill (1): Find the fourth proportion for the following 6 , 4 , 8 , 15
Solution
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H.W: P.B P.33 no.1 , 2
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31
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
(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
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
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H.W: P.B P.33 no.3 , 4
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33
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
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
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
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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
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
(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 = -------------------------------------------------------------------
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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
Solution
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 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
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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
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37
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
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
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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
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Drill (2):
35 × 1000 000
1

38
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
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 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
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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
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39
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
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
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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
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
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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
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 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
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41
Date: -- / -- / 20--
Day: ………………
Date: -- / -- / 14--
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

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