1. Index Fractions Simplest form of a fraction Operations Exercises
Fractions
Matem´ticas 2o E.S.O.
a
Alberto Pardo Milan´s
e
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2. Index Fractions Simplest form of a fraction Operations Exercises
1 Fractions
2 Simplest form of a fraction
3 Operations
4 Exercises

3. Index Fractions Simplest form of a fraction Operations Exercises
Fractions
Alberto Pardo Milan´s
e Fractions

4. Index Fractions Simplest form of a fraction Operations Exercises
Fractions
Parts of a fraction
A fraction is a number that represents a part of something.
a
Fractions are written in the form , where a and b are integers,
b
a
and the number b is not zero. Read a over b.
b
The number a is called numerator, and the number b is called
denominator.
13
Example: , 13 is the numerator and 25 is the denominator.
25
A proper fraction is a fraction that is less than one. A fraction
greater than one is called an improper fraction.
12 23
Examples: is a proper fraction. is an improper fraction.
17 15
Alberto Pardo Milan´s
e Fractions

5. Index Fractions Simplest form of a fraction Operations Exercises
Fractions
Equivalent fractions
Equivalent fractions are different fractions that name the same
amount.
Example:
3 6
= because they represent the same amount.
7 14
To find if two fractions are equivalent you have to check that the
cross-products are equal.
Alberto Pardo Milan´s
e Fractions

6. Index Fractions Simplest form of a fraction Operations Exercises
Fractions
Amplify and reduce fractions
To find equivalent fractions, multiply or divide the numerator and
the denominator by the same number. If you multiply by the same
number, you will amplify the
fraction. If you divide by the same factor, you will reduce the fraction.
Examples:
6
• To amplify we multiply the numerator and the denominator
9
6 60
by 10: = .
9 90
6
• To reduce we divide the numerator and the denomina-
9
6 2
tor by 3: = .
9 3
Alberto Pardo Milan´s
e Fractions

7. Index Fractions Simplest form of a fraction Operations Exercises
Simplest form of a fraction
Alberto Pardo Milan´s
e Fractions

8. Index Fractions Simplest form of a fraction Operations Exercises
Simplest form of a fraction
A lowest terms fraction is a fraction that can not be reduced
anymore. To write a fraction in the simplest form find the lowest
terms fraction. To reduce a fraction to the lowest terms fraction,
we can use two methods:
• Divide the numerator and the denominator by the Greatest
Common Factor.
• Divide the numerator and the denominator by any common
factor and keep dividing until they are relatively prime.
Alberto Pardo Milan´s
e Fractions

9. Index Fractions Simplest form of a fraction Operations Exercises
Simplest form of a fraction
Examples:
70
To obtain the lowest terms fraction of we can divide 70 and
105
70 2
105 by GCD(70, 105) = 35, so = .
105 3
70
To reduce to the lowest terms fraction we can divide by 5 and
105
70
keep dividing until there are no common factors but one =
105
14 2
= , (note 2 and 3 are relatively prime ).
21 3
Alberto Pardo Milan´s
e Fractions

10. Index Fractions Simplest form of a fraction Operations Exercises
Operations
Alberto Pardo Milan´s
e Fractions

11. Index Fractions Simplest form of a fraction Operations Exercises
Operations
Add and subtract
To add or subtract fractions with like denominators, add the
numerators and keep the same denominator. To add or subtract
fractions with unlike denominators, first amplify these fractions to
obtain like denominators (using the LCM or any multiple).
Simplify, if possible.
Examples:
4 8 12 4
+ = = .
15 15 15 5
3 1 3 1 6 5 11
To add + using the LCM: + = + = . Because
15 6 15 6 30 30 30
LCM(15, 6) = 30.
Using another common multiple of 15 and 6, for example 60:
3 1 12 10 22 11
+ = + = = .
15 6 60 60 60 30
Alberto Pardo Milan´s
e Fractions

12. Index Fractions Simplest form of a fraction Operations Exercises
Operations
Multiply and divide
To multiply fractions, multiply the numerators and multiply the
denominators then simplify.
12 3 12 · 3 36 18
Example: · = = = .
5 14 5 · 14 70 35
You can get the reciprocal of a fraction by switching its numerator
and denominator.
14 21
Example: The reciprocal of is .
21 14
To
divide by a fraction, multiply by its reciprocal and simplify, if possible.
2 4 2 17 2 · 17 34 17
Examples: : = · = = = .
8 17 8 4 8·4 32 16
Alberto Pardo Milan´s
e Fractions

13. Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Alberto Pardo Milan´s
e Fractions

14. Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 1
Complete:
Three fifths=
A half=
1
= 1
5 5
= 4 =
2 3
Two quarters=
Two thirds= Two and a quarter=
1
= 2
1 7
= 4 =
3 5
An/one eighth=
A quarter= Two and four tenths=
3
= 1
3 6
= 1 =
4 12
One and a half=
Alberto Pardo Milan´s
e Fractions

15. Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 2
Write a fraction in the simplest form beside each of the following
sentences:
There are forty-two girls out of seventy-two people:
The baby snake was just four and three quarters inches long:
Fifteen out of the twenty students have dogs as pets:
I walk five and a quarter miles a day:
Alberto Pardo Milan´s
e Fractions

16. Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 3
An orchard has 72 peach trees, 15 apple trees, and 23 lemon trees.
In the simplest form, what fraction of the trees are peach trees?
Alberto Pardo Milan´s
e Fractions

17. Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 4
George swims seven eighths miles and Mat swims ten twelfths
miles. Who swims farther?
Alberto Pardo Milan´s
e Fractions

18. Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 5
Compare these fractions using the least common denominator:
2 3 9 7 −1 −2 13
, , , , , , .
−6 4 15 5 −3 10 12
Alberto Pardo Milan´s
e Fractions

19. Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 6
Lance and Frank ate seven twelfths of a pizza. If Frank ate a third
of the pizza, how much of the pizza did Lance eat?
Alberto Pardo Milan´s
e Fractions

20. Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 7
Out of the 20 students, a quarter wear jeans, a fifth wear shorts
and a tenth wear a skirt. How many students wear something else?
Alberto Pardo Milan´s
e Fractions

21. Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 8
Tangram means seven boards of skill.
The Tangram is a Chinese
puzzle consisting of seven flat
pieces (called tans) which are
put together to form different
shapes. Study the tans to the
right that form a square. The
side of the square is 1 cm, so
the area is 1 cm2 . Find the
fractional value of each piece.
Alberto Pardo Milan´s
e Fractions

22. Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 9
My car’s gas tank was empty. I paid forty euros and now It is full.
To go to Marbella I need two fifths of the tank. How much money
is this fraction of the tank?
Alberto Pardo Milan´s
e Fractions

23. Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 10
Peter cut six apples into quarters. How many pieces of apple did he
have?
Alberto Pardo Milan´s
e Fractions

24. Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 11
1
Mike cleaned of the yard that is 24 m2 in total . How many
4
square meters are left?
Alberto Pardo Milan´s
e Fractions

25. Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 12
3
Thomas drunk cup of milk, and now he has 24 cl left. How
5
many ml did the cup have originally?
Alberto Pardo Milan´s
e Fractions

26. Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 13
2
Eric is reading a book with 195 pages. He read of the pages
5
today. How many pages are left?
Alberto Pardo Milan´s
e Fractions

27. Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 14
1
Of Paul’s stone collection are white stones. He has a total of 75
5
stones. How many of them are not white?
Alberto Pardo Milan´s
e Fractions

28. Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 15
1
Mom baked cookies and gave of them to Beth. Of the remaining
2
2
ones she gave to Seth. The rest, which was 4 cookies, she ate
3
herself. How many did she bake originally?
Alberto Pardo Milan´s
e Fractions

29. Index Fractions Simplest form of a fraction Operations Exercises
Exercises
Exercise 16
1
This time Mom baked cookies again, and gave of them to Beth.
2
1
Of the remaining ones she gave to Seth. There were 2 cookies
3
left. How many did she bake this time?
Alberto Pardo Milan´s
e Fractions