FOUR RULES FOR FRACTIONS

4

5

numerator

denominator

The language of fractions

5

3improper fraction

2

3

4mixed number

To simplify a fraction you divide the numerator and denominator by a common factor.

6

8

3

4

This can be shown on a diagram:

=

2

2

=

Examples

1 Simplify

6

9

6

9=

3

3

2

3

2 Simplify

14

35

14

35=

7

7

2

5

3 Simplify

36

42

36

42=

6

6

6

7

4 Change to a mixed number.

5

4

5

4=

1

1

4

note: 4 quarters make one whole one

5 Change to a mixed number.

8

3

8

3=

2

2

3

note: 3 thirds make one whole one

Adding and subtracting fractions

To add or subtract fractions a common denominator is needed first.

Example

1 Calculate

1

5

2

3

first write both fractions with a common denominator of 15

So

1

5

2

3

3

15

10

15

1

5

3

15 and

2

3

10

15

13

15

2 Calculate

first write both fractions with a common denominator of 14

So

4

7

1

2

8

14

7

14

4

7

8

14 and

1

2

7

14

1

14

4

7

1

2

3 Calculate

first write both fractions with a common denominator of 20

So 2

2

51

1

42

8

201

5

20

2

5

8

20 and

1

4

5

20

3

13

20

2

2

51

1

4

Multiplying and dividing fractions

Example

1 Calculate

1

5

2

3

multiply the numerators, multiply the denominators

1

5

2

3

12

5 3

2

15

2 Calculate 1

3

42

1

5

multiply the numerators, multiply the denominators.

7 11

4 5

77

20

first change to improper fractions

1

3

4

7

4 and 2

1

5

11

5

1

3

42

1

5

7

4

11

5

change to a mixed number

3

17

20

3 Calculate

5

8

3

5

multiply the numerators, multiply the denominators.

5 5

8 3

25

24

dividing by is the same as multiplying by

5

8

3

5

5

8

5

3

change to a mixed number

1

1

24

3

5

5

3

4 Calculate 1

1

22

3

4

multiply the numerators, multiply the denominators.

3 4

2 11

12

22

dividing by is the same as multiplying by 1

1

22

3

4

3

2

11

4

simplify

6

11

11

4

4

11

first change to improper fractions

1

1

2

3

2 and 2

3

4

11

4

3

2

4

11