top of page

## Fraction Drills

Study Nuggets

Select from the following fraction drills to start

A. Simplifying fractions

C. Multiplying fractions

D. Dividing fractions

E. Adding and subtracting mixed numbers

F. Multiplying mixed numbers

G. Dividing mixed numbers

H. Practical problems.

## A.   Simplifying fractions

Fractions can be simplified by dividing both the numerator and denominator by a common factor until there is no more common factor.

e.g.

-

20

12

=

-

5

3

(4 is a common factor of 12 and 20, so divide both by 4)

WORKOUT TIME: Simplify or Cancel down the following fractions.

(Click Check Answers when you have finished)

1.)

-

21

15

2.)

-

60

24

3.)

-

45

27

4.)

-

120

50

5.)

-

125

75

## B.   Adding and subtracting fractions

To add or subtract fractions, both fractions must have the same DENOMINATOR

e.g.

-

4

3

+

-

5

3

(4 is a common factor of 12 and 20, so divide both by 4)

Step 1:  Find the smallest number that both denominators divide completely (the lowest common multiple). In this case it is 20.

Step 2:  Make both fractions have a denominator of 20

Step 3:  Now add the fractions: only the top numbers are added or subtracted

-

4

3

=

-

20

15

-

5

4

=

-

20

16

-

20

15

+

-

20

16

-

20

31

=

=

-

20

11

1

WORKOUT TIME: Simplify or Cancel down the following fractions.

(Click Check Answers when you have finished)

1.)

-

6

2

+

-

6

1

=

2.)

-

5

3

+

-

5

2

=

3.)

-

10

9

-

-

10

7

=

4.)

-

4

3

-

-

4

2

=

5.)

-

25

13

+

-

25

11

=

6.)

-

3

2

+

-

6

5

=

7.)

-

10

3

+

-

5

4

=

8.)

-

20

11

+

-

10

7

=

9.)

-

15

13

-

-

3

2

=

10.)

-

8

7

-

-

2

1

=

11)

-

4

1

+

-

6

1

=

12)

-

7

3

+

-

5

2

=

13)

-

20

9

+

-

8

7

=

14)

-

4

3

-

-

3

2

=

15)

-

5

3

-

-

2

1

=

## C.   Multiplying fractions

To multiply fractions, simply multiply the NUMERATORS and DENOMINATORS

e.g.

-

4

3

X

-

5

4

Note: Always simplify fractions when you can

-

20

12

=

-

5

3

=

WORKOUT TIME: Simplify or Cancel down the following fractions.

(Click Check Answers when you have finished)

1.)

-

5

4

x

-

5

2

=

2.)

-

12

5

x

-

10

6

=

3.)

-

10

9

x

-

7

3

=

4.)

-

4

3

x

-

5

1

=

5.)

-

5

1

x

-

6

5

=

## D.   Dividing fractions

Fractions can be divided using the KFC (Keep Flip Change) method.

e.g.

-

4

3

÷

-

5

4

x

-

4

5

-

4

3

=

=

-

16

15

WORKOUT TIME:

1.)

-

5

4

÷

-