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## Fraction Drills

Study Nuggets

Select from the following fraction drills to start

A. Simplifying fractions

C. Multiplying fractions

D. Dividing fractions

## 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

÷

-

5

2

=

2.)

-

12

5

÷

-

10

6

=

3.)

-

10

9

÷

-

7

3

=

4.)

-

4

3

÷

-

5

1

=

5.)

-

5

1

÷

-

6

5

=

## E.   Adding and Subtracting mixed numbers

To add and subtract mixed numbers, change them first into top heavy fractions.

Add or subtract and change back into mixed numbers

WORKOUT TIME: Simplify or Cancel down the following fractions.

(Click Check Answers when you have finished)

1.)

+

=

-

2

1

5

-

2

1

5

2.)

=

3.)

=

4.)

=

6.)

+

=

-

2

1

5

-

2

1

5

7.)

=

8.)

=

9.)

=

a.) Ann mixes

-

2

1

5

cups of self-

raising flour with

-

3

2

3

all-purpose flour. How many

cups are there in total?

b.) She has to take out

-

4

1

2

cups. How many cups are there

now?

cups of

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