Equivalent Fractions

Raising and Reducing

Pizza Remaining

3/4

6/8 9/12

Multiply by 1

5 x 1 =

235 x 1 =

2/3 x 1 =

a x 1 =

5

235

2/3

a

What is 1?

12

2 1

5

5

1453

453 1

a

a

Raising Fractions

14

3x

3 2 64 2 8

x

3 3 94 3 12

x

Raising Fractions

To raise fractions, increase the denominator.

Multiply numerator and denominator (top and bottom) of the fraction by the same number.

This is the same thing as multiplying by 1.

Raising Fractions

Multiply numerator and denominator (top and bottom) of the fraction by the same number.

This is the same thing as multiplying by 1.

15

6

3

3

5

2

Raising Fractions

Raise 3/8 to 56ths.

Multiply numerator and denominator (top and bottom) of the fraction by the same number.

568

3

Raising Fractions

Raise 3/8 to 56ths.

Multiply numerator and denominator (top and bottom) of the fraction by the same number.

3 7 218 7 56

Reducing Fractions

Opposite of raising.

Make the denominator smaller.

Divide numerator and denominator by the same number.

21 7 356 7 8

Reducing Fractions

Might take more than one step.

More than one way.

Divide numerator and denominator by the same number.

40 2 20 2 10 2 556 2 28 2 14 2 7

Reducing Fractions

Divide numerator and denominator by the same number.

4477

Reducing Fractions

Divide numerator and denominator by the same number.

44 11 477 11 7

Proper and Improper

An improper fraction has a numerator as large or larger than the denominator.

A proper fraction has a numerator smaller than the denominator.

5

12,5

5,1

2,5

8

8 2 5 12, , ,

9 35 10 51

Mixed vs. Improper

A mixed number is a whole number and a fraction part.

A mixed number can be written as an improper fraction.

5

17

5

23

Work this on paper.

We have 5 full crates of apples and one crate with only 7 apples. The full crates each contain 30 apples.

How many apples altogether?

Mixed to Improper.

Multiply the 5 crates times the 30 in each crate and add the 7 left over.

To change a mixed number to improper, multiply the whole number by the denominator and add the numerator. Keep the denominator the same.

30

157

30

730*5

N DxW NW

D D

Mixed to improper

Try some.

8

37

2

15

7

23

Mixed to improper

Try some. 2 2337 7

1 1152 2

3 5978 8

Try this on paper.

We have 135 pencils and boxes that hold 12 each.

How many full boxes? How many loose pencils?

How did you get your answer?

Try this on paper.

We have 135 pencils and boxes that hold 12 each.

How many full boxes? 11 How many loose pencils? 3

How did you get your answer?

Divided 135 by 12. The remainder was the left over.

135/12 = 11 3/12

Improper to Mixed

Divide.

Try these.

3

51

215

3

41

Answers

23

12

4113

3

15 72

5117

3