Equivalent Fractions

Raising and Reducing

Pizza

Pizza

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

Rasing Fractions

A man walks into the pizza store and orders a medium pizza.

The clerk asks “ Would you like that cut in 8 pieces or 6?”

The man replied “ Make it 6. I don’t think I can eat 8.”

Rasing Fractions

To raise fractions make the denominator larger.

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

This is the same thing as multiplying by 1.

Rasing 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

Rasing 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

Simplifying 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

Simplifying Fractions

Divide numerator and denominator by the same number.

4477

Simplifying Fractions

Divide numerator and denominator by the same number.

44 11 477 11 7

Proper and Improper

An improper fraction has a numerator larger than the denominator.

A proper fration 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 has a whole and fraction part.

A mixednumber can be written as an improper and visa versa.

5

17

5

23

Work this on paper.

We have 5 full crates of apples and one crate with only7 apples. The full crates contain 30 apples.

How many apples altogether?

Work this on paper.

We have 5 full crates of apples and one crate with only7 apples. The full crates contain 30 apples.

How many apples altogether?

157 apples.

How did you get the answer?

Mixed to Improper.

You multiplied the 5 times 30 and added the 7

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

30

157

30

75

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.

D

RW

RWND

D

N

R

5

23

23125

5

12

Try these.

3

51

215

3

41

Answers

23

12

4113

3

15 72

5117

3