Multiplying Fractions

Get ready to become an expert at multiplying fractions & mixed

numbers!

The Good News?

Multiplying fractions is SO much easier than adding or subtracting. No

common denominators are involved! How great is that? As long as you

know basic multiplication facts and how to simplify fractions, you will be able to multiply fractions without a

problem!

The Bad News?

Some students have been taught (or just believe) that you “cross

multiply” fractions. That isn’t true!

Cross reduce? Absolutely! Cross multiply? Never!

When you multiply by a number less than 1 , but greater than 0…

A number that is less than 1, but greater than 0 is a proper fraction.

When multiplying by a proper fraction, you are actually making the number smaller because you are breaking it down into

smaller parts.

Multiplying by whole numbers results in a larger number, like this! 5 x 2 = 10

However, multiplying by a fraction results in a smaller number. When you take a fraction of

something (like half of a candy bar) you are taking less than the original amount!

Multiplying results in smaller numbers?

14 34 316 X =

We start with ¼ of

something and only

want ¾ of that ¼. We only want a part of it!

What are the steps?

To multiply fractions:

1. Cross reduce if possible.2. Multiply straight across.

3. Simplify if necessary.

numerator x numeratordenominator x denominator

37

112x

Click through to see how you solve

this type of problem.

Example:

1. Cross reduce if possible.3 and 12 can both be

divided by 3.17

14x 2. Multiply straight

across.

3. Simplify if necessary (not in this case).

128

Solve:

35

49

xSolve on your own. Click through to see

the answer!1. Cross reduce.

3 and 9 can both be divided by 3.

2. Multiply straight across.

3. Simplify if necessary (not in this case).

15

43

x

415

Solve:

78

15

xSolve on your own. Click through to see

the answer!1. Cross reduce if possible.

(not in this case).

2. Multiply straight across.

3. Simplify if necessary (not in this case).

78

15

x

740

Solve:

56

23

xSolve on your own. Click through to see

the answer!1. Cross reduce if possible. 2 and 6 can both be

divided by 2.

2. Multiply straight across.

3. Simplify if necessary (not in this case).

53

13

x

59

Are Mixed Numbers the Same?

Multiplying mixed numbers is not exactly the same as multiplying

fractions. There is one extra step!

You can’t just multiply the whole numbers and then multiply the

fractions.

So what do we do?

Multiplying Mixed Numbers

Steps:

1. Turn mixed numbers into improper fractions.2. Cross reduce if possible.3. Multiply straight across.

4. Simplify if necessary.

numerator x numeratordenominator x denominator

12

254 x

3

Do you remember how to turn a fraction into a mixed number?

1. Multiply the denominator by the whole number.

2. Add the numerator onto the product.

3. Write the sum as the new numerator. Keep the denominator the same.

Yes, I remember. I can skip this

part!

Oops, I forgot. Show me how!

x x

+ +

92

175x

14

59

Click through to see how you solve

this type of problem.

Example:

2. Cross reduce if possible.9 and 9 can be divided by

9.4 and 32 can be divided

by 4.11

81

x

3. Multiply straight across.

4. Simplify if necessary.

81

2 x 3

1. Turn mixed numbers into improper fractions.

94

329x

= 8

15

12

Click through to see how you solve

this type of problem.

Solve:

2. Cross reduce if possible.

5 and 15 can be divided by 5.

211

32

x

3. Multiply straight across.

4. Simplify if necessary.

632

4 x 7

1. Turn mixed numbers into improper fractions.

215

152x

= 3112

12

13

Click through to see how you solve

this type of problem.

Solve:

2. Cross reduce if possible.

10 and 2 can be divided by 2.

51

53

x

3. Multiply straight across.

4. Simplify if necessary.

253

2 x 3

1. Turn mixed numbers into improper fractions.

52

103x

= 8 13

35

14

Click through to see how you solve

this type of problem.

Solve:

2. Cross reduce if possible.

(Not in this case).

285

93

x

3. Multiply straight across.

4. Simplify if necessary.

25215

5 x 2

1. Turn mixed numbers into improper fractions.

285

93x

= 1645