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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 results in smaller numbers?
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!
1
4
X
3
4
=
3
16
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.
numerator x numerator
denominator x denominator
3. Simplify if necessary.
Example:
3
1
x
7
12
1
1
x
7
4
1
28
Click through to see
how you solve this
type of problem.
1. Cross reduce if possible.
3 and 12 can both be
divided by 3.
2. Multiply straight across.
3. Simplify if necessary
(not in this case).
Solve:
Solve on your own.
Click through to see
the answer!
3 x 4
5 9
1 x 4
5
3
4
15
1. Cross reduce.
3 and 9 can both be
divided by 3.
2. Multiply straight across.
3. Simplify if necessary
(not in this case).
Solve:
Solve on your own.
Click through to see
the answer!
7 x 1
8 5
7 x 1
8
5
7
40
1. Cross reduce if possible.
(not in this case).
2. Multiply straight across.
3. Simplify if necessary
(not in this case).
Solve:
Solve on your own.
Click through to see
the answer!
5 x 2
6 3
5 x 1
3
3
5
9
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).
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.
numerator x numerator
denominator x denominator
4. Simplify if necessary.
Do you remember how to turn a
fraction into a mixed number?
Yes, I remember. I
can skip this part!
Oops, I forgot.
Show me how!
+
1
2
4x x 3x
2
5
+
9
17
x
2
5
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.
Example:
Click through to see
how you solve this
type of problem.
1
5
2 x3
4
9
9
32
4 x 9
1
1
x
8
=8
1
8
1
1. Turn mixed numbers
into improper fractions.
2. Cross reduce if possible.
9 and 9 can be divided by 9.
4 and 32 can be divided by 4.
3. Multiply straight across.
4. Simplify if necessary.
Solve:
Click through to see
how you solve this
type of problem.
1
1
4 x7
5
2
21 15
5 x 2
21
1
x
3
2
63
1
= 31
2
2
1. Turn mixed numbers
into improper fractions.
2. Cross reduce if possible.
5 and 15 can be divided by 5.
3. Multiply straight across.
4. Simplify if necessary.
Solve:
Click through to see
how you solve this
type of problem.
1
1
2 x3
2
3
5
10
2 x 3
5
1
x
5
3
25
1
=8
3
3
1. Turn mixed numbers
into improper fractions.
2. Cross reduce if possible.
10 and 2 can be divided by 2.
3. Multiply straight across.
4. Simplify if necessary.
Solve:
Click through to see
how you solve this
type of problem.
3
1
5 x2
5
4
28
9
5 x 3
28
5
x
1. Turn mixed numbers
into improper fractions.
2. Cross reduce if possible.
(Not in this case).
9
3
252
4
= 16
15
5
3. Multiply straight across.
4. Simplify if necessary.