Lesson 10.6 Multiply Fractions
I can multiply a fraction by a fraction.
Steps
1. Multiply the numerators: that answer is the new numerator
2. Multiply the denominators: that answer is the new denominator
3. Put answer into simplest form
a. If improper, divide numerator by denominator
Example
1
4
1
4
2
× =
3
2
1×2
3
4×3
× =
2
12
=
1
6
=
2
12
(multiply numerators and denominators)
(simplify – use the ladder method if needed)
Samples
5
3
8
4
2
2
3
3
5
3
6
5
1) × =
2) × =
3) × =
4)
3
10
5
× =
2
5
3
9
2
5) × =
Bonus material
Cross reducing helps you multiply fractions by giving you smaller numbers.
How does it work? Rearranging the order of the numerators or
denominators.
Why is that allowed? Multiplication is commutative.
Steps
1) Rearrange the numerators or denominators so that numbers with
common factors are above each other.
2) Reduce that fraction to lowest terms
3) Repeat if possible until all fractions are in lowest terms
4) Multiply what the lowest terms fractions
5) Simplify the answer if possible (probably won’t be necessary)
Examples
Notice the 3
on top and
on bottom
Move the 3 from
here to there
1
3
3
3
4
3
A) × =
1
3
4
3
× =
3
10
5
5
3
10
× =
3
5
3
10
× =
=
1
3
2
3
=1
Samples
6
5
5
6
7
4
8
14
4
3
9
2
5
4
6
5
1) × =
2) ×
=
3) × =
4) × =
1
2
1
1
4
4
so 1 × =
Now reduce
First, rearrange
B)
=1
×1=
1
2