1. get all crazy with this “friend”
Multiplying
Fractions
Let’s make fractions
our friends!
Now, let’s not
get all crazy with this “friend”
stuff, Mr. Russler.
Chapter 9

2. Multiplying Fractions
I have some great news when it comes to multiplying fractions…
WE DON’T NEED COMMON DENOMINATORS!
Are you sure?
What’s that?
Sweet!
YES!

3. Multiplying Fractions
When we multiply fractions, we can use the multiplication symbol: A raised dot: Or parenthesis:
𝟏 𝟑 x 𝟐 𝟓
𝟏 𝟑 ∙ 𝟐 𝟓
𝟏 𝟑 𝟐 𝟓

4. Multiplying Fractions
Terms you need to know:
numerator
denominator
Simplify – to reduce a fraction into its simplest form.
Greatest Common Factor (GCF) – the greatest number that evenly divides both numerator and denominator.
Reciprocal – the fraction you get when you exchange the numerator and denominator

5. Multiplying Fractions
𝟏 𝟑 ∙ 𝟐 𝟓
Let’s multiply the following:
To multiply
fractions →
numerator x numerator denominator x denominator
𝟏 ∙ 𝟐 𝟑 ∙ 𝟓 = 𝟐 𝟏𝟓
*Then check to see if the
answer can be simplified.
𝟐 𝟏𝟓
is reduced.

6. Multiplying Fractions
𝟑 𝟒 ×𝟓
Let’s try another one:
Replace 5 with a fraction
𝟑 𝟒 × 𝟓 𝟏 3
Multiply numerators →
Multiply denominators →
𝟑 ×𝟓 𝟒 ×𝟏 = 𝟏𝟓 𝟒 3 4 4) 15
= 3 𝟑 𝟒 12 3

7. Multiplying Fractions
𝟑 𝟖 ∙ 𝟐 𝟑
Let’s try another one:
Multiply numerators →
Multiply denominators →
𝟑 ∙ 𝟐 𝟖 ∙ 𝟑 = 𝟔 𝟐𝟒
𝟔 ÷ 𝟔 𝟐𝟒 ÷ 𝟔 =
𝟔 𝟐𝟒
The GCF of
is 𝟔, so
𝟏 𝟒

8. RECIPROCALS = 𝟏 𝟐 𝟑 × 𝟑 𝟐 = 𝟔 𝟔 REMEMBER … RECIPROCAL MEANS FLIP
Sometimes the product of two fractions is 1
These fractions are RECIPROCALS of each other
Reciprocal – the fraction you get when you flip the numerator and denominator
𝟐 𝟑 × 𝟑 𝟐 =
𝟔 𝟔
= 𝟏
REMEMBER … RECIPROCAL MEANS FLIP

9. Find the reciprocal of each fraction
RECIPROCALS
Find the reciprocal of each fraction
𝟗 𝟏𝟎
𝟏𝟎 𝟗
𝟐 𝟓
𝟓 𝟐

10. Multiplying Fractions
Your Turn!
𝟏. 𝟑 𝟕 ∙ 𝟏 𝟐 𝟐. 𝟒 𝟓 ∙ 𝟑 𝟒
Find the reciprocal of each fraction:
𝟑. 𝟑 𝟖 𝟒. 𝟒 𝟓
𝟓. 𝟑 𝟒
See how you did!
𝟏. 𝟑 𝟏𝟒
𝟐. 𝟑 𝟓
𝟑. 𝟖 𝟑
𝟒. 𝟓 𝟒
5. 𝟒 𝟑

11. 9.2 Multiplication Shortcut
Multiplying
Fractions
There is a
shortcut!?!
9.2 Multiplication Shortcut

12. Multiplying Fractions
Let me show you a simplifying method called cross-cancelling
Reduce or cancel the “diagonals” before you multiply.
Of course I can!
𝟑 𝟖 ∙ 𝟐 𝟑
= 𝟏 𝟒 ∙ 𝟏 𝟏 1
= 𝟏 𝟒 1
I think
I get it! Can
you show me
another one? 4 1

13. Multiplying Fractions
Let’s do a side-by-side.
Standard method:
Cross-cancel method:
𝟏𝟏 𝟏𝟐 ∙ 𝟏𝟒 𝟓𝟓
= 𝟏𝟓𝟒 𝟔𝟔𝟎 1
𝟏𝟏 𝟏𝟐 ∙ 𝟏𝟒 𝟓𝟓 7
= 𝟏 𝟔 ∙ 𝟕 𝟓
= 𝟕 𝟑𝟎 6 5
= 𝟕𝟕 𝟑𝟑𝟎
= 𝟕 𝟑𝟎
Cross-cancelling
is fun, and it
keeps the numbers
way smaller!

14. Multiplying Fractions
Cross-Cancelling
Reduce or cancel the “diagonals” before you multiply. 1
𝟑 𝟒 ∙ 𝟒 𝟓
= 𝟑 𝟏 ∙ 𝟏 𝟓
= 𝟑 𝟓 1 2 6
𝟏𝟒 𝟐𝟓 ∙ 𝟑𝟎 𝟒𝟗
= 𝟐 𝟓 × 𝟔 𝟕
= 𝟏𝟐 𝟑𝟓 5 7

15. Multiplying Fractions
Good luck!
𝟏. 𝟑 𝟖 ∙ 𝟖 𝟏𝟓 𝟐. 𝟏𝟒 𝟐𝟓 ∙ 𝟏𝟎 𝟐𝟏
3. 𝟑 𝟒 ∙ 𝟒 𝟓
See how you did!
1. 𝟏 𝟓
2. 𝟒 𝟏𝟓
𝟑. 𝟑 𝟓