This document provides instructions on how to multiply fractions. It explains that when multiplying two fractions between 0 and 1, the product is smaller than either factor. It then presents the steps to find the fraction of a fraction: 1) read "of" as meaning to multiply, 2) multiply the numerators, 3) multiply the denominators, and 4) simplify the resulting fraction if possible. Several examples are worked through applying these steps.

1. Multiplication
of
Fractions

2. Times You Would Multiply a Fraction
Times a Fraction
• Your family eats 1/8 of 1/2 of a left
over wedding cake.
1/8 of 1/2 or 1/8 x 1/2

3. Times You Would Multiply a Fraction
Times a Fraction
• Jose had already read 1/2 of his novel.
Today he read 1/12 of the 1/2 left.
How much of the book has he read?
1/12 of 1/2 or 1/12 x 1/2

4. Multiplying Fractions
Conceptual Understanding
• When you multiply two fractions that
are between 0 and 1 the product is
smaller than both fractions.
½ x ¾ = 3/8
Look at the diagram on the
next slide to understand why.

5. Multiplying Fractions
Conceptual Understanding
½ x ¾ = 3/8
¼ ¼ ¼ ¼
1/8 1/8 1/8

6. How to Find a Fraction of a
Fraction
• The first thing to remember is “of”
means multiply in mathematics.
of = x

7. How to Find a Fraction of a
Fraction
• Step 1 - When you see a fraction problem
you know when you read “of” in the
problem you multiply.
ofx1
2
4
9

8. How to Find a Fraction of a Fraction
• Step 2 – Multiply your numerators
straight across.
x 4
9
1
2 = 4

9. How to Find a Fraction of a Fraction
• Step 3 – Then multiply your
denominators straight across.
x 4
9
1
2 = 4
18

10. How to Find the Fraction of a
Fraction
• Step 4 – Simplify your answer. In
this case we reduce.
x 4
9
1
2 = 4
18
÷
÷
2
2=
2
9

11. Multiply and Simplify
9
5
1
6 = 9
30 10
3x ÷
÷
3
3 =

12. Multiply and Simplify
3
4
8
9 = 24
36 3
2x ÷
÷
12
12=

13. Multiply and Simplify
4
3
7
2 = 28
6 6)28
4x
24
44 4
6
÷
÷
2
2
= 2
34

14. Multiply and Simplify
9
2
3
4 = 27
8 8)27
3x
24
3
3
8

15. Multiply and Simplify
8
2
7
3 = 56
6 6)56
9x
54
2
2
6
9 2
6
÷ 2
2 =9 1
3÷

16. Multiply and Simplify
3
4
4
2 = 12
8 8)12
1x
8
4
4
8
14
8
÷ 4
4
= 11
2÷

17. Reference:
Yuskaitis, Monica. (2000) Retrieved from
http://portal.bentonvillek12.org/athurman/5th%20Grade
%20Math/Module%205/Multiplication%20of%20mixed
%20numbers.pdf