1. MATHEMATICS 5
Solving Problems Involving
Multiplication of Fractions
Multiplying a Fraction by its Reciprocal
WEEK 7

2. -Solve routine or non-routine problems
involving multiplication without or with
addition or subtraction of fractions and
whole numbers using appropriate problem
solving strategies and tools
-Show that multiplying a fraction by its
reciprocal is equal to 1.
(MELC-Math 5)

3. What is the sum of 3
𝟒
𝟓
and
𝟏
𝟒
?
3
𝟒
𝟓
+
𝟏
𝟒
= 𝟑 +
𝟐𝟎
+
𝟐𝟎
16 5
= 𝟑 +
𝟐𝟏
𝟐𝟎
= 𝟑 + 𝟏
𝟏
𝟐𝟎
= 𝟒
𝟏
𝟐𝟎

4. Butterfly or Cross-Multiplication Method
=7
𝟏𝟐
2
𝟏𝟐
-
=5
8 3
𝟓
𝟏𝟐

5. =
2
3
3
8
x
6
24
2
3
𝑜𝑓
3
8
Multiplying Fractions
= =
𝟏
𝟒
Cancellation Method
1. Look for a pair of numerator
and denominator to cancel or
reduce.
2. Multiply.
2
3
3
8
x =
1
1
𝟏
𝟒
1
4

6. There was
𝟓
𝟖
of a pie left in the fridge.
Liam ate
𝟏
𝟓
of the leftover pie. How much
of a pie did he eat?
The FOUR STEPS in Solving Problems:
1. Understand
2. Plan
3. Solve
4. Check
1. Study
2. Think
3. Act
4. Review

7. There was
𝟓
𝟖
of a pie left in the fridge.
Liam ate
𝟏
𝟓
of the leftover pie. How much
of a pie did he eat?
UNDERSTAND
1. What is asked in the problem?
The amount of pie Liam ate.
2. What are given?
𝟓
𝟖
of a pie left
𝟏
𝟓
of the leftover pie

8. There was
𝟓
𝟖
of a pie left in the fridge.
Liam ate
𝟏
𝟓
of the leftover pie. How much
of a pie did he eat?
PLAN
1. What is the operation will be used?
Multiplication
2. What is the mathematical sentence?
𝟏
𝟓
x
𝟓
𝟖
= N

9. There was
𝟓
𝟖
of a pie left in the fridge.
Liam ate
𝟏
𝟓
of the leftover pie. How much
of a pie did he eat?
SOLVE
𝟏
𝟓
x
𝟓
𝟖
= N
𝟏
𝟓
x
𝟓
𝟖
=
𝟓
𝟒𝟎
=
𝟏
𝟖
Answer: Liam ate
𝟏
𝟖
of the pie.

10. There was
𝟓
𝟖
of a pie left in the fridge.
Liam ate
𝟏
𝟓
of the leftover pie. How much
of a pie did he eat?
CHECK
𝟏
𝟓
x
𝟓
𝟖
=
𝟏
𝟖
Answer: Liam ate
𝟏
𝟖
of the pie.
1
1

11. UNDERSTAND
1. What is asked in the problem?
The weight in pound of each box of cupcakes.
2. What are given?
24 cupcakes
Each cupcake is
𝟐
𝟏𝟓
pound.
6 cupcakes in each box
Pam baked some cupcakes for her friends. She
baked 24 cupcakes. Each cupcake is
𝟐
𝟏𝟓
pound.
If she packed 6 cupcakes in each box, what is
the weight in pounds of each box?

12. Pam baked some cupcakes for her friends. She
baked 24 cupcakes. Each cupcake is
𝟐
𝟏𝟓
pound. If
she packed 6 cupcakes in each box, what is the
weight in pounds of each box?
PLAN
1. What is the operation will be used?
Multiplication
2. What is the mathematical sentence?
𝟐
𝟏𝟓
x 6= N

13. Pam baked some cupcakes for her friends. She
baked 24 cupcakes. Each cupcake is
𝟐
𝟏𝟓
pound. If
she packed 6 cupcakes in each box, what is the
weight in pounds of each box?
SOLVE
𝟐
𝟏𝟓
x 6= N
𝟐
𝟏𝟓
x
𝟔
𝟏
=
𝟏𝟐
𝟏𝟓
=
𝟒
𝟓
Answer: The weight of each
box of cupcakes is
𝟒
𝟓
pound.

14. CHECK 𝟐
𝟏𝟓
x
𝟔
𝟏
=
𝟒
𝟓
Answer: The weight of each
box of cupcakes is
𝟒
𝟓
pound.
2
5
Pam baked some cupcakes for her friends. She
baked 24 cupcakes. Each cupcake is
𝟐
𝟏𝟓
pound.
If she packed 6 cupcakes in each box, what is
the weight in pounds of each box?

15. Showing that Multiplying
a Fraction by its
Reciprocal is Equal to 1

16. Two fractions whose product is 1
are reciprocals of each other.
Reciprocal means multiplicative
inverse.
Example:
3
4
x
4
3
= 1

17. Example:
15
4
x
4
15
= 1
Example:
6 x
1
6
= 1

18. Example:
3
1
4
x
4
13
= 1
13
4
x
4
13
= 1