Fractions – Multiplying – Complete Lesson

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Knowledge Check consequently show progress.

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Demonstration
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competency for independent tasks/activities.

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10 x3 ÷2 -5

x2 x5 +5 ÷5

÷10 -5 x8 ?
16
?
 09/10/22

Multiplying Fractions
 KNOWLEDGE CHECK

2 1
÷ =¿
5 6
 KNOWLEDGE CHECK

2 1 12 2
÷ = =2
5 6 5 5
 Georgie took a of the cake!

She split the piece into 3 and

gave one piece each to Tom and Rob.

How big was the piece Tom ate?

of means
How do we find the area of a field?

8 metres

6 metres

Area = 8 × 6 = 48 metres2
What if we want to find the area of half the length,
and half the width?

4 metres

3 metres

We can see it is a quarter of the whole field.

What if we want to find the area of half the length,
and a third of the width?

What fraction of the field is the area?

1 1 1
4
or
5
or
6 ?
 This is an easy way to multiply fractions.
1
2
1
3

1 1 1
× =
2 3 6
 What is the fraction for… What is the fraction for…

1 1 1 1 1 1
× =¿ × =¿
2 4 8 2 5 10

1 1
2 2
1 1
4 5
 What is the fraction for… What is the fraction for…

1 1 1 2 1 2
× =¿ × =¿
3 4 12 3 4 12

1 2
3 3
1 1
4 4
Draw diagrams in your books to help calculate the answers.
1) 2)
1
1 1 1 1
× =¿ × =¿ 4
3 3 4 5
1
5

3) 3)

1 2 3 2
× =¿ × =¿
3 3 4 3
Draw diagrams in your books to help calculate the answers.
1) 2)
1 1
1 1 1 1 1 1
× = 3 × = 4
3 3 9 4 5 20
1 1
3 5

3) 3)
1 3
1 2 2 3
3 2 6 4
× = × =
3 3 9 4 3 12
2 2
3 3
Can we make
Answers this fraction simpler?
Draw diagrams in your books to help calculate the answers.
1) 2)
1 1
1 1 1 1 1 1
× = 3 × = 4
3 3 9 4 5 20
1 1
3 5

Can we write a rule for multiplying fractions,

3) just using numbers?
3)
1 3
1 2 2 3
3 2 6 4
× = × =
3 3 9 4 3 12
2 2
3 3
Can we make
Answers this fraction simpler?
 1
1 2 2 3
× =
3 3 9
2
3

ANNA says…. To multiply fractions,

multiply the numerator,
then multiply the denominator.

Is Anna right?
To quickly multiply fractions we
multiply the numerators
and multiply the denominators

(1 x 1)
(1)

1 1 1
× =¿
2 3 6
(6)
(2 x 3)
To quickly multiply fractions we
multiply the numerators
and multiply the denominators

(1 x 2)
(2)

1 2 2
× =¿
3 3 9
(9)
(3 x 3)
To quickly multiply fractions we
multiply the numerators
and multiply the denominators

(1 x 2)
Can we simplify
(2) this fraction?

1 2 2 1
× =¿ ¿
4 3 12 6
(12)
(4 x 3)
To quickly multiply fractions we
multiply the numerators
and multiply the denominators

(2 x 1)
Can we simplify
(2) this fraction?

2 1 2
× =¿
3 5 15
(15)
(3 x 5)
To quickly multiply fractions we
multiply the numerators
and multiply the denominators

(3 x 2)
Can we simplify
(6) this fraction?

3 2 6 3
× =¿ ¿
4 5 20 10
(20)
(4 x 5)
To quickly multiply fractions we
multiply the numerators
and multiply the denominators

(5 x 3)
Can we simplify
(15) this fraction?

5 3 15 1
× =¿ ¿
6 5 30 2
(30)
(6 x 5)
 What’s wrong? What’s the answer?

2 4 6 8
Sarah × =
3 5 15 15

2 3 6
Julie × = 2
3 5 15
5
 3 1
× =¿
4 6
4 1
× =¿
5 6
5 2
× =¿
6 7
1 1 5 5
× =¿ × =¿
3 5 7 6
2 1 1 3
× =¿ 1 × =¿
3 4 2 4
3 2 3 1
× =¿ 2 ×1 =¿
4 5 4 2
 3 1 3 1
× = =
4 6 24 8
4 1 4 2
× = =
5 6 30 15
5 2 10 5
× = =
Answers 6 7 42 21
1 1 1 5 5 25
× = × =
3 5 15 7 6 42
2 1 2 1 1 3 9 1
× = = 1 × = =1
3 4 12 6 2 4 8 8
3 2 6 3 3 1 33 1
× = = 2 ×1 = =4
4 5 20 10 4 2 8 8
 Ben, Bob and Bill split a pizza equally.
Ben gave half his pizza to
his sister, Anna.

What fraction of the whole Pizza did Anna get?

Ben Bob Bill

Anna

Anna got of the whole pizza. 1 1 1 1 1

𝑜𝑓 × =¿
2 3 2 3 6
Jim, Jane, Jack and John split a pizza equally.

Jim gave half his pizza to

his brother, David.

What fraction of the whole Pizza did David get?

Jim Jane Jack John

David

David got of the whole pizza. 1 1 1 1 1

𝑜𝑓 × =¿
2 4 2 4 8
 Mary split her birthday cake into 8 equal pieces.

Sally split one of the pieces into two.

1 What fraction of the whole cake is

one of Sally’s pieces?
8

1
16 1 1 1 1 1
𝑜𝑓 × =¿
2 8 2 8 16
 Mary split her birthday cake into 7 equal pieces.

Sally split one of the pieces into 3.

What fraction of the whole cake is

1
one of Sally’s pieces?
7

1
21 1 1 1 1 1
𝑜𝑓 × =¿
3 7 3 7 21
Calculate of

1
3

1
6 1 1 1 1 1
𝑜𝑓 × =¿
3 2 3 2 6
Calculate of

1
3

1
12 1 1 1 1 1
𝑜𝑓 × =¿
4 3 4 3 12
Calculate of

2
3

1 1
12 12
1 2 1 22 1
𝑜𝑓 × =
¿ ¿
4 3 4 312 6
Calculate of

2
3

1 1 1 1 1 1
12 12 12 12 12 12

3 2 3 26 1
𝑜𝑓 × =
¿ ¿
4 3 4 312 2
 Draw diagrams in your books to help calculate the answers.

of = of = of =

of = of = of =
 Draw diagrams in your books to help calculate the answers.

of = of = of = =

of = of = of = =
 Multiplying Fractions : Amber Multiplying Fractions : Amber

1. a) 4 2 b) 1 5 1. a) 4 2 b) 1 5
5
× = 15 7
× = 14 5
× = 15 7
× = 14

Simplify! Simplify!
c) 2 5 d) 2 8 c) 2 5 d) 2 8
5
× 6
= = × 3
= 27 5
× 6
= = × 3
= 27

3. Calculate the area of this rectangle. 3. Calculate the area of this rectangle.
5 3 5 3
2. a) × =¿ 5 2. a) × =¿ 5
7 4 m 7 4 m
6 6
6 4 3 6 4 3
b) × =¿ m b) × =¿ m
7 9 4 7 9 4

Multiplying Fractions : Green Multiplying Fractions : Green

5 3 6 2 5 3 6 2
1. a) × =¿ b) × =¿ 1. a) × =¿ b) × =¿
7 4 7 3 7 4 7 3
4 3 7 5 4 3 7 5
c) × =¿ d) × =¿ c) × =¿ d) × =¿
9 8 10 7 9 8 10 7
2 3 2 3
2. a) How can we calculate this? 1 × =¿ 2. a) How can we calculate this? 1 × =¿
3 4 3 4
3 3 4 2 3 3 4 2
b) 1 × =¿ c) 1 × 1 =¿ b) 1 × =¿ c) 1 × 1 =¿
4 5 5 7 4 5 5 7

3. a) Can we make this calculation easier before multiplying? 3. a) Can we make this calculation easier before multiplying?
(Look again at Question 1 part d) 4 3 (Look again at Question 1 part d) 4 3
× =¿ × =¿
5 4 5 4
 Multiplying Fractions : Amber

1. a) 4 2 b) 1 5
5
× = 15 7
× = 14

Simplify!
c) 2 5 d) 2 8
5
× 6
= = × 3
= 27

3. Calculate the area of this rectangle.

5 3
2. a) × =¿ 5
7 4 m
6
6 4 3
b) × =¿ m
7 9 4

Multiplying Fractions : Green

5 3 6 2
1. a) × =¿ b) × =¿
7 4 7 3
4 3 7 5
c) × =¿ d) × =¿
9 8 10 7
2 3
2. a) How can we calculate this? 1 × =¿
3 4
3 3 4 2
b) 1 × =¿ c) 1 × 1 =¿
4 5 5 7

3. a) Can we make this calculation easier before multiplying?

(Look again at Question 1 part d) 4 3
× =¿
5 4
 Multiplying Fractions : Amber
4 2 8 5 1 5

Answers
1. a) b)
5
× 3
= 15 7
× 2
= 14

Simplify!
c) 2 5 10 1 d) 4 2 8
5
× 6
= 30
= 3 9
× 3
= 27

3. Calculate the area of this rectangle.

5 3 15
2. a) × = 15 5 5
7 4 28 = m2 m
24 8 6
6 4 24 8 3
b) × = = m
7 9 63 21 4

Multiplying Fractions : Green

5 3 15 6 2 12 4
1. a) × = b) × = =
7 4 28 7 3 21 7
4 3 12 1 7 5 35 1
c) × = = d) × = =
9 8 72 6 10 7 70 2
2 3 5 3 15 5 1
2. a) How can we calculate this? 1 × = × = = =1
3 4 3 4 12 4 4
3 3 21 1 4 2 81 11
b) 1 × = =1 c) 1 × 1 = =2
4 5 20 20 5 7 35 35

3. a) Can we make this calculation easier before multiplying?

(Look again at Question 1 part d) 4 3 3
× =
5 4 5
Answers
Answers
 Georgie took a of the cake!

She split the piece into 4 and

gave one piece to Tom, Ann and Rob.

How big was the piece Ann got?

of means
Check your success!

I can multiply fractions with 1 as the numerator.

I can multiply fractions with any numerator.

I can multiply mixed numbers.

Check your success!

I can multiply fractions with 1 as the numerator.

I can multiply fractions with any numerator.

I can multiply mixed numbers.

Write a text message to a friend describing…

How to multiply
fractions.
 Questions?
Comments?
Suggestions?

…or have you found a mistake!?

Any feedback would be appreciated .

Please feel free to email:

tom@goteachmaths.co.uk