This document provides teaching materials for a lesson on subtracting fractions, including: - An overview of the lesson structure with sections like starter problems, demonstrations, examples, and assessments. - Instructions for printing handouts and selecting different slide options. - Example subtraction problems worked through step-by-step with explanations. - Practice problems for students with answers provided. - Tips for subtracting fractions with different denominators, like finding a common denominator. The lesson aims to build students' skills in subtracting fractions through examples, explanations, and independent practice problems.

1. Fractions – Subtracting – Complete Lesson
Preview the presentation to check ability-level, AFL questions,
and the animations during demonstrations.
It is recommended to delete slides/sections not needed for your class.

2. Starter
A task at the beginning of the lesson that reviews a skill required
for the learning.
Knowledge Check
Questions to assess students’ current understanding and to
consequently show progress.
Real-Life Example A ‘hook’ to raise interest and provide a concrete example.
Demonstration
Slides for a teacher to lead students – didactically or via
questioning – through a mathematical method.
AFL Questions
Assessment For Learning Questions, used to assess students’
competency for independent tasks/activities.
Plenary An opportunity for students to prove/evaluate their learning.

3. To print handouts from slides -
Select the slide from the left. Then click:
File > Print > ‘Print Current Slide’
To print multiple slides -
Click on a section title to highlight all those slides,
or press ‘Ctrl’ at the same time as selecting slides to
highlight more than one. Then click:
File > Print > ‘Print Selection’
To print double-sided handouts -
Highlight both slides before using ‘Print Selection’.
Choose ‘Print on Both Sides’ and ‘Flip on Short Edge’.
Printing

4. 36
??
x4
+7
÷10
x4 ÷6 x3 x5
÷6
x3
÷2
8

5. 31 August 2023
Subtracting Fractions

6. 1
3
−
1
4
=
KNOWLEDGE CHECK
2
3
−
1
5
=
3
4
−
2
5
=

7. 1
3
−
1
4
=
1
12
KNOWLEDGE CHECK
2
3
−
1
5
=
7
15
3
4
−
2
5
=
7
20

8. Josh had
1
2
of a pizza and Tammy took a
1
4
slice.
How much was left?
1
4
1
4
1
2
2
4

9. Sally had
3
4
of a pizza and Ben took a
1
2
slice.
How much was left?
1
2
1
4
3
4
2
4

10. 1
2
To subtract fractions, they must have the same denominator
(they must be split into the same size pieces)
1
4
?
− =
2
4
1
4
If all the denominators are the same, the calculation is easy!

11. 1
3
To subtract fractions, they must have the same denominator
(they must be split into the same size pieces)
1
6
?
− =
2
6
1
6
If all the denominators are the same, the calculation is easy!

12. 1
3
To subtract fractions, they must have the same denominator
(they must be split into the same size pieces)
1
5
?
− =
5
15
2
15
If all the denominators are the same, the calculation is easy!
3
15

15. Shade
1
2
of the shape.
Shade
1
4
of the shape.
Write the answer
as a fraction
=
3
4
1
2
=
3
6
=
1
6
1
3
=
2
6
Adding Fractions
2
3
=
4
6
=
5
6
1
6
3
4
=
6
8
=
5
8
1
8
1)
2)
3)
2
3
=
6
9
2
9
4
5
=
16
20
1
4
=
5
20
3
5
=
9
15
1
3
=
5
15
4)
5)
6)
2
3
=
14
21
4
7
=
12
21
7)
Example:
Complete the equivalent fractions for each calculation.

16. Shade
1
2
of the shape.
Shade
1
4
of the shape.
Write the answer
as a fraction
=
3
4
1
2
=
3
6
=
1
6
1
3
=
2
6
Adding Fractions
2
3
=
4
6
=
5
6
1
6
3
4
=
6
8
=
5
8
1
8
1)
2)
3)
2
3
=
6
9
2
9
4
5
=
16
20
1
4
=
5
20
3
5
=
9
15
1
3
=
5
15
4)
5)
6)
2
3
=
14
21
4
7
=
12
21
7)
Example:
Complete the equivalent fractions for each calculation.
What rule can we write for
subtracting fractions
without drawing boxes?

17. Shade
1
2
of the shape.
Shade
1
4
of the shape.
Write the answer
as a fraction
=
3
4
1
2
=
3
6
=
1
6
1
3
=
2
6
Adding Fractions
2
3
=
4
6
=
3
6
1
6
3
4
=
6
8
=
5
8
1
8
1)
2)
3)
2
3
=
6
9
=
4
9
2
9
4
5
=
16
20
=
11
20
1
4
=
5
20
3
5
=
9
15
=
4
15
1
3
=
5
15
4)
5)
6)
2
3
=
14
21
=
2
21
4
7
=
12
21
7)
Example:
Complete the equivalent fractions for each calculation.
Answers

18. 2
4
1
4
1
4
=
−
1
2
1
4
=
−
Double the denominator
Double the numerator
We need the denominators to be the same.
Which fraction should we change to make the calculation easy?

19. 4
12
3
12
1
12
=
−
1
3
1
12
=
−
Denominator × 4
Numerator × 4
We need the denominators to be the same.
Which fraction should we change to make the calculation easy?
=
1
4

20. 9
16
2
16
7
16
=
−
3
4
7
16
=
−
Denominator × 4
Numerator × 4
We need the denominators to be the same.
Which fraction should we change to make the calculation easy?
=
1
8

21. Example Complete these calculations in your book.
1) Choose which fraction
you need to change
2) Make an equivalent fraction
3) Subtract the fractions!
1
2
−
1
6
=
2
3
−
1
6
=
1
4
+
1
8
=
2
3
−
2
9
=
3
4
−
5
12
=
5
9
−
1
3
=
3
5
−
7
15
=
2
3
−
1
4
=
4
5
−
2
7
=
(Remember to simplify your answer!)

22. Example Complete these calculations in your book.
1) Choose which fraction
you need to change
2) Make an equivalent fraction
3) Subtract the fractions!
1
2
−
1
6
=
2
6
=
1
3
2
3
−
1
6
=
3
6
=
1
2
1
4
+
1
8
=
1
8
2
3
−
2
9
=
4
9
3
4
−
5
12
=
4
12
=
1
3
5
9
−
1
3
=
2
9
3
5
−
7
15
=
2
15
2
3
−
1
4
=
5
12
4
5
−
2
7
=
18
35
(Remember to simplify your answer!)
Answers

23. Example Complete these calculations in your book.
1) Choose which fraction
you need to change
2) Make an equivalent fraction
2
3
−
4
9
=
3
4
+
3
16
=
1
2
−
3
10
=
2
3
−
1
2
=
2
3
−
3
5
=
3
4
−
3
5
=
5
6
−
1
4
=
5
9
−
2
5
=
3
7
8
− 1
2
3
=
(Remember to simplify your answer!)
3) Subtract the fractions!

24. Example Complete these calculations in your book.
1) Choose which fraction
you need to change
2) Make an equivalent fraction
2
3
−
4
9
=
2
9
3
4
−
3
16
=
9
16
1
2
−
3
10
=
2
10
=
1
5
2
3
−
1
2
=
1
6
2
3
−
3
5
=
1
15
3
4
−
3
5
=
3
20
5
6
−
1
4
=
14
24
=
7
12
5
9
−
2
5
=
7
45
3
7
8
− 1
2
3
= 2
5
24
(Remember to simplify your answer!)
3) Subtract the fractions!
Answers

25. 3
6
2
6
− =
1
6
Numerator
& Denominator
× 3
Numerator
& Denominator
× 2
What common denominator could we use?
1
2
1
3
=
−
When we add or subtract fractions we must have a
common denominator.

26. 18
30
5
30
− =
13
30
Numerator
& Denominator
× 6
Numerator
& Denominator
× 5
What common denominator could we use?
3
5
1
6
=
−
When we add or subtract fractions we must have a
common denominator.

27. 15
18
8
18
− =
7
18
Numerator
& Denominator
× 3
Numerator
& Denominator
× 2
What common denominator could we use?
5
6
4
9
=
−
When we add or subtract fractions we must have a
common denominator.

29. 3
6
2
6
− =
1
6
Numerator
& Denominator
× 3
Numerator
& Denominator
× 2
1
2
1
3
=
−
EXAMPLE
What common denominator
could we use?

30. 9
12
4
12
− =
5
12
Numerator
& Denominator
× 3
Numerator
& Denominator
× 4
3
4
1
3
=
−
EXAMPLE
What common denominator
could we use?

31. 15
20
8
20
− =
7
20
Numerator
& Denominator
× 5
Numerator
& Denominator
× 4
3
4
2
5
=
−
EXAMPLE
What common denominator
could we use?

32. 25
30
18
30
− =
7
30
Numerator
& Denominator
× 5
Numerator
& Denominator
× 6
5
6
3
5
=
−
EXAMPLE
What common denominator
could we use?

33. 14
18
9
18
− =
5
18
Numerator
& Denominator
× 2
Numerator
& Denominator
× 3
7
9
3
6
=
−
EXAMPLE
What common denominator
could we use?

34. 21
24
9
24
− =
12
24
Numerator
& Denominator
× 3
Numerator
& Denominator
× 2
7
8
3
12
=
−
EXAMPLE
What common denominator
could we use?
=
1
2

35. 1
3
−
1
4
=
EXAMPLE
1
4
−
1
5
=
2
3
−
2
5
=
4
5
−
1
6
=
6
7
−
3
5
=
4
5
+
3
8
=

36. 1
3
−
1
4
=
1
12
EXAMPLE
1
4
−
1
5
=
1
20
2
3
−
2
5
=
4
15
4
5
−
1
6
=
19
30
6
7
−
3
5
=
9
35
4
5
−
3
8
=
17
40
Answers

37. 2
3
−
1
4
=
2
3
1)
8
12
−
3
12
=
5
12
Subtracting Fractions with Different Denominators
a) 4
5
−
1
4
=
2
3
16
20
−
5
20
=
11
20
b) 5
6
−
3
5
=
2
3
25
30
−
18
30
=
7
30
c)
3
7
−
1
3
=
2
3
9
21
−
7
21
=
2
21
4
5
−
5
7
=
2
3
e) 9
10
−
3
8
=
2
3
f)
d)
5
9
−
1
6
=
7
18
2) a)
7
10
−
1
6
=
16
30
b)
5
8
−
5
12
=
5
24
c)
18
21
−
10
14
=
1
7
d)
5
9
−
7
15
=
e)
7
8
−
5
9
= f)
3)
4
5
−
1
4
−
3
8
=
c) 2
5
6
− 1
5
8
=
d)
4
5
−
1
2
−
1
4
=
a)
2
3
−
1
6
−
2
9
=
b)
2
3
−
1
4
=
2
3
1)
8
12
−
3
12
=
5
12
Subtracting Fractions with Different Denominators
a) 4
5
−
1
4
=
2
3
16
20
−
5
20
=
11
20
b) 5
6
−
3
5
=
2
3
25
30
−
18
30
=
7
30
c)
3
7
−
1
3
=
2
3
9
21
−
7
21
=
2
21
4
5
−
5
7
=
2
3
e) 9
10
−
3
8
=
2
3
f)
d)
5
9
−
1
6
=
7
18
2) a)
7
10
−
1
6
=
16
30
b)
5
8
−
5
12
=
5
24
c)
18
21
−
10
14
=
1
7
d)
5
9
−
7
15
=
e)
7
8
−
5
9
= f)
3)
4
5
−
1
4
−
3
8
=
c) 2
5
6
− 1
5
8
=
d)
4
5
−
1
2
−
1
4
=
a)
2
3
−
1
6
−
2
9
=
b)

39. 2
3
−
1
4
=
2
3
1)
8
12
−
3
12
=
5
12
Subtracting Fractions with Different Denominators
a) 4
5
−
1
4
=
2
3
16
20
−
5
20
=
11
20
b) 5
6
−
3
5
=
2
3
25
30
−
18
30
=
7
30
c)
3
7
−
1
3
=
2
3
9
21
−
7
21
=
2
21
4
5
−
5
7
=
2
3
e) 9
10
−
3
8
=
2
3
f)
d)
5
9
−
1
6
=
7
18
2) a)
7
10
−
1
6
=
16
30
b)
5
8
−
5
12
=
5
24
c)
18
21
−
10
14
=
1
7
d)
5
9
−
7
15
=
e)
7
8
−
5
9
= f)
3)
4
5
−
1
4
−
3
8
=
c) 2
5
6
− 1
5
8
=
d)
4
5
−
1
2
−
1
4
=
a)
2
3
−
1
6
−
2
9
=
b)

40. 2
3
−
1
4
=
2
3
1)
8
12
−
3
12
=
5
12
Subtracting Fractions with Different Denominators
a) 4
5
−
1
4
=
2
3
16
20
−
5
20
=
11
20
b) 5
6
−
3
5
=
2
3
25
30
−
18
30
=
7
30
c)
3
7
−
1
3
=
2
3
9
21
−
7
21
=
2
21
4
5
−
5
7
=
2
3
28
35
−
25
35
=
3
35
e) 9
10
−
3
8
=
2
3
36
40
−
15
40
=
21
40
f)
d)
5
9
−
1
6
=
7
18
2) a)
7
10
−
1
6
=
16
30
b)
5
8
−
5
12
=
5
24
c)
18
21
−
10
14
=
1
7
d)
5
9
−
7
15
=
4
45
e)
7
8
−
5
9
=
23
72
f)
3)
4
5
−
1
4
−
3
8
=
7
40
c) 2
5
6
− 1
5
8
= 1
5
24
d)
=
8
15
Answers
4
5
−
1
2
−
1
4
=
1
20
a)
2
3
−
1
6
−
2
9
=
5
18
b)

41. Extension
Jane has a one-litre bottle of fizzy drink.
She fills four cups
that each hold one-seventh of the liquid.
She then fills a bigger cup, that holds two-fifths of the liquid.
She wants to give herself one-third of the bottle.
Is this possible?

42. Extension
Jane has a one-litre bottle of fizzy drink.
She fills four cups
that each hold one-seventh of the liquid.
She then fills a bigger cup, that holds two-fifths of the liquid.
She wants to give herself one-third of the bottle.
Is this possible?
1 −
1
7
−
1
7
−
1
7
−
2
5
=
1 −
3
7
−
2
5
=
35
35
−
21
35
−
10
35
=
11
35
11
33
=
1
3
She does not
have enough.
Answer

43. You are only allowed to use the numbers 2, 3, 4 and 5
What is the largest
addition total
you can make?
What is the smallest
subtraction total
you can make?

44. You are only allowed to use the numbers 2, 3, 4 and 5
What is the largest
addition total
you can make?
What is the smallest
subtraction total
you can make?
5
2
4
3
2
3
4
5
3
5
6
−
2
15

45. I can subtract fractions with the same
denominator.
I can subtract fractions with different
denominators.
I can subtract mixed numbers.
Check your success!

46. I can subtract fractions with the same
denominator.
I can subtract fractions with different
denominators.
I can subtract mixed numbers.
Check your success!

47. Write a text message to a friend describing…
How to subtract
fractions that have
different
denominators.

48. Questions?
Comments?
Suggestions?
…or have you found a mistake!?
Any feedback would be appreciated .
Please feel free to email:
tom@goteachmaths.co.uk