1. Convert any mixed numbers to improper fractions 2. Find the lowest common denominator (LCD) between the fractions 3. Write the fractions with the LCD as the denominator 4. Add or subtract the numerators 5. Simplify the resulting fraction, and convert back to a mixed number if possible

1. Adding and Subtracting
Fractions

2. • To add and subtract fractions with the same denominator.
• To add and subtract fractions with different denominators.
• To add and subtract mixed number fractions.
• To add and subtract fractions.
Learning Objective
Success Criteria

3. Find the lowest common multiple for each pair of numbers.
Starter: Lowest Common Multiple
3 and 4
1
5 and 6
2
3 and 6
3
4 and 8
4
5 and 10
5
12
30
6
8
10
Extension
Find the missing numbers for each fraction.
1. – = —
2. – = —
3. – = —
2
5
?
20
5
8
?
40
5
6
25
?

4. Find the lowest common multiple for each pair of numbers.
Starter: Lowest Common Multiple
3 and 4
1
5 and 6
2
3 and 6
3
4 and 8
4
5 and 10
5
12
30
6
8
10
Extension
Find the missing numbers for each fraction.
1. – = —
2. – = —
3. – = —
2
5
8
20
5
8
25
40
5
6
25
30

5. To add fractions which have the same denominator, you must add only the
numerators together.
Adding and Subtracting Fractions
with the Same Denominator
— + — = —
2
10
5
10
7
10
Practice Question
Prove that – + – is –
2
6
2
6
2
3
=

6. 2 chairs + 3 chairs = 5 chairs
Adding and Subtracting Fractions
with Different Denominators
What would 2 chairs + 7 rulers be?
We can’t add them together because they aren’t the same object. We can
only add them together when they are the same. This is the same for
fractions.
7 rulers – 5 rulers = 2 rulers

7. Adding and Subtracting Fractions
with Different Denominators
What could we do to the fractions so we can add them?
Discuss this with the person next to you.
At the moment you can’t add these fractions together because they have
different denominators.
2
– + —
3
10
5
Remember, they must have the same denominator before you can add the
fractions together.

8. Adding and Subtracting Fractions
with Different Denominators
2
– + —
3
10
5
We need to find the lowest common multiple for 5 and 10.
1
This needs to be the denominator for both fractions.
2
Now that the denominators are the same, perform the addition.
4
10
10
– + —
— + —
5 10
? 3
10
2 3
– = —
2
5
4
10
— + — = —
4
10
3
10
7
10
Now write the equivalent fraction for
3 –
5
2

9. Adding and Subtracting Fractions
with Different Denominators
5
– - –
1
4
8
We need to find the lowest common multiple for 8 and 4.
1
This needs to be the denominator for both fractions.
2
Now that the denominators are the same, perform the subtraction.
4
8
8
— - —
— - —
8 4
5 ?
8
5 1
– = —
1
4
2
8
— - — = —
5
8
2
8
3
8
Now write the equivalent fraction for
3 –
4
1

10. Adding and Subtracting Fractions
with Different Denominators
1
– + –
2
7
4
We need to find the lowest common multiple for 4 and 7.
1
This needs to be the denominator for both fractions.
2
Now that the denominators are the same, perform the subtraction.
4
28
— + —
4 7
1 2
— + — = —
7
28
8
28
15
28
Now write the equivalent fraction for
3 –
4
1
28
? ?
— + —
28
4 7
1 2
28
— + —
28
— + —
7 8

11. Adding and Subtracting Fractions
with Different Denominators
3
– - –
2
5
4
We need to find the lowest common multiple for 4 and 5.
1
This needs to be the denominator for both fractions.
2
Now that the denominators are the same, perform the subtraction.
4
20
— - —
4 5
3 2
— - — = —
15
20
8
20
7
20
Now write the equivalent fractions.
3
20
? ?
— - —
20
4 5
3 2
20
15 8
20
— - — — - —

12. Adding and Subtracting Fractions
with Different Denominators
Adding and Subtracting Fractions with Different Denominators Activity Sheets

13. Adding and Subtracting Mixed
Number Fractions
How could we calculate the following?
Discuss with the person next to you.
1
2 – + 3 –
1
3
4

14. Adding and Subtracting Mixed
Number Fractions
Convert your mixed number fractions to improper fractions.
1
2 — + 3 —
4 3
– + —
9
4
10
3
1 1
Find the lowest common multiple for 4 and 3.
2
12
This needs to be the denominator for both fractions.
3
– + —
4 3
— + —
?
12
?
12
9 10

15. Adding and Subtracting Mixed
Number Fractions
Write the equivalent fractions.
4
Now that the denominators are the same, perform the addition.
5
Don’t forget to write your answer as a mixed number fraction, if
appropriate.
6
– + —
4 3
— + —
9
12
10
12
27 40
— + — = —
27
12
40
12
67
12
— = 5 —
12 12
67 7

16. Adding and Subtracting Mixed
Number Fractions
Convert your mixed number fractions to improper fractions.
1
Find the lowest common multiple for 5 and 4.
2
This needs to be the denominator for both fractions.
3
— - —
5 4
2 1
3 2
— - —
5
17
4
9
20
— - —
5
17
4
9
— - —
20
? ?
20

17. Adding and Subtracting Mixed
Number Fractions
Write the equivalent fractions.
4
Now that the denominators are the same, perform the subtraction.
5
Don’t forget to write your answer as a mixed number fraction, if
appropriate.
6
— - —
5 4
17 9
— - —
20
68
20
45
— - — = —
20
68
20
45
20
23
20
23
— = 1 —
20
3

18. Adding and Subtracting Mixed
Number Fractions
Adding and Subtracting Mixed Number Fractions Activity Sheet

19. Challenge:
Write a 5-step guide on how to add and subtract fractions.