Adding and Subtracting Fractions

• 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

Find the lowest common multiple for each pair of numbers.

Starter: Lowest Common Multiple

3 and 41

5 and 62

3 and 63

4 and 84

5 and 105

12

30

6

8

10

ExtensionFind the missing numbers for each fraction.

1. – = —

2. – = —

3. – = —

25

?20

58

?40

56

25?

Find the lowest common multiple for each pair of numbers.

Starter: Lowest Common Multiple

3 and 41

5 and 62

3 and 63

4 and 84

5 and 105

12

30

6

8

10

ExtensionFind the missing numbers for each fraction.

1. – = —

2. – = —

3. – = —

25

820

58

2540

56

2530

To add fractions which have the same denominator, you must add only the numerators together.

Adding and Subtracting Fractions with the Same Denominator

— + — = —210

510

710

Practice QuestionProve that – + – is –2

626

23

=

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

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– + —3105

Remember, they must have the same denominator before you can add the fractions together.

Adding and Subtracting Fractions with Different Denominators

2– + —3105

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

– = —25

410

— + — = —410

310

710

Now write the equivalent fraction for 3 –52

Adding and Subtracting Fractions with Different Denominators

5– - –148

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 45 ?

8

5 1

– = —14

28

— - — = —58

28

38

Now write the equivalent fraction for 3 –41

Adding and Subtracting Fractions with Different Denominators

1– + –274

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 71 2

— + — = —728

828

1528

Now write the equivalent fraction for 3 –41

28? ?— + —

28

4 71 2

28— + —

28— + — 7 8

Adding and Subtracting Fractions with Different Denominators

3– - –254

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 53 2

— - — = —1520

820

720

Now write the equivalent fractions.3

20? ?— - —

20

4 5

3 2

20

15 8

20— - — — - —

Adding and Subtracting Mixed Number Fractions

How could we calculate the following?

Discuss with the person next to you.

12 – + 3 –134

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

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

1227 40

— + — = —2712

4012

6712

— = 5 —12 1267 7

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 13 2

— - —5

17

4

9

20

— - —5

17

4

9

— - —20

? ?

20

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