Adding and subtracting fractions

The Maths Habit

Two bars of chocolate are the same size. Ben and Sam each take 2 shaded pieces. Do they have the same amount?

Ben3 small pieces
Sam2 small pieces

No. Ben has more. His big piece is 2 small pieces.

What fraction of each bar is shaded?

35
14
58

Numerator
The top number of a fraction. It tells you how many parts you have.
35
Denominator
The bottom number of a fraction. It tells you how many equal parts the whole is cut into.
35
Equivalent fractions
Fractions that are the same amount.
1224

same size parts ✓
topbottom+topbottom=top + topbottom
  1. 1Make the bottoms the same.Check the parts are the same size.
  2. 2Add the tops.Count the shaded parts. If the sign is −, take away.
  3. 3Keep the bottom.The parts do not change size.

Work out 27 + 37.

1Make the bottoms the same.
27same ✓
37
2Add the tops.
27+37=57
3Keep the bottom.

Work out 45 − 15.

1Make the bottoms the same.
45same ✓
15
2Take away the tops.
45−15=35
3Keep the bottom.

Work out 27 + 37.

1Make the bottoms the same.
27same ✓
37
2Add the tops.
27+37=57
3Keep the bottom.
1Make the bottoms the same.2Add (or take away) the tops.3Keep the bottom.

Work out 49 + 19.

1Make the bottoms the same.
49same ✓
19
2Add the tops.
49+19=59
3Keep the bottom.

Work out 27 + 37.

1Make the bottoms the same.
27same ✓
37
2Add the tops.
27+37=57
3Keep the bottom.
1Make the bottoms the same.2Add (or take away) the tops.3Keep the bottom.

Work out 67 − 47.

1Make the bottoms the same.
67same ✓
47
2Take away the tops.
67−47=27
3Keep the bottom.

Work out 27 + 37.

1Make the bottoms the same.
27same ✓
37
2Add the tops.
27+37=57
3Keep the bottom.
1Make the bottoms the same.2Add (or take away) the tops.3Keep the bottom.

Work out 311 + 511.

1Make the bottoms the same.
311same ✓
511
2Add the tops.
311+511=811
3Keep the bottom.

1Make the bottoms the same.2Add (or take away) the tops.3Keep the bottom.

1Work out 13 + 13.

1Make the bottoms the same.
13same ✓
13
2Add the tops.
13+13=23
3Keep the bottom.

2Work out 67 − 27.

1Make the bottoms the same.
67same ✓
27
2Take away the tops.
67−27=47
3Keep the bottom.

3Work out 15 + 35.

1Make the bottoms the same.
15same ✓
35
2Add the tops.
15+35=45
3Keep the bottom.

4Work out 79 − 59.

1Make the bottoms the same.
79same ✓
59
2Take away the tops.
79−59=29
3Keep the bottom.

Every part is cut in two. What fraction is shaded now?

24
26
68

cut again: same size parts ✓
topbottom+topbottom=top + topbottom
  1. 1Make the bottoms the same.Cut the bigger parts again, so all the parts are the same size.
  2. 2Add the tops.Count the shaded parts. If the sign is −, take away.
  3. 3Keep the bottom.The parts do not change size.

Work out 12 + 14.

1Make the bottoms the same.
12=24
14
2Add the tops.
24+14=34
3Keep the bottom.

Work out 14 + 38.

1Make the bottoms the same.
14=28
38
2Add the tops.
28+38=58
3Keep the bottom.

Work out 12 + 14.

1Make the bottoms the same.
12=24
14
2Add the tops.
24+14=34
3Keep the bottom.
1Make the bottoms the same.2Add (or take away) the tops.3Keep the bottom.

Work out 15 + 110.

1Make the bottoms the same.
15=210
110
2Add the tops.
210+110=310
3Keep the bottom.

Work out 12 + 14.

1Make the bottoms the same.
12=24
14
2Add the tops.
24+14=34
3Keep the bottom.
1Make the bottoms the same.2Add (or take away) the tops.3Keep the bottom.

Work out 78 − 12.

1Make the bottoms the same.
78
12=48
2Take away the tops.
78−48=38
3Keep the bottom.

Work out 12 + 14.

1Make the bottoms the same.
12=24
14
2Add the tops.
24+14=34
3Keep the bottom.
1Make the bottoms the same.2Add (or take away) the tops.3Keep the bottom.

Work out 29 + 13.

1Make the bottoms the same.
29
13=39
2Add the tops.
29+39=59
3Keep the bottom.

Adding and subtracting fractions worksheet, page 1

Adding and subtracting fractions worksheet, page 2

Answer sheet

Is it right?
Thumbs up: right. Thumbs down: wrong.

  1. 25 + 15 = 310

    Wrong: keep the bottom

  2. 38 + 48 = 78

    Right

  3. 12 + 14 = 26

    Wrong: make the bottoms the same

  4. 57 − 27 = 37

    Right

  5. 34 − 18 = 24

    Wrong: make the bottoms the same

  1. Work out 12 + 13. Both bottoms change.

    56

  2. Work out 13 + 16. Give your answer in its simplest form.

    12

  3. Work out 34 + 12. Write your answer as a mixed number.

    114

  1. Work out 13 + 19.

    49
    1Make thebottomsthe same.13=9192Addthe tops.3Keepthe bottom.+=

  2. Work out 910 − 15.

    710
    1Make thebottomsthe same.91015=2Take awaythe tops.3Keepthe bottom.−=

  3. Work out 14 + 58.

    78
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