Addition and Subtraction Word Problems

Two kinds of add and subtract stories

When you read an addition or subtraction word problem, it almost always belongs to one of two families. Spotting the family is the secret to choosing the right operation every time.

• Part-whole stories — two or more parts make a whole, or a whole has a part removed. 47 boys and 28 girls make a whole class of 75.
• Comparison stories — two amounts are set side by side and you find the difference. Tom has 17 more stickers than Mia.

If you would like a refresher on the operations themselves first, read Addition and Subtraction Made Easy. This lesson is all about turning stories into number sentences.

A four-step plan

Use the same routine on every problem and they stop feeling tricky.

1. Read the problem twice — once for the story, once for the numbers.
2. Draw a bar model so you can see the parts and the whole.
3. Decide add or subtract from the picture, not just from keywords.
4. Solve and check — does the answer make sense in the story?

Keyword clues (handle with care)

Usually add (+)	Usually subtract (−)
altogether, total, in all, both	how many more, how many fewer
sum, combined, joined	left, remain, take away
... more than (to find the larger)	difference, decrease

Keywords are signposts, not rules. "How many more" sits in the subtract column even though it contains the word "more" — that catches many people out, so always picture the story.

Worked example 1 — part-whole, finding the total

A fruit stall sells 47 apples in the morning and 28 apples in the afternoon. How many apples were sold altogether?

Draw it: one whole bar made of two parts, 47 and 28.

| 47 apples | 28 apples |
|<------- total ------->|

The two parts are known; the whole is missing, so we add.

47 + 28 = 75 apples.

Check: 75 − 28 = 47, which gives the morning back. ✓

Worked example 2 — part-whole, finding a missing part

A class has 30 children. 18 are having school lunch. How many brought a packed lunch?

Here the whole (30) is known and one part (18) is known. The missing piece is the other part, so we subtract.

30 − 18 = 12 children.

Check: 18 + 12 = 30, the whole class. ✓

Notice the same bar model handles both: when the whole is missing you add the parts; when a part is missing you subtract from the whole.

Worked example 3 — comparison, "how many more"

Tom has 52 stickers. Mia has 35 stickers. How many more does Tom have?

Comparison problems use two bars side by side, lined up at the start:

Tom: | 35 ........ | gap |
Mia: | 35 ........ |

The gap between them is the answer, and to find a gap you subtract the smaller from the larger.

52 − 35 = 17 stickers more.

Check: 35 + 17 = 52, which rebuilds Tom's total. ✓

Worked example 4 — comparison giving the larger amount

A jug holds 60 ml more than a cup. The cup holds 150 ml. How much does the jug hold?

This time the difference (60) is known and we want the larger amount. The jug bar is the cup bar plus the extra, so we add.

150 + 60 = 210 ml.

Check: 210 − 150 = 60, the stated difference. ✓ The same words "more than" led to subtraction in example 3 and addition here — which is exactly why the bar model beats guessing from keywords.

Practice activity

Draw a bar model for each, then solve. Check every answer by putting it back into the story.

1. A car park has 64 spaces. 39 are full. How many are empty?
2. Aisha read 26 pages on Monday and 38 pages on Tuesday. How many pages altogether?
3. A red ribbon is 85 cm long. A blue ribbon is 58 cm long. How much longer is the red ribbon?
4. There are 45 children on a trip. 27 are girls. How many are boys?
5. A film is 30 minutes longer than a cartoon. The cartoon lasts 25 minutes. How long is the film?

Answers: 1) 64 − 39 = 25 2) 26 + 38 = 64 3) 85 − 58 = 27 4) 45 − 27 = 18 5) 25 + 30 = 55 minutes.

Why this matters

Adding and subtracting are the two most common things you do with numbers in real life — totting up a bill, working out change, comparing scores, sharing out. Once you can tell a part-whole story from a comparison story and sketch a quick bar model, you will choose the right operation without second-guessing. For problems that mix in multiplying and dividing, move on to Multiplication and Division Word Problems, and for stories that need several operations together, see Multi-Step Word Problems.