Addition & subtraction word problems
Theory
A word problem tells a story with numbers. The skill is choosing the right operation: add to find a total or a new amount after more arrives, subtract to find what is left, the difference or a missing amount. This Year 5 maths page shows how to read a problem, decide on the operation, calculate and check, including two-step problems.
Addition problems join amounts: a total, altogether, in all, or more arriving.
Subtraction problems take away or compare: how many are left, how many more or fewer, the difference, or how much is still needed.
A two-step problem needs two calculations, such as adding passengers who get on and subtracting passengers who get off.
The words are clues, but always think about what is happening. “How many more” is a subtraction even though it says “more”.
Every addition fact gives two subtraction facts:
How to solve a word problem
- Read the problem and find the question.
- Decide: are parts joining (add) or is a part taken away or compared (subtract)? A bar model helps.
- Calculate using a mental or written strategy.
- Answer in a sentence with units, and check it makes sense.
| \(\text{O: }7 + 6\) | \(=\) | \(13\ (\text{carry } 1)\) |
| \(\text{T: }2 + 8 + 1\) | \(=\) | \(11\ (\text{carry } 1)\) |
| \(\text{H: }4 + 3 + 1\) | \(=\) | \(8\) |
There are \(813\) students.
| \(1500 - 640\) | \(=\) | \(860\) |
\(860\) L is left.
| \(\text{O: }15 - 8\) | \(=\) | \(7\) |
| \(\text{T: }11 - 7\) | \(=\) | \(4\) |
| \(\text{H: }8 - 5\) | \(=\) | \(3\) |
There are \(347\) more sheep than goats.
| \(410 - 245\) | \(=\) | \(165\) |
He got \(165\) stickers. Check: \(245 + 165 = 410\).
| \(64 - 27\) | \(=\) | \(37\) |
| \(37 + 39\) | \(=\) | \(76\) |
There are \(76\) passengers.
| \(3800 - 1450\) | \(=\) | \(2350\) |
\(\$2350\) is left.
| \(\text{O: }10 - 5\) | \(=\) | \(5\) |
| \(\text{T: }12 - 6\) | \(=\) | \(6\) |
| \(\text{H: }6 - 4\) | \(=\) | \(2\) |
Selling takes pies away, so subtract. \(265\) pies are left. Mo’s answer is more than the shop started with, so it cannot be right.
Common pitfalls
Frequently asked questions
How do I know whether to add or subtract?
Add when parts join to make a total. Subtract when something is taken away, when you compare two amounts, or when you know the total and need a missing part.
What words mean subtraction?
Left, remaining, difference, how many more, how many fewer, how much further, change and how much is needed often mean subtraction.
What is a two-step problem?
A problem that needs two calculations, such as \(64 - 27 = 37\) then \(37 + 39 = 76\).
How do I check a word problem answer?
Estimate first, then ask whether the answer makes sense. An amount left over must be less than the starting amount.
What is a bar model?
A drawing of the whole as a long bar split into parts. It shows whether you need to add the parts or subtract a part from the whole.