Addition & subtraction
Missing Numbers
Sometimes a number sentence has a gap. We can use a symbol like a square or a circle to show a missing number or a missing +, -, x or ÷ sign. Then we work out what it should be.
A symbol stands for something missing
In a number sentence such as 30 - □ = 27, the square stands for a number we do not know yet. We can also use a symbol for a missing operation sign, like 28 □ 72 = 100. Our job is to work out what the symbol should be so the sentence is true.
Use the inverse to find a missing number
Addition and subtraction are inverse operations — they undo each other. So 650 + □ = 1000 can be rewritten as 1000 - 650 = □. For a subtraction like □ - 14 = 8, we add to go backwards: 8 + 14 = □. Choosing the inverse is often the quickest way.
Count on using a number line
You can also find a missing number by counting on. For 650 + □ = 1000, start at 650 and take big jumps: +50 to 700, then +300 to 1000. Add the jumps: 50 + 300 = 350. The larger the jump, the more efficient the method.
Find a missing operation sign
For 55 = 70 □ 15, try each sign. 70 + 15 = 85 (too big) but 70 - 15 = 55 (correct), so the missing sign is -. Always check your answer by reading the whole sentence again.
Worked examples
Missing number with the inverse
- Read 650 + □ = 1000 as 'how many more make 1000?'
- Rewrite it as a subtraction: 1000 - 650 = □.
- Work out 1000 - 650 = 350.
Answer: The missing number is 350.
Missing subtrahend
- Look at 30 - □ = 16.
- The whole is 30 and one part is 16, so subtract: 30 - 16.
- 30 - 16 = 14.
Answer: The missing number is 14.
Missing operation sign
- Look at 28 □ 72 = 100.
- Try +: 28 + 72 = 100. That is correct.
- Check: 28 + 72 really does equal 100.
Answer: The missing sign is +.
Where you see this in real life
- Working out how much more money you need to reach 100 pence.
- Filling in the missing score to reach a target in a game.
- Checking a shopping total: 'I paid, what change should I get?'
- Solving number puzzles for fun, just like a jigsaw.
Key words
- Symbol
- A shape such as □ or ○ used to stand for a missing number or sign.
- Missing number
- The number you need to work out to make a sentence true.
- Operation sign
- A +, -, x or ÷ sign that tells you what to do.
- Inverse operations
- Operations that undo each other, like addition and subtraction.
- Count on
- To find a difference by jumping forwards on a number line.