Multiply two numbers near 100

Work out how far each is below 100 and let those gaps do the work.

The question

What is 96 × 97?

The trick

Find how far each number is below 100. Subtract one gap from the other number for the left half, and multiply the two gaps for the right half.

96−34×39312

Worked example

196 is 4 below 100, and 97 is 3 below 100
2Left half: 96 − 3 = 93 (you get the same from 97 − 4)
3Right half: 4 × 3 = 12
4Join them: 9312

So: 9312

Remember it like this

Both numbers are standing below 100. Cross over and subtract, then multiply the two gaps.

In the exam

The right half must be exactly two digits. If the gaps multiply to a single digit, pad it with a zero: 94 × 99 → 93 and 6 → write 9306, not 936.

Why it works

Writing the numbers as (100−a)(100−b) expands to 10000 − 100(a+b) + ab, which is 100 × (100 − a − b) + ab. The left half is the hundreds part, the right half is ab.

Explain this to my childGet the words to teach it, in your language

Try it yourself

0/4 correct

1
98 × 97
98 × 97
2
94 × 99
94 × 99
3
95 × 96
95 × 96
4
99 × 98
99 × 98