Number sense · 5-minute lesson

Multiply numbers close to 100

When both numbers are just below 100, their small gaps from 100 can do much of the work for you.

Step by step

1. Find the gaps

   97 is 3 below 100. 96 is 4 below 100.

2. Build the left part

   Subtract across: 97 − 4 = 93. You can also use 96 − 3 = 93.

3. Build the right part

   Multiply the gaps: 3 × 4 = 12. Use two places on the right, giving 93 | 12, or 9312.

Keep two places on the right

For 98 × 97, the gaps multiply to 6. Write it as 06: 95 | 06 = 9506. If the gap product exceeds 99, carry its hundreds to the left. For 89 × 88, the left part is 77 and the gap product is 132: 7700 + 132 = 7832.

Why it works

(100 − a)(100 − b) = 100(100 − a − b) + ab. The cross-subtraction gives the hundreds part, and multiplying the gaps gives the part you add to it.

Try it yourself

Work through each example before opening the answers.