Multiplying and dividing by two digits; divisibility · Usually met around P4
Multiplying near 100
Front: cross-subtract. Back: gap × gap.
How to do it
Method
Front: cross-subtract. Back: gap × gap
96 × 97: 96 − 3 = 93, 4 × 3 = 12 → 9312
Another way
Column multiplication
96 × 7 = 672, 96 × 90 = 8640, 672 + 8640 = 9312
In full
96 × 97: they are 4 and 3 below 100. Front = 96 − 3 = 93 (97 − 4 gives the same). Back = 4 × 3 = 12 → 9312. The back always has two digits: 99 × 98 → 97 and 02 → 9702. If it goes past two digits, carry: 89 × 89 → 7800 + 121 = 7921. Column multiplication gets the same answer, but near 100 this trick is much quicker.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
96 × 93
Show the answer and working
Answer: 96 × 93 = 8928
96 × 93: 96 is 4 short of 100, 93 is 7 short. Front 96 − 7 = 89, back 4 × 7 = 28, front then back → 8928
Example 2
92 × 91
Show the answer and working
Answer: 92 × 91 = 8372
92 × 91: 92 is 8 short of 100, 91 is 9 short. Front 92 − 9 = 83, back 8 × 9 = 72, front then back → 8372
Example 3
91 × 91
Show the answer and working
Answer: 91 × 91 = 8281
91 × 91: 91 is 9 short of 100, 91 is 9 short. Front 91 − 9 = 82, back 9 × 9 = 81, front then back → 8281
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