Split one number
Long multiplication is hard to hold in your head because it asks you to carry digits. Splitting is easier. Break one number into parts you can multiply on sight, multiply each part, then add the results.
Take 23 × 7. Split 23 into 20 and 3. Then 20 × 7 = 140 and 3 × 7 = 21, and 140 + 21 = 161.
The same move works with two two-digit numbers. For 43 × 27, split 27 into 20 and 7: 43 × 20 = 860 and 43 × 7 = 301, and 860 + 301 = 1161.
A few pairs have a shortcut that is quicker still. Three are worth learning by heart: multiplying by 11, squaring a number that ends in 5, and multiplying two numbers that both sit just below 100.
Four worked questions
23 × 7. Split 23 into 20 and 3. 20 × 7 = 140, then 3 × 7 = 21, then 140 + 21 = 161.
34 × 11. Ten times 34 is 340. Add 34 again to get 374. That is all multiplying by 11 ever is.
65 × 65. The number being squared ends in 5. Multiply the 6 by the next number up, 7, which gives 42. Put 25 on the end: 4225.
97 × 96. Both sit below 100. The gaps are 3 and 4. Take one gap off the other number, 97 − 4 = 93, and that is the hundreds: 9300. Then multiply the gaps, 3 × 4 = 12, and add: 9312.
One near 100
Here is 98 × 96. The gaps below 100 are 2 and 4.
The first step is done for you: 98 − 4 = 94, so the hundreds are 9400.
Stopping there is the usual slip. The two gaps still have to be multiplied and added.
Try it
What is 98 × 96?
- 9408
- 9400
Show the answer
9408
Correct. 9400 is the hundreds, and 2 × 4 = 8 adds the rest, so the answer is 9408.
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