Bigger multiplication
Multiply two-digit numbers in your head with friendly shortcuts.
Best in your head · no pen, no calculator why?
Opens at level 10. You're level 1. You can read and practice here now.
the idea
Multiplying bigger numbers in your head means turning one hard product into a few facts you already know.
more of the idea
Three moves do most of the work. Split a number into tens and ones, and multiply each part. Round a factor like 19 up to 20, then take away the extra copy: 19 × 24 is 20 copies of 24, minus one. Or make a round factor: 5, 25 and 50 are pieces of 10 and 100, and halving one factor while doubling the other keeps the product the same.
techniques
Split and combine
- Split the two-digit number into tens and ones.
- Multiply each part by the one-digit number.
- Add the two products.
27 × 6
- 20 × 6 = 120.
- 7 × 6 = 42.
- 120 + 42 = 162.
Answer: 162
Round, then fix by one copy
- Round that factor: 19 becomes 20.
- Multiply the other number by the round one.
- 19 is one copy short of 20, so take one copy away. For 51, add one copy.
- A copy is the whole other number, never 1.
29 × 14
- 30 × 14 = 420.
- That is one copy of 14 too many.
- 420 − 14 = 406.
Answer: 406
Make a round factor
- × 5 is × 10, then halve. × 50 is × 100, then halve.
- × 25 is × 100, then ÷ 4, because four 25s make 100.
- With 15, 35 or 45, halve the even factor and double the other: 16 × 35 is 8 × 70.
- Halving one factor and doubling the other keeps the product the same.
25 × 36
- × 25 is × 100, then ÷ 4.
- 36 × 100 = 3,600.
- 3,600 ÷ 4 = 900.
Answer: 900
watch out for
- Adding the ones instead of multiplying them. 18 × 7 is 70 plus 8 × 7, which is 126, not 70 plus 15.
- Taking away 1 instead of one whole copy. 19 × 24 is 480 minus 24, which is 456, not 479.
- Halving one factor and forgetting to double the other. That halves the whole answer.
- Losing a zero. 25 × 48 is close to 25 × 50, which is 1,250, so 120 is far too small.
practice
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Two-digit × one-digit
worked example
34 × 5
- Split 34 into 30 + 4: 30 × 5 = 150 and 4 × 5 = 20.
- 150 + 20 = 170.
Answer: 170
× 5, × 25, × 50
worked example
50 × 56
- × 50 is × 100 then halve: 56 × 100 = 5,600, and half of that is 2,800.
Answer: 2,800
Near round numbers
worked example
9 × 19
- Use 10 × 19 = 190, then remove the one extra copy of 19: 171.
Answer: 171
Double and halve
worked example
50 × 14
- Halve 14 and double 50: 7 × 100 = 700. The product doesn't change.
Answer: 700