Stage 6 · Big numbers & speed
Long multiplication
Split the multiplier into tens and ones.
How to do it
Method
Split the multiplier into tens and ones
34 × 27 = 34 × 20 + 34 × 7 = 680 + 238 = 918
Another way
Column multiplication
34 × 7 = 238, 34 × 20 = 680, 238 + 680 = 918
In full
Split the multiplier into tens and ones, multiply by each, and add — the distributive property: 34 × 27 → 34 × 20 = 680, 34 × 7 = 238, 680 + 238 = 918. To multiply by a whole ten, multiply by its tens digit, then put a zero on the end: 34 × 2 = 68, so 34 × 20 = 680. Three digits times two work the same: 215 × 32 → 215 × 30 = 6450, 215 × 2 = 430, 6450 + 430 = 6880. Estimate first as a check: 34 × 27 is about 30 × 30 = 900. Another way is to multiply in columns: by the ones first, 34 × 7 = 238; then by the tens, 34 × 20 = 680, on a second row; then the two rows are added, 238 + 680 = 918 — the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
28 × 13
Show the answer and working
Answer: 28 × 13 = 364
28 × 13: split 13 into 10 and 3, 28 × 10 = 280, 28 × 3 = 84, 280 + 84 = 364
Example 2
90 × 13
Show the answer and working
Answer: 90 × 13 = 1170
90 × 13: split 13 into 10 and 3, 90 × 10 = 900, 90 × 3 = 270, 900 + 270 = 1170
Example 3
97 × 24
Show the answer and working
Answer: 97 × 24 = 2328
97 × 24: split 24 into 20 and 4, 97 × 2 = 194, 97 × 20 = 1940, 97 × 4 = 388, 1940 + 388 = 2328
Example 4
21 × 230
Show the answer and working
Answer: 21 × 230 = 4830
21 × 230: the order can swap, so work out 230 × 21. 230 × 21: split 21 into 20 and 1, 230 × 2 = 460, 230 × 20 = 4600, 230 × 1 = 230, 4600 + 230 = 4830
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