Mental multiplication and division
Use place value, known and derived facts to multiply and divide mentally, including multiplying by 0 and 1, dividing by 1, and multiplying together three numbers
What a learner can do afterwards
- Calculate 40 × 6 = 240 mentally using place value
- Explain why any number × 0 = 0 and any number × 1 = the number itself
- Multiply three numbers mentally by choosing a useful pair first (e.g. 2 × 7 × 5 = 2 × 5 × 7 = 70)
1 · Read
You already know your times tables. Now you can use that knowledge to solve bigger problems in your head, without writing anything down.
To work out 40 × 6, first solve the easy fact: 4 × 6 = 24. Then remember that 40 is really 4 tens, so multiply your answer by 10. 24 × 10 = 240.
Two facts are so useful you can use them straight away, with no working out. Any number times 0 is 0, because you have zero groups of that number. Any number times 1 stays exactly the same, because one group of something is just that many.
Look for a pair that makes 10, 20, or 100. Multiply that pair first, then multiply by the number that is left.
Use facts you already know, apply the shortcut for × 0 and × 1, and reorder three numbers to find an easy pair first.
More to read
Key ideas: multiply a two-digit multiple of 10 by a two-digit multiple of 10
Multiples of 10 are easy if you use place value. First, hide the zeros and multiply the basic facts. Then bring the zeros back. For 30 x 40: hide to get 3 x 4 = 12. Each number had one zero, so the answer needs two zeros: 1200. For 40 x 6: 4 x 6 = 24, and one zero returns to make 240. Count the zeros in the question, count them in your answer, and the two counts must match. That check catches most slip-ups.
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15 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.