Mental multiplication and division (age 9+)
Multiply and divide numbers mentally drawing upon known facts, including related facts and place-value adjustments
What a learner can do afterwards
- Calculate 40 × 60 mentally by using 4 × 6 = 24 then appending zeros
- Derive 7 × 15 by calculating 7 × 10 + 7 × 5
- Calculate 360 ÷ 9 mentally using 36 ÷ 9 = 4
1 · Read
You already know your times tables and division facts. You can use those same facts to solve much bigger problems in your head, just by paying attention to place value.
To work out 7 × 15, split 15 into 10 and 5. Then 7 × 10 = 70 and 7 × 5 = 35. Add them: 70 + 35 = 105.
To work out 360 ÷ 9, drop the zero and find 36 ÷ 9 = 4 first. Then put the zero back on your answer: 40.
Two tricks to remember: split a number into tens and ones and add the results, or drop a zero, use the smaller fact, then put the zero back on.
Break a big problem into a fact you already know, then adjust for the extra zero or the extra pieces.
More to read
Use the distributive property to break apart multiplication problems into known facts
Multiplying can feel easier if you break one of the numbers into smaller pieces first.
Try 9 × 6. Think of 9 as 10 minus 1. 9 × 6 = (10 × 6) − (1 × 6) = 60 − 6 = 54
You can also break numbers apart by adding. 8 × 4 = (5 × 4) + (3 × 4) = 20 + 12 = 32
Once you know a few facts really well, like your 5s and 10s, you can use them to figure out trickier facts. Split the harder number into two friendly numbers, multiply each piece, then add or subtract the results back together.
Multiply by using place value strategies and the distributive property
When a multiplication problem looks big, place value can help you shrink it down.
Say you want 40 × 60. Ignore the zeros for a moment and just multiply 4 × 6, which is 24. Since 40 has one extra zero and 60 has one extra zero, tack both zeros back onto 24 to get 2400.
The same idea works for splitting numbers apart. To find 7 × 15, think of 15 as 10 + 5. Multiply 7 × 10 = 70 and 7 × 5 = 35, then add them together to get 105.
Place value strategies let you use facts you already know, like your times tables, to solve much bigger problems in your head.
Divide by using familiar strategies
Division facts you already know can unlock much bigger problems.
Take 360 ÷ 9. Hidden inside it is a fact you probably already know: 36 ÷ 9 = 4. Since 360 has one extra zero compared to 36, add that zero to your answer too, so 360 ÷ 9 = 40.
This works because dividing a number that ends in zero connects closely to dividing the number without the zero. Once you know 36 ÷ 9 = 4, you also know 3600 ÷ 9 = 400.
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