Written multiplication and division
Long multiplication
Split the second number into tens and ones.
Multiply by each part, then add the two rows. The row for the tens starts with a zero in the ones column, because the tens digit is worth ten times as much.
- 463 × 27
- 463 × 7 = 3241
- 463 × 20 = 9260 (a zero in the ones column first)
- 3241 + 9260 = 12501
The grid method gives the same rows: write 463 as 400 + 60 + 3, multiply each part by 20 and by 7, then add all six answers.
Short and long division
In short division, divide into each digit from the left and carry the remainder to the next digit.
If the divisor does not go into a digit, write 0 in the answer and carry on.
- £42.56 ÷ 7
- work in pence: 4256 ÷ 7
- 7 into 42 is 6, 7 into 5 is 0 remainder 5, 7 into 56 is 8
- 4256 ÷ 7 = 608, so each share is £6.08
For a two-digit divisor, take away big multiples of it (chunking), or write out the long division. Check by multiplying back.
- 1036 ÷ 28
- 28 × 30 = 840
- 1036 − 840 = 196
- 28 × 7 = 196
- 30 + 7 = 37
Decimals by place value
To multiply decimals, ignore the decimal points, multiply the whole numbers, then put back as many decimal places as the question had in total.
- 2.6 × 0.07
- 26 × 7 = 182
- 1 + 2 = 3 decimal places in the question
- 182 ÷ 1000 = 0.182
To divide by a decimal, multiply both numbers by the same power of 10 until you divide by a whole number. The answer does not change.
- 5.6 ÷ 0.08
- multiply both by 100: 560 ÷ 8
- 560 ÷ 8 = 70
Dividing by a number less than 1 makes the answer bigger. 5.6 ÷ 0.08 is more than 5.6.
Remainders in context
Read what the question wants.
"How many coaches are needed?" rounds up, because the people left over still need a seat. "How many boxes can be filled?" rounds down, because a part-filled box does not count.
Check by multiplying back
Pick any division you have done by hand.
Multiply your answer by the divisor, add any remainder, and see if you get back to the number you started with. This check takes a few seconds and catches most slips with zeros.
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