Written calculation methods

Use the column method.

1. Write the numbers one above the other, with the decimal points lined up, and fill gaps with zeros.
2. Work from the right, carrying (adding) or exchanging (subtracting).
3. Keep the decimal point in line in the answer.

Example: work out 45.7 + 8.26.

1. 45.70 + 8.26
2. Hundredths: 0 + 6 = 6; tenths: 7 + 2 = 9
3. Ones: 5 + 8 = 13, write 3 and carry 1; tens: 4 + 1 = 5
4. 53.96

Harder example: work out 12.4 − 3.75.

1. 12.40 − 3.75
2. Hundredths: exchange, 10 − 5 = 5
3. Tenths: exchange, 13 − 7 = 6
4. Ones: exchange, 11 − 3 = 8
5. 8.65

Two signs next to each other can be swapped for one:

When you multiply or divide:

1. Ignore the signs and work out the answer.
2. If the signs were the same, the answer is positive.
3. If they were different, the answer is negative.

Example: work out −3 − (−8), −6 × −4 and 15 ÷ −3.

1. −3 − (−8) = −3 + 8 = 5
2. 6 × 4 = 24; same signs, so −6 × −4 = 24
3. 15 ÷ 3 = 5; different signs, so 15 ÷ −3 = −5

In the column method, you multiply by each digit of the second number in turn, then add.

1. Multiply by the ones digit.
2. Multiply by the tens digit: write a 0 in the ones column first.
3. Add the rows.

Example: work out 346 × 27.

1. 346 × 7 = 2422
2. 346 × 20 = 6920
3. 2422 + 6920 = 9342

The grid method gets the same answer by splitting both numbers into parts:

6000 + 800 + 120 + 2100 + 280 + 42 = 9342

To multiply decimals:

1. Take out the decimal points and multiply the whole numbers.
2. Count the decimal places in the numbers you multiplied.
3. Give the answer that many decimal places.

Multiplying by 0.1 is the same as dividing by 10; multiplying by 0.01 is the same as dividing by 100.

Example: work out 2.4 × 0.35.

1. 24 × 35 = 840
2. 2.4 has 1 decimal place and 0.35 has 2: 3 in total.
3. 840 with 3 decimal places is 0.840
4. 0.84

Example: work out 6.3 ÷ 100.

1. Dividing by 100 moves every digit two places right.
2. 0.063

Short division (the bus stop method) is for dividing by a small number.

1. Divide into the first digit, write the answer on top and carry the remainder to the next digit.
2. Repeat to the end. For a decimal answer, add zeros after the point and keep going.

Example: work out 852 ÷ 6.

1. 8 ÷ 6 = 1 remainder 2, so carry 2: 25
2. 25 ÷ 6 = 4 remainder 1, so carry 1: 12
3. 12 ÷ 6 = 2
4. 142

Long division is the same idea for a two-digit divisor, with the subtraction written out.

Example: work out 7248 ÷ 24.

1. 72 ÷ 24 = 3, and 3 × 24 = 72, remainder 0
2. Bring down the 4: 4 ÷ 24 = 0, remainder 4
3. Bring down the 8: 48 ÷ 24 = 2
4. 302

Make the number you're dividing by a whole number first.

1. Multiply both numbers by 10, 100 or 1000 until the divisor is a whole number. This doesn't change the answer.
2. Divide as normal.

Example: work out 7.2 ÷ 0.04.

1. Multiply both by 100: 7.2 ÷ 0.04 = 720 ÷ 4
2. 720 ÷ 4 = 180

Harder example: work out 3.45 ÷ 0.15.

1. Multiply both by 100: 345 ÷ 15
2. 34 ÷ 15 = 2 remainder 4, so carry 4: 45
3. 45 ÷ 15 = 3
4. 23

Check: dividing by a number less than 1 gives a bigger answer, and 23 × 0.15 = 3.45.