Non-calculator papers rely on accurate written methods. Add and subtract by lining up the decimal points. Multiply decimals by working with whole numbers and then placing the decimal point, and use long multiplication for larger numbers. Divide with short division, and divide by a decimal by first multiplying both numbers by 10 or 100 so that you divide by a whole number.
Key methods
- Adding and subtracting: line up the decimal points and fill gaps with zeros
- Multiplying decimals: multiply as whole numbers, then count the decimal places
- Dividing by a decimal: multiply both numbers by the same power of 10 first
- Negatives: same signs give a positive answer; different signs give a negative answer
Adding and subtracting decimals
Line up the digits by place value, which means lining up the decimal points. Fill any gaps with zeros so every number has the same number of decimal places, then work column by column from the right, carrying or borrowing as needed. For 23.4 − 8.65, write 23.40 − 8.65.
Multiplying whole numbers and decimals
For long multiplication, multiply by each digit in turn, shifting one place left for the tens digit, and add the rows. A grid method, splitting each number into tens and units, gives the same result.
To multiply decimals, ignore the decimal points, multiply as whole numbers, then count the total number of decimal places in the question and put that many in the answer. 2.4 × 0.3: 24 × 3 = 72, with two decimal places, gives 0.72.
Dividing, including by a decimal
Short division works from left to right, carrying each remainder to the next digit. To divide by a decimal, multiply both numbers by 10, 100 or 1000 until you are dividing by a whole number; this does not change the answer. So 6.3 ÷ 0.07 becomes 630 ÷ 7 = 90.
Calculating with negative numbers
When multiplying or dividing, two numbers with the same sign give a positive answer and two with different signs give a negative answer. When adding and subtracting, think of a number line: subtracting a negative is the same as adding, so 4 − (−6) = 10.
Checking with an estimate
Round each number to one significant figure to check that an answer is sensible. 34 × 26 is roughly 30 × 30 = 900, so an answer of 884 is believable, while 8840 is not.
Worked examples
Example 1. Work out 23.4 − 8.65.
- Line up the points: 23.40 − 8.65.
- Subtract column by column, borrowing where needed.
Answer: 14.75.
Example 2. Work out 34 × 26.
- 34 × 6 = 204.
- 34 × 20 = 680.
- Add the rows: 204 + 680.
Answer: 884.
Example 3. Work out 252 ÷ 7.
- 7 into 25 goes 3, remainder 4.
- Carry the 4 to make 42; 7 into 42 goes 6.
Answer: 36.
Example 4. Work out 2.4 × 0.3.
- Multiply as whole numbers: 24 × 3 = 72.
- The question has two decimal places in total.
Answer: 0.72.
Example 5. Work out 6.3 ÷ 0.07.
- Multiply both numbers by 100: 630 ÷ 7.
- 630 ÷ 7 = 90.
Answer: 90.
Example 6. A school buys 18 theatre tickets at £3.45 each. Work out the total cost.
- 18 × 345 = 6210 (working in pence).
- 6210p = £62.10.
Answer: £62.10.
Common mistakes
- Not lining up the decimal points. Write 23.40 − 8.65, not 23.4 − 8.65 with the digits misaligned.
- Losing the decimal places when multiplying. Count the decimal places in the question and put them in the answer.
- Dividing by a decimal directly. Multiply both numbers by a power of 10 so the divisor is a whole number.
- Sign errors with negatives. A negative times a negative is positive; subtracting a negative means adding.
- Writing money with one decimal place. £62.1 should be written £62.10.
How written calculation is examined
Written methods are tested throughout the non-calculator papers of Edexcel GCSE (1MA1) and Edexcel International GCSE (4MA1), at both tiers. Questions often:
- ask for a calculation with decimals
- set a money problem that needs multiplication or division
- combine negative numbers in a context such as temperature or depth
- ask you to check an answer using an estimate
Build speed and accuracy with the GCSE number revision engine and the order of operations worksheet.
These methods support calculating with fractions and percentages. Estimation is covered in rounding and estimation.
Frequently asked questions
How do you multiply decimals without a calculator?
Multiply the numbers as if they were whole numbers, then put in as many decimal places as there were in the question altogether.
How do you divide by a decimal?
Multiply both numbers by 10, 100 or 1000 until you are dividing by a whole number, then divide as normal.
What is a negative times a negative?
A positive number. For example, −7 × −6 = 42.