Cambridge Primary Checkpoint 0845 · Topic 3 of 10

Calculation and order of operations

Mental and written methods for adding, subtracting, multiplying and dividing, checking answers, and doing calculations in the right order.

📌 Key points

Use facts you know: 7 × 8 = 56, so 70 × 80 = 5600 and 5.6 ÷ 8 = 0.7.
You can add or multiply in any order (4 × 9 = 9 × 4), but not subtract or divide.
Partitioning helps: 23 × 6 = 20 × 6 + 3 × 6 = 120 + 18 = 138.
In written methods, line up the digits by place value. Line up the decimal points when adding or subtracting decimals.
A remainder can be written as a whole number, a fraction or a decimal: 17 ÷ 4 = 4 r 1 = 414 = 4.25.
Order of operations: brackets first, then multiplication and division, then addition and subtraction.
Multiplication and division are done from left to right, and so are addition and subtraction.
Check answers by estimating (round the numbers first) or by using the inverse operation.

Inverse operation: The operation that undoes another: + and − are inverses, and so are × and ÷.
Product: The answer when you multiply numbers.
Quotient: The answer when you divide one number by another.
Remainder: The amount left over when a number does not divide exactly.
Estimate: A rough answer found by rounding the numbers first.
Partitioning: Splitting a number into parts, e.g. 47 = 40 + 7, to make it easier to work with.
Order of operations: The rule for what to do first: brackets, then × and ÷, then + and −.

Work out 36 − (4 + 8) × 2 ÷ 3.

Brackets first: 4 + 8 = 12, so the calculation is 36 − 12 × 2 ÷ 3.
Multiplication and division next, from left to right: 12 × 2 = 24, then 24 ÷ 3 = 8.
Subtraction last: 36 − 8 = 28.
Answer: 28.

💡 Test tip

In word problems, decide which operation you need, make an estimate, and check your answer is close to it.

Test yourself8 questions from a bank of 22. A new mix every time.