Work out 20 − 3 × (2 − 5)2 + 12 ÷ 4.
- Bracket: 2 − 5 = −3.
- Power: (−3)2 = 9.
- Multiply and divide: 3 × 9 = 27 and 12 ÷ 4 = 3.
- Left to right: 20 − 27 + 3 = −4.
Answer: −4
The four operations
Maths · Number. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
The four operations are adding, subtracting, multiplying and dividing. You must use them with integers, fractions and decimals, including negative numbers, and without a calculator.
When a calculation has several operations, the order of operations decides what is done first: brackets, then powers, then multiplication and division, then addition and subtraction. Operations of equal rank are done from left to right.
For negative numbers, multiplying or dividing two numbers with the same sign gives a positive answer, and different signs give a negative answer. For decimals, it is safest to work with whole numbers first and then put the decimal point back.
Rules to remember
- Order: Brackets, Indices (powers), Division and Multiplication, Addition and Subtraction.
- (+) × (+) = (+), (−) × (−) = (+), (+) × (−) = (−); the same pattern holds for division.
- Subtracting a negative is the same as adding: a − (−b) = a + b
- (−a)2 is positive and (−a)3 is negative.
- Multiplying decimals: multiply as whole numbers, then count the decimal places: 0.3 × 0.02 = 0.006.
- Dividing by a decimal: multiply both numbers by 10 or 100 first: 4.8 ÷ 0.06 = 480 ÷ 6 = 80.
Common mistake
Working from left to right and ignoring the order, such as 2 + 3 × 4 = 20. Multiply first: 2 + 12 = 14.
Worked example
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