Order of operations and calculators

When a calculation has several operations, do them in this order, called BIDMAS:

1. Brackets
2. Indices (powers and roots)
3. Division and Multiplication, from left to right
4. Addition and Subtraction, from left to right

Example: work out 3 + 4 × 2².

1. Indices: 2² = 4, so 3 + 4 × 4
2. Multiplication: 4 × 4 = 16, so 3 + 16
3. 19

Harder example: work out (8 − 3)² − 12 ÷ 4 × 2.

1. Brackets, then indices: (8 − 3)² = 5² = 25
2. Left to right: 12 ÷ 4 = 3, then 3 × 2 = 6
3. 25 − 6 = 19

A fraction line works like brackets: work out the whole top and the whole bottom before you divide.

1. Work out the top (numerator).
2. Work out the bottom (denominator).
3. Divide.

The same goes for a square root sign over a calculation: √(9 + 16) means work out 9 + 16 first.

Example: work out (5 + 7) ÷ (2 × 3), written as a fraction with 5 + 7 on top and 2 × 3 underneath.

1. Top: 5 + 7 = 12
2. Bottom: 2 × 3 = 6
3. 12 ÷ 6 = 2

Example: work out √(9 + 16).

1. 9 + 16 = 25
2. √25 = 5

Note that √9 + √16 = 3 + 4 = 7, which is different.

Calculators follow BIDMAS, so put in brackets wherever the question has a fraction line or a hidden bracket.

• Fraction key: enters a fraction with a top and a bottom.
• S⇔D key: switches an answer between a fraction (or surd) and a decimal.
• Ans key: uses the last answer, so you never retype a rounded number.

Check an answer with an estimate: round each number to 1 significant figure first.

Example: work out (4.7 + 2.9) ÷ (3.2 − 1.3) and check it.

1. Type ( 4.7 + 2.9 ) ÷ ( 3.2 − 1.3 ) =
2. The calculator gives 7.6 ÷ 1.9 = 4
3. Estimate: (5 + 3) ÷ (3 − 1) = 8 ÷ 2 = 4, so the answer is sensible.