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3.4 Order of operations

3.4 Order of operations

When calculations involve more than one operation, such as addition and multiplication, always make
sure you do the operations in the correct order.

BIDMAS can help you remember the correct order of operations.
BIDMAS stands for Brackets, Indices (powers), Division, Multiplication, Addition and Subtraction.
BIDMAS describes the order in which you must do operations.
Work out Brackets and Indices %rst, followed by
Divisions and Multiplications, and %nally
Additions and Subtractions.

Worked example 3.4
4 2
Work these out. a 4 + 2 × 6 b 6 − 2(3 + 9) c d (29 − 5 )
2 3
8
a 4 + 2 × 6 = 4 + 12 Start by working out the multiplication: 2 × 6 = 12.
= 16 Then work out the addition: 4 + 12 = 16.
b 6 − 2(3 + 9) = 6 − 2 × 12 Start by working out the calculation in brackets: 3 + 9 = 12.
= 6 − 24 Then work out the multiplication: 2 × 12 = 24.
= −18 Finally, work out the subtraction: 6 − 24 = −18.
4 2 16
2
c = Start with the index and work out 4 = 16.
8 8
= 2 Then work out the division: 16 ÷ 8 = 2.
2
2
d (29 − 5 ) = (29 − 25) Work out the 5 before calculating the expression in the brackets: 5 = 25.
2 3
3
= 4 3 Then work out the expression in the brackets: 29 − 25 = 4.
= 64 Finally, work out 4 = 64.
3
) Exercise 3.4
1 Work these out.
a 8 + 3 × 4 b 12 × 2 − 5 c 16 − 27 d 18 − 5 × 6 e 4 × 3 − 7 × 2
3
f 24 + 60 g 8(12 − 9) h 13 + 2 j 8 + 6 k 100 − 2(12 + 13)
2
2
2
8 12
2 Write the correct sign, =, < or >, to go in the box between the expressions.
2
a 16 + 2 × 4 30 − 48 b 50 − 6 3(26 − 19)
8
c 5 + (11 − 6) 41 − 3 × 4 d 60 + 51 7 − 0.5 × 4
2
2
4 3
e 46 − 2(3 + 5) 3(4 − 5) f (12 − 4) 5 + 72
2
2
2
2
3 Work out if the answers to these calculations are right (!) or wrong (").
If the answer is wrong, work out the correct answer.
a 6 + 3 × 2 = 18 b 3(16 − 3 ) + 9 = 30 c 5 − (8 − 6) = 27
3
2

30 3 Place value, ordering and rounding