152 CALCULATING •^ THE ORDER OF OPERATIONSThe order of operations
Some calculations are more complex than just two numbers with one
operation. Sometimes we need to carry out calculations where there are
several different operations to do. It's very important that we know which
order to do them in so that we get the answer right.Addition
Finally, we do any addition and
subtraction calculations. Look at this
calculation. We know that we do division
before addition, so: 9 ÷ 3 + 12 = 3 + 12 = 15Brackets
Look at this calculation. Two of the numbers
are inside a pair of brackets. Brackets tell us
that we must work out that part first. So, first
we must find the sum of 2 + 3, then multiply 4
by that sum to find the total.Orders (or indices)
Powers or square roots are known
as orders or indices. We looked at these types
of numbers on pages 36-39. We work these
out after brackets. Here, we first work out 3² is
9, then 2 × 9 = 18, and finally add 5 to get 23.Division
We work out division and multiplication
calculations next. In this example, even
though the division is written after the
addition, we divide first. So, 4 ÷ 2 = 2
and then 6 + 2 = 8Multiplication
Division and multiplication are of
equal importance, so we work them out
from left to right through a calculation.
Look at this example. We divide first, then
multiply: 8 ÷ 2 × 3 = 4 × 3 = 124 × (2 + 3) = 20 5 + 2 × 3² = 23
6 + 4 ÷ 2 = 8 8 ÷ 2 × 3 = 12
10 − 3 + 4 = 11
Subtraction
Addition and subtraction are of equal
importance, like multiplication and division, so
we work them out from left to right. Here, we
subtract first, then add: 10 − 3 + 4 = 7 + 4 = 119 ÷ 3 + 12 = 15
BODMAS
We can remember the order that we should do calculations by learning the word
“BODMAS” (or "BIDMAS"). It stands for brackets, orders (or indices), division,
multiplication, addition, and subtraction. We should always work out calculations
in this order, even if they are ordered differently when the calculation is written down.152-153_Order_of_Operations.indd 152 29/02/2016 18:57