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3.4 Order of operations

4 This is part of Zalika’s homework.

+
Question Work out: a − 5 × 2 b − c 18 22
2
−
83
Answers a − ê
b 14 − ê = 100
2
c ¸ − 3 = 2
All of her answers are wrong.
For each part:
i explain the mistake that Zalika has made
ii work out the correct answer.

5 Oditi and Shen work out the value of the expression 2(a + 5b) when a = 4 and b = 3.

I think the value of the expression I think the value of the expression
is 114 because 4 + 53 = 57, is 54 because 4 + 5 = 9, 9 × 3 = 27,
then 2 × 57 = 114. and 2 × 27 = 54.

Is either of them correct? Explain your answer.
6 Work out the value of each expression when x = 6 and y = 2.
a 3x + y b 2x − 4y c (2x − 3y) d 2(3x − 6y) 2
2
2
2

Summary

You should now know that: You should be able to:

+ When you multiply any number by a decimal number + Calculate with decimals mentally, using jottings
between 0 and 1, the answer is smaller than the where appropriate.
number you started with. + Multiply by decimals, understanding where to
+ When you divide any number by a decimal number put the decimal point by considering equivalent
between 0 and 1, the answer is greater than the calculations.
number you started with. + Divide by decimals by transforming the calculation
+ The decimals 0.1, 0.01, 0.001, … can all be written as to division by an integer.
1
negative powers of 10. 0.1 = 10 = 10 , + Recognise the effects of multiplying and dividing
−1
1
1
−3
0.01 = 100 = 10 , 0.001 = 1000 = 10 , … by numbers between 0 and 1.
−2
1
−1

+ The first significant figure in a number is the first + Recognise the equivalence of 0.1, 10 and 10 .
non-zero digit in the number. + Multiply and divide numbers by 10 to the power of
+ When you round a number to a given number of any positive or negative integer.

significant figures you must keep the value of the + Round numbers to a given number of decimal
rounded answer consistent with the number you are places or significant figures; use rounding to give

rounding. solutions to problems with an appropriate degree
+ You can use BIDMAS (Brackets, Indices or powers, of accuracy.
Division, Multiplication, Addition, Subtraction) to + Use the order of operations, including brackets
remember the correct order of operations. and powers.
3 Place value, ordering and rounding 31