1. The bracket first: −14 + 13 = −1. Then square: (−1)² = 1.

(+0.9) × (−4) + 0.68 = □

−2.92. Multiply first: same signs give a positive, different signs a negative, and the size is 0.9 × 4. Then add 0.68: −2.92.

(−5) × (9 − 18) = 45 True or false?

True. 9 − 18 is negative, and negative times negative is positive. Work it through and compare with 45.

Directed numbers · Ages 12–13

The four operations mixed

Brackets, powers, times and divide, plus and minus; the sign first at each step.

How to do it

Method

Brackets, powers, times and divide, plus and minus; the sign first at each step

(−2) × [3 − (−1)] + 5 = −8 + 5 = −3

Another way

Split the signs

−5 + 8 − 3 + 2 = (8 + 2) − (5 + 3) = 2

In full

The order is the same as for positive numbers: brackets, then powers, then times and divide, then plus and minus. At each step, settle the sign, then the size: (−2) × [3 − (−1)] + 5 = (−2) × 4 + 5 = −8 + 5 = −3. With only plus and minus, you can split the positives from the negatives and then combine: −5 + 8 − 3 + 2 = (8 + 2) − (5 + 3) = 2; going left to right gives the same.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
(−14 + 13)² =
Show the answer and working
Answer: 1
The bracket first: −14 + 13 = −1. Then square: (−1)² = 1.
Example 2
(+0.9) × (−4) + 0.68 =
Show the answer and working
Answer: −2.92
Multiply first: same signs give a positive, different signs a negative, and the size is 0.9 × 4. Then add 0.68: −2.92.
Example 3
(−5) × (9 − 18) = 45
True or false?
Show the answer and working
Answer: True
9 − 18 is negative, and negative times negative is positive. Work it through and compare with 45.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.22 + (−8) × 6 =
Answer:
2.(−7) + 4 × (−9) =
Answer:
3.−22 + 14 − 8 + 14: the positives add to , the negatives to −, so the answer is .
Fill in each blank
Answer:
4.(−8) × (2 − 18) = 130
True or false?
Answer:
5.(−0.9) × (−2) + 0.62 =
Answer:

All the answers

1. −26
2. −43
3. 28, 30, −2
4. False
5. 2.42

Free worksheet: The four operations mixedWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

VIP practice notes and papers

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working

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