Mixed addition/subtraction problems | Year 7

01 / LEARN

The idea, step by step

Include every term

For addition and subtraction at the same priority level, work left to right. Alternatively, rewrite each subtraction as adding an opposite, keeping brackets until the sign is clear.

In $- 8 + 12 - 7$ , the first two terms give 4, but the calculation is not finished. Subtracting the remaining 7 changes the result to −3. Check each line against the expression before it.

Keep a running record

In a temperature, height or money problem, write the starting value and apply every change. Rises and deposits add positive amounts; falls and payments subtract positive amounts. Interpret the final sign in context.

Check by undoing the changes, or by comparing the total positive and negative movement. This lesson uses addition and subtraction; multiplication and division of negative integers are developed later.

A running temperature record
Stage	Change	Temperature
Start	—	6°C
Falls	−11°C	−5°C
Rises	+4°C	−1°C

A common trap

Once a running total becomes positive, later negative changes can be ignored.

Instead: Continue until every term or event has been applied.

02 / WORKED EXAMPLES

See the thinking

Example 1

Three terms

Evaluate $- 8 + 12 - 7$ .

First $- 8 + 12 = 4$ .
Then $4 - 7 = - 3$ .

−3

Example 2

Two temperature changes

The temperature is 6°C. It falls 11°C, then rises 4°C. Find the finish.

The fall gives $6 - 11 = - 5$ °C.
The rise gives $- 5 + 4 = - 1$ °C.

−1°C

Check your understanding

Evaluate $- 4 + 9 - 8$ .

Show answer

−3

The first sum is 5, then $5 - 8 = - 3$ .

03 / WORKSHEET

Your turn

6 questions · 13 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Evaluate $- 3 + 9 - 8$ .
2 marks
Evaluate $7 - 12 + (- 4)$ .
2 marks
Evaluate $- 10 - (- 6) + 5$ .
2 marks
An account starts with 18 dollars. A payment of 25 dollars is made, then 4 dollars is refunded. Find the balance.
2 marks
Find the integer that completes $- 5 + □ = 3$ .
2 marks
Are $- 4 - (- 7)$ and $- 4 + 7$ equal? Explain.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Evaluate $- 3 + 9 - 8$ .
2 marks
$- 3 + 9 = 6$ .
$6 - 8 = - 2$ .
−2
Evaluate $7 - 12 + (- 4)$ .
2 marks
$7 - 12 = - 5$ .
$- 5 + (- 4) = - 9$ .
−9
Evaluate $- 10 - (- 6) + 5$ .
2 marks
Subtracting −6 gives $- 10 + 6 = - 4$ .
Then $- 4 + 5 = 1$ .
1
An account starts with 18 dollars. A payment of 25 dollars is made, then 4 dollars is refunded. Find the balance.
2 marks
The payment gives $18 - 25 = - 7$ .
The refund adds 4: $- 7 + 4 = - 3$ .
−3 dollars
Find the integer that completes $- 5 + □ = 3$ .
2 marks
The move from −5 to 3 is eight units right.
Check $- 5 + 8 = 3$ .
8
Are $- 4 - (- 7)$ and $- 4 + 7$ equal? Explain.
3 marks
Subtracting −7 adds its opposite +7.
Both expressions equal $- 4 + 7 = 3$ .
Yes; both equal 3.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum

Positive and negative numbers in context; comparing and ordering integers; number lines and directed change; adding integers; subtracting integers; mixed addition/subtraction problems. Multiplication/division of negative integers is a labelled preview, not the Year 7 core endpoint.

Official curriculum source ↗

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