Understand the idea.
Include every term
In an expression using only addition and subtraction, work left to right and keep every remaining term. A positive intermediate result is only a checkpoint; later subtractions may take the running total below zero again.
Alternatively, rewrite subtraction as addition of the opposite. Then collect positive and negative amounts to check the final value. Preserve the sign attached to each amount, so a subtraction does not accidentally become an addition.
Keep a running record
For a sequence of events, record the starting value followed by each signed change. Temperature rises and deposits add; temperature falls and payments subtract. Keep units consistent and interpret the final sign using the original reference.
Check by undoing the changes in reverse order. If the final value was found by subtracting 11 then adding 4, undo it by subtracting 4 then adding 11. You should recover the starting value.
| Stage | Change | Temperature |
|---|---|---|
| Start | — | 6°C |
| Falls | −11°C | −5°C |
| Rises | +4°C | −1°C |
See the method in action.
Three terms
Evaluate .
Worked solution
- 1
Calculate the first two terms.
Twelve positive units cancel eight negative units, leaving four.
- 2
Apply the remaining subtraction.
The expression still requires a decrease of seven.
- 3
Check by combining all directed amounts.
Twelve positive units oppose fifteen negative units, leaving three negative units.
−3
Two temperature changes
The temperature is 6°C. It falls 11°C, then rises 4°C. Find the finish.
Worked solution
- 1
Apply the fall in temperature.
A fall of eleven degrees decreases the starting temperature of six degrees.
- 2
Apply the later rise.
The rise increases the temperature but is not enough to reach zero.
- 3
Undo both changes as a check.
Reversing the rise and then the fall recovers the starting temperature.
−1°C
Try it yourself.
Check your understanding
Evaluate .
Show answer & reasoning
−3
Work left to right: , then . The final subtraction must still be applied after the running total becomes positive.
Keep practising
6 worksheet questions · 13 marks
Read the questions online
- Evaluate .2 marks
- Evaluate .2 marks
- Evaluate .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 .2 marks
- Are and equal? Explain.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Evaluate .2 marks
.
.
−2 - Evaluate .2 marks
.
.
−9 - Evaluate .2 marks
Subtracting −6 gives .
Then .
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 .
The refund adds 4: .
−3 dollars - Find the integer that completes .2 marks
The move from −5 to 3 is eight units right.
Check .
8 - Are and equal? Explain.3 marks
Subtracting −7 adds its opposite +7.
Both expressions equal .
Yes; both equal 3.
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 ↗