Number
Negative numbers and order of operations
Follow signs, brackets and powers.
Predict, test and explain
Step 1 of 3
Predict
What is −3 − (−2)?
Adding a positive number moves right; adding a negative number moves left.
Check the working
| Quantity | Value |
|---|---|
| Result | -1 |
Explore and compare
Choose the investigation above. Predict what will change before you move a control.
Try it in the simulation. Change one thing at a time.
Notes and saved values stay in this tab. They disappear when you reload.
Hints, self-check and connections
Try a self-check
Fixed values, separate from the diagram controls.
Evaluate. Watch which minus sign is inside the brackets.
Hint
In the first term, square 3 before applying the minus sign.
Reveal answer
0. The first term is −9; the bracketed negative number squares to 9.
Build an explanation
Hint 1
Calculate brackets first, then powers. −3² means −(3²) = −9, while (−3)² = 9.
Hint 2
Multiply and divide next, working from left to right. A product or quotient with unlike signs is negative.
Hint 3
Add and subtract last, working from left to right. Subtracting a negative adds: a − (−b) = a + b.
Worked example
This example uses fixed values, separate from the diagram controls.
Calculate −3² + 2(−4) − (−5).
- Calculate the power: −3² = −9.
- Calculate the product: 2(−4) = −8.
- Subtracting −5 adds 5, so the expression becomes −9 − 8 + 5.
- Work from left to right: −17 + 5 = −12.
Answer: −12
Connect this idea
Watch out: An unbracketed minus sign is not part of the base of a power: −3² = −9, whereas (−3)² = 9.