STAGE 1.1 · 8 PRACTICE PROBLEMS · 2 NEW-CONTEXT APPLICATIONS
Signed Numbers & Order of Operations
Goal: Track direction and group operations before calculating.
Before you begin: Before starting, explain one example from each prerequisite. If an idea is unfamiliar, follow the prerequisite lesson links.
Numbers describe position and change
A negative position is below the chosen zero. A negative change moves toward smaller numbers. Subtracting a change reverses that change.
Signs belong to numbers
Multiplication by a negative reverses direction. Two reversals restore the original direction; a product with an odd number of negative factors is negative.
Read the structure first
Resolve grouping, then powers, then multiplication and division from left to right, then addition and subtraction from left to right. Equal-priority operations do not jump the queue.
Evaluate 7 − 2(5 − 9).
- Inside parentheses: 5 − 9 = −4.
- Multiply: 2(−4) = −8.
- Subtracting −8 adds 8.
15
A sensor reads −11°C and warms by 6°C, then cools by 4°C. What does it read?
- Start at −11.
- Warming gives −5; cooling gives −9.
−9°C
Common pitfalls
Possible mix-up: Subtracting always makes a number smaller.
Subtracting a negative makes it larger.
Possible mix-up: Multiply before dividing, wherever multiplication appears.
Multiplication and division have equal priority; read left to right.
Explain it to yourself
Explain why −5 − (−8) and −5 + (−8) have different signs.
Preview the eight practice prompts
- Compute −14 + 9.
- Compute 6 − (−13).
- Compute (−7)(−4) − 10.
- Evaluate 42 ÷ 7 × 3 − 5.
- Evaluate 5 − 3(2 − 6).
- What number n makes −8 − n = 5?
- An elevator starts on floor 4, moves down 9 floors, then up 6. Basement floors are negative and ground is 0. Which floor is it on? New context
- A game adds −6 points for each of three penalties, then removes one of those penalties. Starting from 20 points, what is the final score? New context