Real problems mix the operations. The order of operations still applies, signs and all.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Fractions and decimals too
A rational number is any fraction, decimal, or integer, positive or negative.
Check the sign first
Before calculating, decide whether the answer should be positive or negative. It catches slips.
Let the context decide
A temperature drop, a debt, or a descent are all negatives. Read what the situation says.
Order of operations still applies
Signs do not change the order: brackets, exponents, multiplication and division left to right, then addition and subtraction. Adding signs to a calculation makes it longer, not structurally different.
Use brackets around negative numbers
Write 3 × (−2) rather than 3 × −2. Two operation symbols in a row are hard to read and easy to misparse. Brackets cost nothing and remove the ambiguity, which matters more as expressions get longer.
Work out the sign separately
For (−3) × (−4) × (−2), count the negatives: three of them, an odd number, so the answer is negative. Then multiply the magnitudes: 24. Answer: −24. Separating the sign from the size makes long products much more reliable.
Signed numbers in real problems
Temperature changes, elevation, bank balances, and gains and losses in a game all need signed arithmetic. Reading the situation to decide which quantities are negative is often harder than the calculation, and worth doing explicitly.
Step 2: Try It Yourself
Tap and try it out.
Adding 4 walks 4 to the right.
Step 3: Watch an Example
One step at a time.
Watch Ana Work Through a Drop
A temperature falls 3 degrees each hour for 4 hours from 5 degrees.
- Step 1
She writes the change as 4 × (−3), which is −12.
Step 4: Your Turn
Practice makes it stick.
The Dive
Problem 1 of 3
A diver at −12 m descends 4 m more, then rises 7. What is the depth now?
The Debt
Problem 2 of 3
Five people each owe 8 pounds. What is the total, as a negative?
The Cooling
Problem 3 of 3
The temperature falls 2 degrees an hour for 6 hours from 4 degrees. What is it now?
Mixed Signs
1 of 4
−5 + 3 × (−2) = ?
2 of 4
(−12) ÷ 4 + 5 = ?
3 of 4
2 × (−7) + 10 = ?
4 of 4
(−3) × (−4) − 5 = ?
Step 5: Quick Check
Show what you know.
Question 1 of 2
−4 + 5 × (−3) = ?
Question 2 of 2
What is worth doing before calculating?
What You Learned
- The order of operations still applies with signs.
- A rational number can be a fraction, a decimal, or an integer.
- Predict the sign before calculating.