➕ Algebra 1 · Equations
Order of Operations: true or false
Decide fast, then read the reason. Wrong answers are the best teachers, so every statement explains itself.
All statements and answers
In 8 + 2 × 5, you multiply before you add, so the value is 18.
✓ True. 2 × 5 = 10, then 8 + 10 = 18.
10 − 4 + 3 equals 3, because addition comes before subtraction.
✗ False. Addition and subtraction share a level, so go left to right: 10 − 4 = 6, then 6 + 3 = 9. The value 3 belongs to 10 − (4 + 3), a different expression.
12 ÷ 3 × 4 equals 1.
✗ False. Division and multiplication tie, so go left to right: 12 ÷ 3 = 4, then 4 × 4 = 16. The value 1 comes from dividing by 3 × 4 = 12 first.
−72 equals 49.
✗ False. The exponent touches only the 7, so −72 = −49. Only (−7)2 equals 49.
(4 + 1) × 6 and 4 + 1 × 6 have different values.
✓ True. (4 + 1) × 6 = 30, but 4 + 1 × 6 = 10. Parentheses change which operation happens first.
6 + 2 × (9 − 4) equals 40.
✗ False. Parentheses first: 9 − 4 = 5. Then 2 × 5 = 10. Then 6 + 10 = 16. The value 40 comes from adding 6 + 2 first, which ignores the rank of multiplication.
20 ÷ (2 + 3) = 4.
✓ True. Parentheses first: 2 + 3 = 5. Then 20 ÷ 5 = 4.
The fraction with top 9 + 15 and bottom 4 + 4 equals 3.
✓ True. The bar groups each part: (9 + 15) ÷ (4 + 4) = 24 ÷ 8 = 3.
Every calculator follows the order of operations.
✗ False. Some basic calculators carry out each operation as you press the keys, so they can show 9 instead of 7 for 1 + 2 × 3. Scientific and graphing calculators follow the order. When unsure, test with a problem whose answer you know.
7 − 2 − 1 = 4.
✓ True. Subtraction goes left to right: 7 − 2 = 5, then 5 − 1 = 4. Doing 2 − 1 first would give 6, which is the value of 7 − (2 − 1).
When x = −8, the value of x2 is −64.
✗ False. Substitute with parentheses: (−8)2 = 64. A negative times a negative is positive.
Inside parentheses the order of operations still applies, so (4 + 3 × 6) equals 22.
✓ True. Multiply first: 3 × 6 = 18. Then 4 + 18 = 22.