➕ Algebra 1 · Equations
Order of Operations practice questions
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Evaluate 20 − 4 × 3 + 2.
Answer: 10. Multiply first: 4 × 3 = 12, giving 20 − 12 + 2. Then go left to right: 20 − 12 = 8, and 8 + 2 = 10. The answer 6 comes from adding 12 + 2 before subtracting, and 50 comes from working strictly left to right.
Evaluate 72 ÷ 9 × 4.
Answer: 32. Division and multiplication tie, so go left to right: 72 ÷ 9 = 8, then 8 × 4 = 32. The answer 2 comes from multiplying 9 × 4 first, and 8 stops one step too early.
Evaluate 5 + 3 × (7 − 3)2.
Answer: 53. Parentheses first: 7 − 3 = 4. Exponent next: 42 = 16. Multiply: 3 × 16 = 48. Add: 5 + 48 = 53. The answer 149 squares the product 3 × 4, and 128 adds 5 + 3 too early.
Evaluate −42 + 32.
Answer: −7. The exponent touches only the 4, so −42 = −(42) = −16. Also 32 = 9. Add: −16 + 9 = −7. The answer 25 treats the first term as (−4)2 = 16.
Evaluate the fraction whose numerator is 6 + 4 × 3 and whose denominator is 9 − 3.
Answer: 3. The bar groups the top and the bottom. Top: 4 × 3 = 12, then 6 + 12 = 18. Bottom: 9 − 3 = 6. Divide: 18 ÷ 6 = 3. The answer −1 divides by only the 9, and 8 divides only the 12.
Evaluate 50 − 2[6 + (10 − 8)2].
Answer: 30. Innermost group first: 10 − 8 = 2. Exponent: 22 = 4. Brackets: 6 + 4 = 10. Multiply: 2 × 10 = 20. Subtract: 50 − 20 = 30. The answer 480 subtracts 50 − 2 before multiplying, and 34 forgets the exponent.
Four friends split a pizza bill of 36 dollars and a drinks bill of 12 dollars equally. Which calculation gives each friend’s share, and what is it?
Answer: (36 + 12) ÷ 4 = 12 dollars. The whole bill is 36 + 12, and that total is split four ways, so the addition needs parentheses: (36 + 12) ÷ 4 = 48 ÷ 4 = 12 dollars. Without parentheses, 36 + 12 ÷ 4 divides only the drinks bill and gives 39.
Evaluate x2 − 5x when x = −6.
Answer: 66. Substitute with parentheses: (−6)2 − 5(−6). Exponent: (−6)2 = 36. Multiply: 5(−6) = −30. Then 36 − (−30) = 36 + 30 = 66. The answer −6 squares without the parentheses (getting −36), and 6 forgets that subtracting a negative adds.