IAAT - Iowa Algebra Aptitude Order of Operations Questions and Answers — Questions and Answers
Question 1: What is the value of the expression 48 ÷ 2(9 + 3)?
- 2
- 288 (Correct answer)
- 4
- 72
Correct answer: 288
Following the order of operations (PEMDAS/BODMAS), first solve the operation inside the parentheses: 9 + 3 = 12. The expression becomes 48 ÷ 2 × 12. Next, perform multiplication and division from left to right. First, calculate 48 ÷ 2 = 24. Then, calculate 24 × 12 = 288.
Question 2: A student was asked to evaluate the expression 60 - 4² ÷ 2 × 3. Their work is shown below. Step 1: 60 - 16 ÷ 2 × 3 Step 2: 44 ÷ 2 × 3 Step 3: 22 × 3 Step 4: 66 In which step did the student make their first mistake?
- Step 1
- Step 2 (Correct answer)
- Step 3
- Step 4
Correct answer: Step 2
The student's first error occurred in Step 2. After correctly calculating the exponent in Step 1 (4² = 16), the next operations according to PEMDAS are division and multiplication from left to right. The student incorrectly performed subtraction (60 - 16) before division. The correct second step should have been to calculate 16 ÷ 2.
Question 3: Where should parentheses be placed in the expression 5 + 3 × 8 - 2² to make its value equal to 60?
- 5 + 3 × (8 - 2²)
- (5 + 3 × 8) - 2²
- (5 + 3) × 8 - 2² (Correct answer)
- 5 + (3 × 8 - 2²)
Correct answer: (5 + 3) × 8 - 2²
Placing parentheses around (5 + 3) forces this addition to be performed first. The expression becomes (5 + 3) × 8 - 2², which simplifies to 8 × 8 - 2². Next, evaluate the exponent: 8 × 8 - 4. Then, perform the multiplication: 64 - 4. Finally, the subtraction gives the desired value of 60.
Question 4: What is the value of the expression: 3 × [20 - (2 + 4)² ÷ 9]?
- 12
- 52
- 48 (Correct answer)
- 16
Correct answer: 48
Work from the innermost grouping symbols outward. First, calculate inside the parentheses: (2 + 4) = 6. The expression becomes 3 × [20 - 6² ÷ 9]. Inside the brackets, evaluate the exponent: 6² = 36. The expression is now 3 × [20 - 36 ÷ 9]. Still inside the brackets, perform division before subtraction: 36 ÷ 9 = 4. The expression simplifies to 3 × [20 - 4]. Perform the subtraction in the brackets: 20 - 4 = 16. Finally, perform the multiplication: 3 × 16 = 48.
Question 5: A family buys 4 adult movie tickets for $12 each and 3 child tickets for $8 each. They also buy a large popcorn for $10 and use a coupon for $5 off the entire purchase. Which expression correctly calculates their total cost?
- 4 + 3 × 12 + 8 + 10 - 5
- 4 × (12 + 8) + 3 × 10 - 5
- 4 × 12 + 3 × 8 + 10 - 5 (Correct answer)
- (4 + 3) × (12 + 8) + 10 - 5
Correct answer: 4 × 12 + 3 × 8 + 10 - 5
To find the total cost, you must first calculate the cost of the adult tickets (4 × $12) and the child tickets (3 × $8). Then, you add the cost of the popcorn ($10) and subtract the coupon ($5). The multiplications must be performed before the addition and subtraction, representing the costs of the groups of tickets.
Question 6: Which of the following expressions has a value of 20?
- 8 + 3 × 4 (Correct answer)
- (8 + 3) × 4
- 40 ÷ 5 - 3 × 2
- 2 + (9 - 1) × 2
Correct answer: 8 + 3 × 4
To evaluate 8 + 3 × 4, the order of operations requires performing multiplication before addition. First, calculate 3 × 4 = 12. Then, perform the addition: 8 + 12 = 20. The other expressions evaluate to 44, 2, and 18, respectively.
IAAT - Iowa Algebra Aptitude Order of Operations Questions and Answers
What is the value of the expression 48 ÷ 2(9 + 3)?