PARCC Basic Operations Practice Questions 2 — Questions and Answers
Question 1: What is 1,248 × 35?
- 41,680
- 43,680 (Correct answer)
- 43,860
- 44,680
Correct answer: 43,680
1,248 × 35 = 1,248 × 30 + 1,248 × 5 = 37,440 + 6,240 = 43,680.
Multiplying larger numbers is easier when you break them apart using the distributive property. This strategy is sometimes called 'partial products.' 1,248 × 35 = 1,248 × (30 + 5) = (1,248 × 30) + (1,248 × 5) = 37,440 + 6,240 = 43,680 Let's verify each partial product: - 1,248 × 30: multiply 1,248 × 3 = 3,744, then multiply by 10 = 37,440 ✓ - 1,248 × 5: 1,000 × 5 = 5,000; 200 × 5 = 1,000; 48 × 5 = 240; total = 6,240 ✓ Adding: 37,440 + 6,240 = 43,680. Multi-digit multiplication is a foundational skill assessed on the PARCC exam. Using partial products or the standard algorithm both produce the correct answer. Estimation can help check: 1,200 × 35 = 42,000, so 43,680 is a reasonable answer for 1,248 × 35.
Question 2: Divide: 5,796 ÷ 12
- 481
- 483 (Correct answer)
- 485
- 493
Correct answer: 483
12 × 483 = 5,796. Alternatively, 5,796 ÷ 12: 12 × 400 = 4,800; remainder 996; 12 × 83 = 996; total 483.
Long division of 5,796 ÷ 12: Step 1: How many times does 12 go into 57? 12 × 4 = 48, 12 × 5 = 60 (too big). So 4 times. Write 4; subtract: 57 − 48 = 9. Bring down 9: 99. Step 2: How many times does 12 go into 99? 12 × 8 = 96, 12 × 9 = 108 (too big). So 8 times. Write 8; subtract: 99 − 96 = 3. Bring down 6: 36. Step 3: How many times does 12 go into 36? 12 × 3 = 36. Write 3; subtract: 36 − 36 = 0. Result: 483 with remainder 0. Verification: 483 × 12 = 483 × 10 + 483 × 2 = 4,830 + 966 = 5,796 ✓ Long division is a multi-step process that requires careful tracking of remainders. Always verify your answer by multiplying the quotient by the divisor to see if you get the original dividend.
Question 3: What is 456 − 287?
- 159
- 169 (Correct answer)
- 171
- 179
Correct answer: 169
456 − 287: Borrow from the tens: 16 − 7 = 9; borrow again: 14 − 8 = 6... actually: 456 − 287 = 169. Check: 287 + 169 = 456 ✓
To subtract 287 from 456 using the standard algorithm: Ones column: 6 − 7. Since 6 < 7, borrow from the tens place. Borrow 1 ten from 5 tens: tens becomes 4; ones becomes 16. 16 − 7 = 9. Write 9 in the ones column. Tens column: 4 − 8. Since 4 < 8, borrow from the hundreds place. Borrow 1 hundred from 4 hundreds: hundreds becomes 3; tens becomes 14. 14 − 8 = 6. Write 6 in the tens column. Hundreds column: 3 − 2 = 1. Write 1 in the hundreds column. Result: 169. Verification: 287 + 169 = 456 ✓ Regrouping (borrowing) in subtraction requires careful tracking of which digits have been modified. A common error is forgetting to reduce the digit you borrowed from. Always check subtraction by adding your answer to the subtracted number to see if you get the original number.
Question 4: What is the value of 3² + 4² ?
- 25 (Correct answer)
- 30
- 49
- 7
Correct answer: 25
3² = 9 and 4² = 16. Sum: 9 + 16 = 25.
This problem tests the order of operations and understanding of exponents. The exponent (²) means the base number is multiplied by itself. 3² = 3 × 3 = 9 4² = 4 × 4 = 16 3² + 4² = 9 + 16 = 25 Note: a common mistake is to compute (3 + 4)² = 7² = 49. However, by the order of operations, exponents must be evaluated BEFORE addition. So you must square each number first, then add. This is actually related to the famous Pythagorean theorem: in a right triangle with legs of length 3 and 4, the hypotenuse has length 5, because 3² + 4² = 5² (9 + 16 = 25). This well-known Pythagorean triple (3, 4, 5) often appears in PARCC math problems involving geometry and the Pythagorean theorem.
Question 5: Which of the following is equivalent to 72 ÷ 8 × 3?
- 3
- 27 (Correct answer)
- 192
- 48
Correct answer: 27
Using left-to-right order for multiplication and division: 72 ÷ 8 = 9, then 9 × 3 = 27.
Order of operations (PEMDAS/BODMAS) states that multiplication and division have the same priority and are performed from left to right. This is a critical rule that many students misapply. For 72 ÷ 8 × 3: Step 1: Work left to right. First operation: 72 ÷ 8 = 9. Step 2: Next operation: 9 × 3 = 27. The answer is 27. A common mistake is to perform multiplication before division because M comes before D in PEMDAS. However, multiplication and division are at the same level—they are performed left to right. If you had done the multiplication first: 8 × 3 = 24, then 72 ÷ 24 = 3, you would get the wrong answer of 3. Similarly, addition and subtraction share equal priority and are performed left to right. Remember: PEMDAS describes levels of priority, and within each level, you work left to right. This rule is fundamental to all mathematical calculation and is directly tested on the PARCC exam.
Question 6: A factory produces 2,340 widgets per hour. How many widgets does it produce in a 9-hour shift, minus 180 defective ones?
- 20,880 (Correct answer)
- 21,060
- 21,240
- 21,420
Correct answer: 20,880
Total produced: 2,340 × 9 = 21,060. Subtract defective: 21,060 − 180 = 20,880.
This is a multi-step word problem requiring multiplication followed by subtraction. Step 1: Find the total widgets produced in 9 hours. 2,340 × 9: 2,000 × 9 = 18,000 300 × 9 = 2,700 40 × 9 = 360 Total: 18,000 + 2,700 + 360 = 21,060 Step 2: Subtract the defective widgets. 21,060 − 180 = 20,880 The factory produces 20,880 non-defective widgets during the shift. Multi-step word problems are a major component of PARCC math assessments. They require you to (1) identify what the problem is asking, (2) determine the sequence of operations, (3) execute each operation accurately, and (4) verify the answer makes sense in context. Estimation check: 2,300 × 9 ≈ 20,700, and subtracting roughly 200 gives approximately 20,500. Our answer of 20,880 is in that ballpark, confirming it is reasonable.
PARCC Basic Operations Practice Questions 2
What is 1,248 × 35?