Q1: What is 23 × 4 using partial products? (a) 80 (b) 92 (c) 100 (d) 84
Solution:
Ans: (b) Explanation: Break 23 into 20 + 3. Multiply: \(20 \times 4 = 80\) and \(3 \times 4 = 12\). Add the partial products: \(80 + 12 = 92\).
Q2: Which shows the correct partial products for 34 × 6? (a) 180 and 24 (b) 120 and 18 (c) 210 and 30 (d) 150 and 24
Solution:
Ans: (a) Explanation: Break 34 into 30 + 4. The partial products are \(30 \times 6 = 180\) and \(4 \times 6 = 24\). Adding them gives \(180 + 24 = 204\).
Q3: What is the first partial product when multiplying 52 × 3? (a) 150 (b) 6 (c) 100 (d) 50
Solution:
Ans: (a) Explanation: Break 52 into 50 + 2. The first partial product is the tens place: \(50 \times 3 = 150\).
Q4: Find the product of 18 × 5 using partial products. (a) 85 (b) 90 (c) 80 (d) 95
Solution:
Ans: (b) Explanation: Break 18 into 10 + 8. The partial products are \(10 \times 5 = 50\) and \(8 \times 5 = 40\). Adding them: \(50 + 40 = 90\).
Q5: What is 47 × 2 broken into partial products? (a) 40 × 2 and 7 × 2 (b) 20 × 2 and 27 × 2 (c) 45 × 2 and 2 × 2 (d) 30 × 2 and 17 × 2
Solution:
Ans: (a) Explanation: The correct way to use place value is to break 47 into tens and ones: 40 and 7. So we multiply \(40 \times 2\) and \(7 \times 2\).
Q6: What is 25 × 7 using partial products? (a) 165 (b) 175 (c) 185 (d) 155
Solution:
Ans: (b) Explanation: Break 25 into 20 + 5. The partial products are \(20 \times 7 = 140\) and \(5 \times 7 = 35\). Adding them: \(140 + 35 = 175\).
Q7: If you multiply 63 × 4, what is the partial product for the ones place? (a) 240 (b) 12 (c) 60 (d) 24
Solution:
Ans: (b) Explanation: Break 63 into 60 + 3. The ones place partial product is \(3 \times 4 = 12\).
Q8: What is the sum of the partial products for 81 × 6? (a) 480 (b) 486 (c) 490 (d) 476
Solution:
Ans: (b) Explanation: Break 81 into 80 + 1. The partial products are \(80 \times 6 = 480\) and \(1 \times 6 = 6\). Adding: \(480 + 6 = 486\).
Section B: Fill in the Blanks
Q9: When using partial products to multiply 42 × 5, we break 42 into __________ and __________.
Solution:
Ans: 40 and 2 Explanation: Using place value, we separate the tens place (40) and the ones place (2) to create partial products.
Q10: The partial product of 30 × 8 is __________.
Solution:
Ans: 240 Explanation: Multiply \(30 \times 8 = 240\). This represents multiplying the tens place value.
Q11: To find 56 × 3 using partial products, we add __________ and __________.
Solution:
Ans: 150 and 18 Explanation: Break 56 into 50 + 6. The partial products are \(50 \times 3 = 150\) and \(6 \times 3 = 18\).
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