Q1: What is the partial product of 4 × 23 when you break it down using place value? (a) 4 × 20 and 4 × 3 (b) 4 × 2 and 4 × 3 (c) 23 × 1 and 23 × 4 (d) 4 × 10 and 4 × 13
Solution:
Ans: (a) Explanation: When using partial products, we break 23 into place value parts: 20 and 3. Then multiply each part by 4 to get \(4 \times 20 = 80\) and \(4 \times 3 = 12\). Option (b) incorrectly breaks 23 into 2 instead of 20. Options (c) and (d) use incorrect decompositions.
Q2: Using partial products, what is 5 × 47? (a) 200 (b) 235 (c) 215 (d) 245
Solution:
Ans: (b) Explanation: Break 47 into 40 and 7. \(5 \times 40 = 200\) \(5 \times 7 = 35\) Add the partial products: \(200 + 35 = 235\). Option (c) results from calculation error, while (a) and (d) are common mistakes.
Q3: Which shows the correct partial products for 6 × 34? (a) 18 and 24 (b) 180 and 24 (c) 60 and 34 (d) 30 and 204
Solution:
Ans: (b) Explanation: Break 34 into 30 and 4. \(6 \times 30 = 180\) \(6 \times 4 = 24\) These are the correct partial products. Option (a) incorrectly uses 18 instead of 180. Options (c) and (d) do not correctly apply the partial products method.
Q4: What is the sum of the partial products for 7 × 52? (a) 354 (b) 364 (c) 374 (d) 344
Solution:
Ans: (b) Explanation: Break 52 into 50 and 2. \(7 \times 50 = 350\) \(7 \times 2 = 14\) Add the partial products: \(350 + 14 = 364\). The other options result from common calculation errors.
Ans: (a) Explanation: Using partial products, we break 68 into its place values: 60 and 8. Then we write \(3 \times 60 + 3 \times 8\). Option (b) incorrectly uses 6 instead of 60. Option (d) uses subtraction which is not the partial products method for this problem.
Q6: What are the partial products when multiplying 8 × 93? (a) 720 and 24 (b) 72 and 24 (c) 80 and 93 (d) 800 and 24
Solution:
Ans: (a) Explanation: Break 93 into 90 and 3. \(8 \times 90 = 720\) \(8 \times 3 = 24\) These are the correct partial products. Option (b) incorrectly calculates \(8 \times 90\) as 72. Options (c) and (d) are incorrect decompositions.
Ans: (b) Explanation: Break 56 into 50 and 6. \(4 \times 50 = 200\) \(4 \times 6 = 24\) The sum is \(200 + 24 = 224\). Option (a) uses 20 instead of 24. Option (c) uses 20 instead of 200. Option (d) has incorrect values.
Q8: When using partial products to solve 9 × 45, what is the first partial product if you start with the tens place? (a) 360 (b) 45 (c) 90 (d) 405
Solution:
Ans: (a) Explanation: Breaking 45 into 40 and 5, the first partial product from the tens place is \(9 \times 40 = 360\). Option (c) incorrectly calculates this as 90. Options (b) and (d) do not represent the correct partial product.
Section B: Fill in the Blanks
Q9: When using partial products, we break numbers apart by their __________ before multiplying.
Solution:
Ans: place value Explanation: The partial products method requires breaking numbers into their place values (such as tens and ones) before multiplying each part separately.
Q10: The partial products for 6 × 72 are 420 and __________.
Solution:
Ans: 12 Explanation: Breaking 72 into 70 and 2: \(6 \times 70 = 420\) and \(6 \times 2 = 12\). These are the two partial products.
Q11: To find the final answer when using partial products, you __________ all the partial products together.
Solution:
Ans: add Explanation: After finding each partial product, we add them together to get the final answer.
Q12: The partial product of 5 × 80 is __________.
Solution:
Ans: 400 Explanation: Multiplying \(5 \times 80 = 400\). This is one of the partial products when multiplying by a two-digit number with 80 as a place value part.
Q13: When multiplying 7 × 36, if you break 36 into 30 and 6, the partial product for the ones place is __________.
Solution:
Ans: 42 Explanation: The ones place partial product is \(7 \times 6 = 42\). The tens place partial product would be \(7 \times 30 = 210\).
Q14: The sum of the partial products 240 and 16 equals __________.
Solution:
Ans: 256 Explanation: Adding the two partial products: \(240 + 16 = 256\). This gives us the final product.
Section C: Word Problems
Q15: A bakery makes 8 boxes of cookies each day. Each box contains 35 cookies. Using partial products, how many cookies does the bakery make in one day?
Solution:
Ans: Break 35 into 30 and 5. \(8 \times 30 = 240\) \(8 \times 5 = 40\) Add the partial products: \(240 + 40 = 280\) Final Answer: 280 cookies
Q16: Maria reads 6 pages of her book every night. If she continues this for 42 nights, how many total pages will she read? Use partial products to solve.
Solution:
Ans: Break 42 into 40 and 2. \(6 \times 40 = 240\) \(6 \times 2 = 12\) Add the partial products: \(240 + 12 = 252\) Final Answer: 252 pages
Q17: A toy store has 7 shelves. Each shelf holds 64 action figures. How many action figures are in the store in total? Solve using partial products.
Solution:
Ans: Break 64 into 60 and 4. \(7 \times 60 = 420\) \(7 \times 4 = 28\) Add the partial products: \(420 + 28 = 448\) Final Answer: 448 action figures
Q18: A farmer plants 9 rows of tomato plants. Each row has 53 plants. Using the partial products method, find the total number of tomato plants.
Solution:
Ans: Break 53 into 50 and 3. \(9 \times 50 = 450\) \(9 \times 3 = 27\) Add the partial products: \(450 + 27 = 477\) Final Answer: 477 tomato plants
Q19: A school bus makes 4 trips each day. Each trip is 78 miles long. How many miles does the bus travel in one day? Use partial products to find your answer.
Solution:
Ans: Break 78 into 70 and 8. \(4 \times 70 = 280\) \(4 \times 8 = 32\) Add the partial products: \(280 + 32 = 312\) Final Answer: 312 miles
Q20: A bookstore orders 5 boxes of notebooks. Each box contains 86 notebooks. How many notebooks did the bookstore order in total? Show your work using partial products.
Solution:
Ans: Break 86 into 80 and 6. \(5 \times 80 = 400\) \(5 \times 6 = 30\) Add the partial products: \(400 + 30 = 430\) Final Answer: 430 notebooks
The document Worksheet (with Solutions): Multiply With Partial Products is a part of the Grade 4 Course Math Grade 4.
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