Multi-Digit Multiplication — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
To multiply 36 × 14 using partial products, find 36 × 4 = 144 and 36 × 1 = 36, then add 144 + 36 = 180.
Corrected: To multiply 36 × 14 using partial products, find 36 × 4 = 144 and 36 × 10 = 360, then add 144 + 360 = 504.
The original wrote 36 × 1 = 36 instead of 36 × 10 = 360, forgetting that the 1 in 14 stands for 10. With the correct partial products (144 + 360), the answer is 504, not 180.
2. Fix the sentence:
Using the area model for 43 × 25, split 25 into 20 and 5, so the partial products are 43 × 20 = 860 and 43 × 5 = 215, giving 860 + 215 = 1,085.
Corrected: Using the area model for 43 × 25, split 25 into 20 and 5, so the partial products are 43 × 20 = 860 and 43 × 5 = 215, giving 860 + 215 = 1,075.
The partial products 860 and 215 are correct, but 860 + 215 = 1,075, not 1,085. The original added the ones digits wrong (0 + 5 = 5, not 5 + 0 = 5 with an extra 10).
3. Fix the sentence:
734 × 6 = 4,304 because 4 × 6 = 24, carry the 2, then 3 × 6 = 18 plus 2 = 20, carry the 2, then 7 × 6 = 42 plus 2 = 44.
Corrected: 734 × 6 = 4,404 because 4 × 6 = 24, write 4 carry 2, then 3 × 6 = 18 plus 2 = 20, write 0 carry 2, then 7 × 6 = 42 plus 2 = 44.
When you multiply 3 × 6 = 18 and add the carried 2, you get 20, so you write 0 in the hundreds place and carry 2. The original wrote 3 instead of 0, making the product 4,304 instead of the correct 4,404.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. Using partial products, 52 × 13 = 52 × 3 + 52 × 10 = 156 + 520 = 676
52 × 10 = 520 because you multiply 52 by the tens digit of 13. Adding the two partial products gives 156 + 520 = 676.
2. In the area model for 28 × 15, one rectangle is 28 × 10 = 280 and the other is 28 × 5 = 140
The area model splits 15 into 10 and 5. The second rectangle is 28 × 5 = 140, so the total product is 280 + 140 = 420.
3. 645 × 8 = 5,160
Multiply step by step: 5 × 8 = 40 (write 0, carry 4), 4 × 8 = 32 plus 4 = 36 (write 6, carry 3), 6 × 8 = 48 plus 3 = 51. The product is 5,160.
4. The area model breaks a multiplication problem into smaller parts that are easier to solve.
The area model breaks each factor into expanded form (like tens and ones), creating smaller rectangles whose products are easier to calculate and then add together.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Use partial products to solve 47 × 12. Show the two partial products and the final answer.
Sample answer: 47 × 2 = 94 and 47 × 10 = 470. Adding the partial products gives 94 + 470 = 564.
Break 12 into 2 and 10, then multiply each by 47: 47 × 2 = 94 and 47 × 10 = 470. Adding those partial products gives 94 + 470 = 564.
2. A parking lot has 18 rows with 35 spaces in each row. How many parking spaces are there in all?
Sample answer: 18 × 35 = 630. There are 630 parking spaces in the lot.
Multiply 18 × 35 using partial products: 18 × 5 = 90 and 18 × 30 = 540, so 90 + 540 = 630 parking spaces in all.