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:
492 × 7 = 3,344 because 2 × 7 = 14, carry the 1, then 9 × 7 = 63 plus 1 = 64, carry the 6, then 4 × 7 = 28 plus 6 = 34.
Corrected: 492 × 7 = 3,444 because 2 × 7 = 14, write 4 carry 1, then 9 × 7 = 63 plus 1 = 64, write 4 carry 6, then 4 × 7 = 28 plus 6 = 34.
The steps are correct (2 × 7 = 14, 9 × 7 + 1 = 64, 4 × 7 + 6 = 34), but the original wrote the hundreds digit as 3 instead of 4. Since 64 means write 4 and carry 6, the correct product is 3,444.
2. Fix the sentence:
1,308 × 5 = 6,540 because 8 × 5 = 40, carry the 4, then 0 × 5 = 0 plus 4 = 4, then 3 × 5 = 15, carry the 1, then 1 × 5 = 5 plus 1 = 6.
Corrected: 1,308 × 5 = 6,540 because 8 × 5 = 40, write 0 carry 4, then 0 × 5 = 0 plus 4 = 4, then 3 × 5 = 15 write 5 carry 1, then 1 × 5 = 5 plus 1 = 6.
The original used vague "carry the" phrasing instead of clearly stating which digit to write and which to carry. The correct notation is: write 0 carry 4, then write 4, then write 5 carry 1, then write 6. The final product 6,540 is correct either way.
3. Fix the sentence:
To find 56 × 23 using partial products, compute 56 × 3 = 168 and 56 × 2 = 112, then add 168 + 112 = 280.
Corrected: To find 56 × 23 using partial products, compute 56 × 3 = 168 and 56 × 20 = 1,120, then add 168 + 1,120 = 1,288.
In partial products, the 2 in 23 represents 20, not 2. The original computed 56 × 2 = 112 instead of 56 × 20 = 1,120, which gave a product far too small. The correct sum is 168 + 1,120 = 1,288.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 827 × 9 = 7,443
Multiply column by column: 7 × 9 = 63 (write 3, carry 6), 2 × 9 = 18 + 6 = 24 (write 4, carry 2), 8 × 9 = 72 + 2 = 74. The product is 7,443.
2. 3,105 × 3 = 9,315
Multiply each digit by 3: 5 × 3 = 15, 0 × 3 = 0 + 1 = 1, 1 × 3 = 3, 3 × 3 = 9. The product is 9,315.
3. When you regroup in multiplication, you carry the extra amount to the next place value.
When a product in one column is 10 or more, you write the ones digit and carry the tens digit to the next place value. This regrouping step is called carrying.
4. To estimate 389 × 4, round 389 to 400 and multiply: 400 × 4 = 1,600
Rounding 389 to the nearest hundred gives 400, and 400 × 4 = 1,600. This estimate is close to the exact answer of 1,556.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Explain step by step how to multiply 364 × 5.
Sample answer: Multiply 4 × 5 = 20, write 0 carry 2. Then 6 × 5 = 30 plus 2 = 32, write 2 carry 3. Then 3 × 5 = 15 plus 3 = 18. The answer is 1,820.
Start from the ones place: 4 × 5 = 20 (write 0, carry 2), then 6 × 5 = 30 + 2 = 32 (write 2, carry 3), then 3 × 5 = 15 + 3 = 18. Reading the digits gives 1,820.
2. A bookstore receives 24 boxes of books. Each box holds 16 books. How many books does the store receive?
Sample answer: 24 × 16 = 384. The bookstore receives 384 books.
Multiply 24 × 16 using partial products: 24 × 6 = 144 and 24 × 10 = 240, so 144 + 240 = 384 books total.