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 find 4,567 times 8, I just multiply 4 times 8 and get 32 as the answer.
Corrected: To find 4,567 times 8, I multiply each digit by 8 using place value, carrying as needed, to get 36,536 as the answer.
Grade 5 multi-digit multiplication requires multiplying every place value: 8 times 4,567 equals 36,536, not 32.
2. Fix the sentence:
When multiplying 2,345 by 5, I wrote 10,025 because I forgot to carry from the tens place.
Corrected: When multiplying 2,345 by 5, I wrote 11,725 by carefully tracking each carry from ones to tens to hundreds to thousands.
Grade 5 students must apply carries correctly: 5 times 2,345 equals 11,725, demonstrating the standard algorithm with multiple carries.
3. Fix the sentence:
I added 1,234 plus 6 instead of multiplying, so I got 1,240 as my product.
Corrected: I multiplied 1,234 by 6 using the standard algorithm, so I got 7,404 as my product.
Grade 5 vocabulary: a product is the result of multiplying; 1,234 times 6 equals 7,404, far different from 1,234 plus 6 which equals 1,240.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. The product of 4,567 and 8 is 36536.
Grade 5 standard algorithm: 8 times 4,567 equals 36,536 with carries at the ones, tens, and hundreds places.
2. When 2,345 is multiplied by 5, the product is 11725.
Grade 5 students compute 5 times 2,345 equals 11,725 by aligning place values and tracking each carry.
3. Multiplying 1,234 by 6 gives a product of 7404.
In Grade 5, 1,234 times 6 equals 7,404 using the standard multi-digit multiplication algorithm.
4. The result of 3,021 times 7 equals 21147.
Grade 5 multiplication: 7 times 3,021 equals 21,147; the zero still requires multiplying and adding any carried value.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Describe how you multiply 4,567 by 8 step by step.
Sample answer: I write 4,567 with 8 below the ones place. I multiply 8 times 7 equals 56, write 6 and carry 5. Then 8 times 6 equals 48, plus 5 is 53, write 3 and carry 5. Next 8 times 5 equals 40, plus 5 is 45, write 5 and carry 4. Last, 8 times 4 equals 32, plus 4 is 36, write 36. The final product is 36,536.
Grade 5 students must describe the standard algorithm clearly, showing how carries connect each place value step.
2. Why is it important to handle the zero in 3,021 carefully when multiplying by 7?
Sample answer: The zero in the tens place of 3,021 still needs to be multiplied by 7. Even though 7 times 0 is 0, I must add any carry from the previous step. In this problem, 7 times 1 is 7 with no carry, then 7 times 2 is 14 carry 1, then 7 times 0 is 0 plus the carry 1 equals 1. Skipping the zero would shift place values and give a wrong product. The correct answer is 21,147.
Grade 5 multi-digit multiplication treats every digit, including zeros, with the proper place value to get the correct product.