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 245 by 6, I add 245 plus 6 to get 251 as the product.
Corrected: To multiply 245 by 6, I multiply each place value: 6 ones times 245 equals 1,470 as the product.
In Grade 5, the product of 245 and 6 means 245 added to itself 6 times, which equals 1,470, not 251.
2. Fix the sentence:
When multiplying 132 by 4, I write the answer as 428 because 4 times 1 is 4, 4 times 3 is 12, and 4 times 2 is 8.
Corrected: When multiplying 132 by 4, I write the answer as 528 by multiplying right to left with place value: 4 times 2 ones is 8, 4 times 3 tens is 120, and 4 times 1 hundred is 400.
Grade 5 students must use place value alignment; 132 times 4 equals 528, not 428, because each digit represents ones, tens, or hundreds.
3. Fix the sentence:
I multiplied 318 by 7 and got 2,156 by forgetting to add the carried digit.
Corrected: I multiplied 318 by 7 and got 2,226 by adding the carried digit at each step of the standard algorithm.
In Grade 5 multiplication, 7 times 8 is 56, so we write 6 and carry 5; forgetting the carry gives a wrong product like 2,156 instead of the correct 2,226.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. The product of 245 and 6 is 1470.
Grade 5 students compute 6 times 5 equals 30, 6 times 40 equals 240, 6 times 200 equals 1,200, total 1,470.
2. When you multiply 124 by 3, the product is 372.
In Grade 5, 124 times 3 equals 372 because 3 times 100 is 300, 3 times 20 is 60, and 3 times 4 is 12.
3. The result of multiplying 213 by 4 equals 852.
Grade 5 multiplication: 4 times 3 is 12, 4 times 1 ten is 4 tens (with carry), 4 times 2 hundreds is 8 hundreds, total 852.
4. The product when 318 is multiplied by 7 is 2226.
Grade 5 students must track carried digits: 7 times 318 equals 2,226 using the standard multi-digit multiplication algorithm.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Explain how you would multiply 245 by 6 using the standard algorithm.
Sample answer: I line up 245 with 6 below the ones place. I multiply 6 times 5 ones equals 30, write 0 and carry 3. Next I multiply 6 times 4 tens equals 24 tens, plus the carried 3 makes 27 tens, write 7 and carry 2. Then 6 times 2 hundreds equals 12 hundreds, plus the carried 2 makes 14 hundreds. The final product is 1,470.
Grade 5 students must explain place value and carrying when applying the standard multi-digit multiplication algorithm.
2. How does place value help you multiply 132 by 4 correctly?
Sample answer: Place value tells me that the 1 in 132 means 100, the 3 means 30, and the 2 means 2. So when I multiply by 4, I find 4 times 100 equals 400, 4 times 30 equals 120, and 4 times 2 equals 8. Adding the partial products 400 plus 120 plus 8 gives me 528 as the final product.
Grade 5 emphasizes that multi-digit multiplication relies on place value to give each digit the correct value in the product.