This Grade 5 long division worksheet introduces the partial-quotients method as an alternative to the standard algorithm. Students record friendly multipliers like 10, 20, or 50 to chunk away groups of the divisor, then add their partial quotients to find the total quotient. The sheet includes sentence-correction items that highlight common Grade 5 confusions, fill-in problems on labeling partial quotients and remainders, and short-answer prompts that ask students to explain their reasoning step by step.
Style:
Long Division with Multi-Digit Divisors
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
To divide 480 by 16 using partial quotients, I subtract 16 once and write 16 as my first partial quotient.
Rewrite: To divide 480 by 16 using partial quotients, I subtract a multiple of 16 (like 160) and write the multiplier (10) as my first partial quotient.
2. Fix the sentence:
When I add my partial quotient of 30 and 5, I should multiply them together to get the final quotient.
Rewrite: When I have partial quotients of 30 and 5, I should add them together to get the final quotient of 35.
3. Fix the sentence:
If 17 goes into 850 about 50 times, my first partial quotient should be 17 because that is the divisor.
Rewrite: If 17 goes into 850 about 50 times, my first partial quotient should be 50 because that is how many groups of 17 I am removing.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. In partial quotients for 624 ÷ 24, removing 20 groups of 24 leaves 144, so 20 is the first partial quotient.
2. After taking 20 groups and then 6 groups of 24 from 624, the total quotient is the sum of 20 and 6, which is 26.
3. Choosing 10, 20, or 50 as a first partial quotient is called using a friendly multiplier in Grade 5 division.
4. When the remaining number is less than the divisor, the partial-quotients work is finished and you write the remainder.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Use partial quotients to divide 432 ÷ 18 and explain each step in Grade 5 language.
I removed 20 groups of 18 (360) from 432, leaving 72. Then I removed 4 more groups of 18 (72), leaving 0. The partial quotients are 20 and 4, so 432 ÷ 18 = 24 with no remainder.
2. Why might a Grade 5 student prefer partial quotients over the standard algorithm for 728 ÷ 14?
Partial quotients let me use friendly numbers like 50 (50 × 14 = 700), then just 2 more groups of 14, instead of guessing one digit at a time. I get 52 with less risk of place-value mistakes.
Long Division with Multi-Digit Divisors
★ Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1) Fix the sentence:
To divide 480 by 16 using partial quotients, I subtract 16 once and write 16 as my first partial quotient.
Rewrite: To divide 480 by 16 using partial quotients, I subtract a multiple of 16 (like 160) and write the multiplier (10) as my first partial quotient.
2) Fix the sentence:
When I add my partial quotient of 30 and 5, I should multiply them together to get the final quotient.
Rewrite: When I have partial quotients of 30 and 5, I should add them together to get the final quotient of 35.
3) Fix the sentence:
If 17 goes into 850 about 50 times, my first partial quotient should be 17 because that is the divisor.
Rewrite: If 17 goes into 850 about 50 times, my first partial quotient should be 50 because that is how many groups of 17 I am removing.
★ Part B: Fill in the Blank
Write the missing word or number on each line.
1) In partial quotients for 624 ÷ 24, removing 20 groups of 24 leaves 144, so 20 is the first partial quotient.
2) After taking 20 groups and then 6 groups of 24 from 624, the total quotient is the sum of 20 and 6, which is 26.
3) Choosing 10, 20, or 50 as a first partial quotient is called using a friendly multiplier in Grade 5 division.
4) When the remaining number is less than the divisor, the partial-quotients work is finished and you write the remainder.
★ Part C: Short Answer
Answer each question in one or two complete sentences.
1) Use partial quotients to divide 432 ÷ 18 and explain each step in Grade 5 language.
I removed 20 groups of 18 (360) from 432, leaving 72. Then I removed 4 more groups of 18 (72), leaving 0. The partial quotients are 20 and 4, so 432 ÷ 18 = 24 with no remainder.
2) Why might a Grade 5 student prefer partial quotients over the standard algorithm for 728 ÷ 14?
Partial quotients let me use friendly numbers like 50 (50 × 14 = 700), then just 2 more groups of 14, instead of guessing one digit at a time. I get 52 with less risk of place-value mistakes.
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9 Questions
15-20 minutes
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