Free Printable WorksheetMathGrade 5Math Curriculum5.NBT.B.6

5.34 Use Partial Quotients and Area Models for Multi Digit Division Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 5 Math worksheet provides structured practice on 5.34 Use Partial Quotients and Area Models for Multi Digit Division. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Skill description: Select the correct partial-quotients steps or area/array model for a multi-digit division problem. Choose the statement that best justifies the answer using place-value language and an estimation check. Corresponding standards: CCSS 5.NBT.B.6.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Grade 5

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related 5.34 Use Partial Quotients and Area Models for Multi Digit Division skill assessments:

Problem 1Difficulty: Mastery
A student begins 9,403 divided by 84 by subtracting 84 × 100 = 8,400, leaving 1,003. Which next partial-quotients step keeps the work correct?
ASubtract 84 × 20 = 1,680; this is a good next step even if it is more than the amount left.
BSubtract 84 × 10 = 840; then 163 remains.
CSubtract 84 × 1 = 84; the digit 1 has the same value as 10.
DSubtract 10; the partial quotient itself is the amount that should come off the dividend.
Solution & Explanation:A partial quotient tells how many groups of the divisor to remove, so the subtraction amount is divisor times partial quotient. Here 84 × 10 = 840, leaving 163.
Problem 2Difficulty: Mastery
Which set of partial quotients can be added to solve 9,473 divided by 81?
AUse partial quotients 100, 10, and 7; the products total 9,477, so the quotient is 117.
BUse partial quotients 100, 10, and 6; 81 × 100 = 8,100; 81 × 10 = 810; and 81 × 6 = 486, the products total 9,396, leaving a remainder of 77, so the quotient is 116 R 77.
CUse partial quotients 1, 1, and 6; this treats place-value digits as single groups and gives quotient 8.
DUse only partial quotient 120; because 81 × 120 = 9,720 is close to 9,473, stop with quotient 120.
Solution & Explanation:Partial quotients are added to make the quotient. 81 × 100 = 8,100; 81 × 10 = 810; and 81 × 6 = 486; those products total 9,396. The leftover 77 is less than 81, so the answer is 116 R 77.
Problem 3Difficulty: Mastery
A quotient check gives 78 × 119 = 9,282 for 9,357 divided by 78. What should happen to the extra 75?
AWrite 120; any leftover means the quotient rounds up for an exact division answer.
BWrite 119 R 75; the leftover 75 is a remainder because it is less than the divisor 78.
CWrite 119 R 78; the divisor replaces the leftover as the remainder.
DSubtract one more group of 78; 75 is enough to make another full group.
Solution & Explanation:The products account for 9,282. The leftover is 9,357 − 9,282 = 75, and 75 < 78, so the answer is 119 R 75.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 5 Math students. It aligns with educational standard 5.NBT.B.6 (Primary standard selected for prompt fields in this prompt cell: CCSS 5.NBT.B.6. Skill statement in this prompt cell: Select the correct partial-quotients steps or area/array model for a multi-digit division problem. Choose the statement that best justifies the answer using place-value language and an estimation check. Associated standards listed with this skill in this prompt cell: CCSS 5.NBT.B.6. Use this prompt-provided wording as the supporting standard description for this workflow.).

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