Long division (with remainder)

Before handing out the worksheet, briefly introduce the concept with a short oral warm-up or a visual model on the board. Encourage students to talk through their thinking as they work: "What strategy are you using? How do you know that is right?" After completing the worksheet, review any missed problems together and discuss the reasoning rather than just the answer. For extra support, let students use manipulatives or draw pictures alongside the written problems. These long division (with remainder) worksheets work well as daily practice, homework, or a focused review activity.

These long division (with remainder) worksheets for 5th grade give students the structured, hands-on practice they need to build confidence and fluency. Students work through a range of problem formats, from visual models and diagrams to written equations and word problems, so they encounter long division (with remainder) from every angle. Each worksheet is designed to build on prior knowledge while introducing the level of challenge appropriate for 5th grade. Practicing long division (with remainder) at this stage strengthens the mathematical foundations that support more advanced concepts in later grades.

This worksheet is designed for 5th Grade students (Ages 10-11), aligned to Common Core standard 5.NBT.B.6. It can also be used as review for early students at the next grade level or as an introduction for advanced students.

Yes. This worksheet works for homeschool, classroom, and tutoring settings. Print individual pages for targeted practice, or print the full set as a packet. Works great as a morning warm-up, independent center activity, or fast-finisher task.

Fifth graders are expected to fluently multiply multi-digit whole numbers using the standard algorithm (CCSS 5.NBT.B.5) and to find whole-number quotients and remainders with dividends up to four digits and divisors up to two digits (5.NBT.B.6). Multiplication extends to 3-digit by 3-digit and 4-digit by 2-digit numbers, and division includes the standard long-division algorithm with 2-digit divisors. Students also explore properties of multiplication (distributive, associative, commutative) as tools for mental math and as the conceptual foundation for multiplication of fractions and decimals later in the year. Division with remainders is interpreted in context: sometimes the remainder is dropped, sometimes it is rounded up, and sometimes it becomes a fraction. Worksheets covering missing-factor problems (box times 4 equals 368) bridge multiplication and algebraic thinking. Fluency with these operations is a prerequisite for all of the more advanced fifth-grade topics.

Long division with 2-digit divisors is one of the most procedurally demanding skills in elementary school. The standard approach is the Divide-Multiply-Subtract-Bring-Down cycle, but the critical added challenge is estimating how many times a 2-digit divisor goes into the partial dividend. Teach students to round the divisor to its leading digit and estimate: how many times does 30 go into 247? About 8 times. Try 8, multiply, and adjust if the product exceeds the dividend or the remainder equals or exceeds the divisor. The adjustment step (trying 7 or 9 if 8 doesn't work) is where most errors occur. Worksheets should provide space for showing each step (trial quotient, product, subtraction, remainder). A common scaffold is writing the first 10 multiples of the divisor at the top of the work area before starting, so students can look up products instead of computing them mid-problem. Once students are comfortable with no-remainder problems, introduce remainders and practice interpreting them in word problem contexts.

The most frequent errors in multi-digit multiplication are place value errors during partial products (forgetting to add a zero for each shifted row in the standard algorithm), carrying errors (adding the carried digit before multiplying the next column instead of after), and regrouping errors in the final addition of partial products. For the standard algorithm, students who write partial products without proper indentation almost always produce wrong answers. Worksheets with grid paper that enforce correct alignment of each row prevent this. A second common error is multiplying each digit of the top number by each digit of the bottom number without considering place value: in 34 times 56, multiplying 30 times 50 is not the same as 3 times 5. Area model practice, where students explicitly partition each factor and compute four separate products, builds the place-value understanding the standard algorithm requires. Estimation is the most efficient self-check: in 47 times 83, the answer should be close to 50 times 80 equals 4,000, so an answer of 390 immediately signals an error.