Division with Remainders Worksheet

Lesson Overview

About this worksheet

Division with remainders is the bridge between exact division facts and real-world dividing where the divisor doesn’t fit evenly. Students learn to write each answer in the form ‘quotient R remainder,’ to keep the remainder always less than the divisor (the rule that catches the most early mistakes), and – in word problems – to decide what the remainder MEANS in context. This worksheet isolates the remainder skill so students can practice the divmod move on increasingly larger dividends before tackling long division proper.

The reference box at the top of page 1 explains the remainder format using a generic worked example: 67 divided by 5 has the divisor fitting 13 times (13 x 5 = 65) with 2 left over, so the answer is written 13 R 2. The example deliberately uses an operand pair (67, 5) that does not appear in any of the 18 Section A and B problems or any Section C word problem, so students see the rule on independent numbers before applying it.

Section A on page 1 gives students 12 two-digit-dividend divisions in a 4-column grid, ALL with remainders. The dividends range from 23 to 75 and divisors range from 3 to 9, so students get practice with every small-divisor family. Section B on page 2 raises the dividend size to three digits (125 to 502) on a 3-column grid of 6 items, still all with remainders. The three-digit step is where students start to need long-division thinking even if they are using mental partial quotients.

Section C on page 2 has 3 word problems with work boxes. Each problem tests a DIFFERENT remainder interpretation. The bus problem (124 students with 28-student buses) requires rounding UP – 4 R 12 means 5 buses are needed so every student has a seat. The cookie problem (85 cookies in bags of 6) requires dropping the remainder and reporting the 1 leftover cookie. The library problem (73 books across 8 shelves) reports the remainder as ‘left over.’ Page 3 is a complete answer key.

How to Use This Lesson

Read the reference box aloud and walk students through the 67 ÷ 5 = 13 R 2 example, emphasizing the rule that the remainder is always less than the divisor.

Work Section A item 1 (23 ÷ 4) together; ask ‘How many 4s fit in 23?’ (5, because 5 x 4 = 20) and ‘What is left over?’ (3, so the answer is 5 R 3).

Assign the rest of Section A independently or with a partner; remind students to check that EVERY remainder is less than the divisor.

Turn to page 2 and walk through Section B item 13 (125 ÷ 4) as a partial-quotient warmup before students try the rest.

Use Section C item 19 (the bus problem) for a structured discussion: write 124 ÷ 28 = 4 R 12 first, then ask ‘If we only get 4 buses, where do the 12 leftover students sit?’ to motivate rounding up.

Use the answer key on page 3 for self-check or aide spot-check.

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