4th Grade Dividing with Remainders Lesson: Notes and Examples (Free PDF)

4th grade long division lesson – Maths PDF

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This 4th grade long division lesson covers dividing with remainders (Common Core 4.NBT.B.6), with a free PDF to print.

Key takeaway: This lesson helps fourth grade students divide numbers with up to four digits by a one digit divisor, with and without a remainder.

Topic: Dividing with Remainders (4th grade)
Content: One-page lesson with a definition, a worked example and key facts
Standards: 4.NBT.B.6
Answers: Explanations included
Format: Free printable PDF, US Letter, black and white

To divide by a 1-digit number, break the dividend into easy parts, find partial quotients, and add them. Anything left that is smaller than the divisor is the remainder. Check by multiplying the quotient by the divisor and adding the remainder. For example, 47 ÷ 5 = 9 R 2 because 9 × 5 + 2 = 47.

This lesson helps fourth grade students divide numbers with up to four digits by a one digit divisor, with and without a remainder. Also, it builds the idea in steps, using place value, partial quotients, and area models before the quotient is written in a final form.

Students learn to break a dividend into easy parts, such as 156 into 120 and 36, and to divide each part. The lesson also explains how to read the remainder and how to check by multiplying. Then, plan about 25 minutes. Also, work each example on paper beside the lesson, and say aloud which part of the dividend you are dividing at each step.

Grade 4 · Common Core State Standards: 4.NBT.B.6

Key facts in this 4th grade long division lesson

Key facts

Dividend ÷ divisor = quotient with a remainder; the remainder is less than the divisor.
Partial quotients: divide easy parts of the dividend and add the results.
An area model for division starts with the area (dividend) and one side (divisor).
Then, check: quotient × divisor + remainder = dividend.
Think about the story to decide what to do with a remainder.

What does it mean to divide with a remainder?

Division shares a number into equal groups. Sometimes the groups come out even. Sometimes a few are left over. The leftover amount is the remainder.

Division vocabulary

In \(47 \div 5 = 9 \text{ R } 2\): 47 is the dividend, 5 is the divisor, 9 is the quotient, and 2 is the remainder. The remainder is always less than the divisor.

47 dots in groups of 5 make 9 full groups with 2 left over: 47 ÷ 5 = 9 R 2.

How do partial quotients work?

Break the dividend into parts that are easy to divide by the divisor. Divide each part, then add the partial quotients.

156 ÷ 4: the areas 120 and 36 give the partial quotients 30 and 9. So 156 ÷ 4 = 39.

\(156 = 120 + 36\). Since \(120 \div 4 = 30\) and \(36 \div 4 = 9\), the quotient is \(30 + 9 = 39\).

How do you divide a 4-digit number by a 1-digit number?

Use place value. Think of \(2,736\) as 2,400 + 336, and break 336 into 320 + 16.

2,736 ÷ 4 = 600 + 80 + 4 = 684.

Find the largest multiple of the divisor you can take from the dividend, using hundreds, tens, or ones.
Subtract it and write the partial quotient.
Repeat with what is left until it is less than the divisor.
Add the partial quotients. Any amount left is the remainder.

How do you check a division answer?

Multiplication undoes division. Multiply the quotient by the divisor, then add the remainder. The result must equal the dividend.

Check a quotient with remainder: quotient × divisor + remainder.

Example: \(817 \div 4\). Take \(4 \times 200 = 800\). Left: 17. Take \(4 \times 4 = 16\). Left: 1. The quotient is \(200 + 4 = 204\) with remainder 1. Check: \(204 \times 4 + 1 = 817\).

4th grade long division lesson: questions and answers

What is a remainder?

A remainder is the amount left over after you make as many equal groups as possible. In 47 ÷ 5 = 9 R 2, nine groups of 5 use 45, and 2 are left.

Why must the remainder be smaller than the divisor?

If the remainder were as big as the divisor, you could make one more group. Dividing 47 by 5 cannot leave 5 or more, because 5 more would make another group of 5.

What are partial quotients?

Partial quotients are the answers to easier divisions that add up to the full quotient. For 156 ÷ 4, the partial quotients are 30 and 9, so the quotient is 39.

How do I check a division with a remainder?

Multiply the quotient by the divisor and add the remainder. For 817 ÷ 4 = 204 R 1, check 204 × 4 + 1 = 816 + 1 = 817.

What do I do with a remainder in a word problem?

Read the story. Sometimes you ignore the remainder, like full teams. Also, Sometimes you round up, like vans needed for 94 people with 7 seats each. Sometimes you share the leftover, like cutting it into parts.

Common mistakes with this 4th grade long division lesson

Students forget a zero in the quotient. When 817 is divided by 4, the tens place gives zero full groups after regrouping, so the quotient is 204, not 24.
Students leave a remainder that is as large as the divisor. If the leftover is 6 when dividing by 6, one more group fits, so keep dividing.
Students subtract incorrectly in the middle of long division. Write each multiplication and subtraction on its own line so no digits are skipped.

How to study this chapter

Use multiples of the divisor as a helper list. Writing 4, 8, 12, 16, and so on beside a problem makes each partial quotient quick to find.
Estimate before dividing. For 438 divided by 6, think that 6 times 70 is 420, so the answer should be a little more than 70.
Parents can use coins or small objects at home. Also, sharing 47 beans among 5 cups shows the quotient and the remainder in a hands on way.

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