Math Core

Not every division comes out even. If 5 friends share 17 cookies, each friend gets 3, and 2 cookies are left over. Those extra cookies have a name: the remainder. In this lesson you'll learn to find it and write it.

The parts of a division

Every division has names for its numbers. In $17 \div 5$ :

Word	Meaning	In $17 \div 5$
Dividend	the number being divided	17
Divisor	the number you divide by	5
Quotient	how many in each group (or how many groups)	3
Remainder	what is left over	2

We write the answer as $17 \div 5 = 3 \text{ R } 2$ . Read it as "3 remainder 2."

Finding the remainder

Make as many equal groups of 5 as you can. You can make 3 groups, which uses $3 \times 5 = 15$ cookies. That leaves $17 - 15 = 2$ cookies. Two cookies are not enough for another group of 5, so you stop.

You can see this on a number line. Jump forward by 5s from 0 without passing 17:

Three jumps of 5 reach 15. From 15 to 17 is a gap of 2, and that gap is the remainder.

Three full jumps fit. The gap from 15 up to 17 is 2, not enough for another jump.

Definition

Remainder

The remainder is the amount left over after you make as many equal groups as you can. The remainder is always less than the divisor.

Using multiplication facts

You don't have to draw every group. Use a multiplication fact instead:

Find the biggest multiple of the divisor that is not more than the dividend.
The number you multiplied by is the quotient.
Subtract to find the remainder.

Checking a division with a remainder

\text{quotient} \times \text{divisor} + \text{remainder} = \text{dividend}

For $17 \div 5 = 3 \text{ R } 2$ : $3 \times 5 + 2 = 15 + 2 = 17$ . ✓

Worked example: Dividing by 4

Find $23 \div 4$ .

Count by 4s: 4, 8, 12, 16, 20, 24. The number 24 is too big, so stop at 20.

$4 \times 5 = 20$ , so the quotient is 5. Then $23 - 20 = 3$ is left over.

$23 \div 4 = 5 \text{ R } 3$ . Check: $5 \times 4 + 3 = 23$ . ✓

Worked example: Packing crayons

Ms. Diaz has 38 crayons. She puts 6 crayons in each cup. How many cups can she fill, and how many crayons are left?

Find $38 \div 6$ . The multiples of 6 are 6, 12, 18, 24, 30, 36, 42. The number 42 is too big, so use $6 \times 6 = 36$ .

$38 - 36 = 2$ . So $38 \div 6 = 6 \text{ R } 2$ .

She fills 6 cups, with 2 crayons left over.

Worked example: A bigger dividend

Find $50 \div 7$ .

Think: which multiple of 7 is closest to 50 without going over? $7 \times 7 = 49$ , and $7 \times 8 = 56$ is too big.

$50 - 49 = 1$ . So $50 \div 7 = 7 \text{ R } 1$ .

Check: $7 \times 7 + 1 = 50$ . ✓

Common mistake

If your remainder is as big as the divisor (or bigger), you stopped too soon. For $26 \div 4$ , the answer is not 5 R 6. The 6 leftovers hold another group of 4, so the answer is $6 \text{ R } 2$ .

Tip

Type answers with remainders like 7 R 2.

Practice

Practice 1

Owen puts 14 stickers into groups of 4. The number line shows his groups.

Jumps of 4 toward 14.

How many stickers are left over?

Type a number.

Practice 2

Find $29 \div 3$ . Write your answer like 5 R 1.

Type your answer

Practice 3

You divide a number by 5. Which of these can not be the remainder?

Practice 4

Find $61 \div 8$ . Write your answer like 5 R 1.

Type your answer

Practice 5

Mia says $40 \div 6 = 5 \text{ R } 10$ . What is the correct answer?

Practice 6

A number is divided by 7. The quotient is 8 and the remainder is 3. What is the number?

Type a number.

Practice 7

Find $70 \div 9$ . Write your answer like 5 R 1.

Type your answer