Math Core

In a word problem, "7 R 3" is never the whole answer. Nobody rents "7 R 3" vans. You have to decide what the remainder means in the story, and that changes what you write down.

Three things a remainder can mean

Each of these problems uses $27 \div 6 = 4 \text{ R } 3$ , but each answer is different.

Question	What the remainder does	Answer
27 students ride in vans that hold 6. How many vans are needed?	The 3 extra students still need a ride, so add one more van.	5 vans
You have 27 inches of ribbon. Each bow uses 6 inches. How many bows can you make?	3 inches is not enough for a bow, so drop it.	4 bows
27 cards are dealt equally to 6 players. How many cards are left over?	The question asks for the leftovers.	3 cards

Read the question again

After you divide, ask: What does the question want?

Round up when everything must fit or everyone must be included: vans, boxes, tables, days to finish.
Drop the remainder when only complete groups count: full bags, finished bows, whole teams.
Use the remainder when the question asks what is left over.

Worked examples

Worked example: Rounding up

A class of 58 people is going to a party. Each table seats 8. How many tables are needed so everyone has a seat?

$58 \div 8$ : $8 \times 7 = 56$ , and $58 - 56 = 2$ . So $58 \div 8 = 7 \text{ R } 2$ .

Seven tables seat 56 people, but 2 people still need seats. They need one more table.

8 tables are needed.

Worked example: Dropping the remainder

Leo has 50 inches of string. He cuts pieces that are 8 inches long for a craft. How many 8-inch pieces can he cut?

$50 \div 8$ : $8 \times 6 = 48$ , and $50 - 48 = 2$ . So $50 \div 8 = 6 \text{ R } 2$ .

The last 2 inches are too short to make another piece.

Leo can cut 6 pieces.

Worked example: The remainder is the answer

Grandma bakes 45 cookies. She gives the same number to each of her 4 grandchildren, as many as she can. How many cookies does she have left for herself?

$45 \div 4$ : $4 \times 11 = 44$ , and $45 - 44 = 1$ . So $45 \div 4 = 11 \text{ R } 1$ .

Each grandchild gets 11 cookies. The question asks what is left.

Grandma keeps 1 cookie.

Common mistake

Don't round up just because there is a remainder, and don't always throw it away. The same division, $58 \div 8 = 7 \text{ R } 2$ , gives 8 tables for seating 58 people, but only 7 full tables of 8. Let the question decide.

Tip

Check that your answer makes sense in the story. If you answered "7 tables" for 58 people, ask: where do the last 2 people sit?

Practice

Practice 1

Jada collected 34 eggs. A carton holds 12 eggs. How many cartons can she fill completely?

Type a number.

Practice 2

A club has 46 members going on a boat trip. Each boat holds 6 people. How many boats does the club need?

Type a number.

Practice 3

Sam puts 75 marbles into bags of 9. He fills as many bags as he can. How many marbles are left over?

Type a number.

Practice 4

A bakery has 100 cupcakes. Each box holds 6 cupcakes. How many boxes are needed to pack all the cupcakes?

Type a number.

Practice 5

Jen has 38 students in gym class. She wants to make teams of exactly 5 players. She finds $38 \div 5 = 7 \text{ R } 3$ . How many full teams can she make?

Practice 6

A book has 200 pages. Ravi reads 9 pages every day. How many days will it take him to finish the book?

Type a number.

Practice 7

A school has 1,000 stickers. It shares them equally among 7 classes, giving each class as many as possible. How many stickers are left over?

Type a number.