Navigating Complex Scenarios: Multi-step Word Problems with Remainders

When these problems involve division, remainders can add an extra layer of complexity. In this guide, we’ll tackle multi-step word problems that result in remainders, offering strategies to interpret and solve them effectively.

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Step-by-step Guide to Solve Multi-step Word Problems with Remainders:

1. Understanding the Problem: 

Begin by reading the problem carefully. Identify the information given and determine what you’re being asked to find.

2. Breaking Down the Steps: 

Determine the sequence of operations required. This might involve addition, subtraction, multiplication, and division.

3. Handling Remainders: 

When you encounter a division step that results in a remainder:

   – Understand its significance in the context of the problem.

   – Decide whether to round up, round down, or use the remainder as is.

4. Solving the Problem: 

Execute the operations in the correct sequence, keeping track of any remainder.

5. Interpreting the Remainder: 

In the context of the problem, decide how to represent the remainder. For instance, if you divide candies among children, the remainder represents the leftover candies.

Example 1: 

Anna has 53 apples. She wants to pack them in bags with 8 apples in each bag. How many full bags will she have, and how many apples will be left over? 

Solution: 

Dividing 53 by 8 gives 6 with a remainder of 5. 

Anna will have 6 full bags, with 5 apples left over.

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Example 2: 

A school is organizing a trip for 89 students. Each bus can carry 30 students. How many buses are needed, and how many seats will be empty on the last bus? 

Solution: 

Dividing 89 by 30 gives 2 with a remainder of 29. 

The school needs 3 buses (2 full buses and 1 more for the remaining 29 students). In the last bus, 1 seat will be empty.

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Practice Questions: 

1. A bakery has 125 muffins and wants to pack them in boxes of 10. How many full boxes will they have, and how many muffins will be left unpacked?

2. There are 74 students in a competition. They are to be grouped into teams of 9. How many teams will there be, and how many students will not be in a team?

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Answers: 

1. 12 full boxes, 5 muffins left unpacked.

2. 8 teams, 2 students will not be in a team.

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Four Ways to Handle a Remainder

The division is the easy part. The real question is what the leftover means in the story.

Two True Multi-Step Examples

Example A: Pencils for classrooms

A school buys 6 boxes of 48 pencils and splits them evenly among 13 classrooms. How many pencils does each class get, and how many are left?

1. Find the total: 6 × 48 = 288 pencils.
2. Divide: 288 ÷ 13 = 22 R2, because 13 × 22 = 286.
3. Each class gets 22 pencils, and 2 are left over.

Example B: Vans for a field trip

Three classes of 26 students and 4 teachers are going on a trip. Each van holds 12 people. How many vans are needed?

1. Find the total: 3 × 26 + 4 = 78 + 4 = 82 people.
2. Divide: 82 ÷ 12 = 6 R10, because 12 × 6 = 72.
3. Ten people would have no seat, so round up: 7 vans.

Frequently Asked Questions

What is a multi-step word problem?

A multi-step word problem needs more than one operation to reach the answer. You might add or multiply to find a total, then divide and decide what the remainder means. For example, if 4 boxes each hold 15 markers and you share them among 7 tables, first find 4 × 15 = 60, then 60 ÷ 7 = 8 R4, so each table gets 8 markers with 4 left over.

How do you solve multi-step word problems involving remainders?

Read the question, list what you know, and do each operation in order on its own line. When you reach the division, stop and ask what the remainder means. Drop it if only full groups count, round up if everyone needs a place, give the remainder itself if the question asks what is left, or write it as a fraction if the leftover can be split.

What is an example of a multi-step division word problem with remainders?

A class of 26 students and 4 teachers is going on a trip, and each van holds 8 people. First add: 26 + 4 = 30 people. Then divide: 30 ÷ 8 = 3 R6. Three vans carry 24 people, but 6 people still need seats, so the class needs 4 vans. Here the remainder tells you to round up.

What are some multi-step word problems with answers?

Try these two. Leo buys 3 packs of 24 stickers and shares them equally among 5 friends. 3 × 24 = 72, and 72 ÷ 5 = 14 R2, so each friend gets 14 stickers and 2 are left. Next, Maya has 2 ribbons that are each 13 meters long and cuts the total into 4 equal pieces. 26 ÷ 4 = 6 R2, so each piece is 6½ meters.