How to Navigating Complex Scenarios: Multi-step Word Problems with Remainders
Word problems often mirror real-life situations, requiring multiple steps to reach a solution.
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.
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.
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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