Solved Exercises on Division Word Problems in Grade 4

Master division word problems: equal sharing, grouping, remainders, and multi-step problems through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Equal Sharing Problem
Exercise 1
Maria has 24 apples. She wants to share them equally among her 6 friends. How many apples will each friend get?
Definition:

Equal sharing: A type of division problem where a total amount is distributed equally among a certain number of recipients.

Word Problem Solving Method:
  1. Read carefully: Identify what is being divided and how many groups
  2. Identify key information: Total amount, number of groups, what to find
  3. Set up the division: Total ÷ Number of groups = Amount per group
  4. Solve: Perform the division
  5. Check: Verify the answer makes sense in context
Total Apples
24
Number of Friends
6
Apples per Friend
?
Step 1: Identify the problem type

This is an equal sharing problem: 24 apples shared among 6 friends

Step 2: Set up the division

24 ÷ 6 = ?

Step 3: Solve using known facts

I know that 6 × 4 = 24, so 24 ÷ 6 = 4

Step 4: Verify the answer

Check: 4 × 6 = 24 ✓

Step 5: Answer in context

Each friend will get 4 apples.

24 ÷ 6 = 4
Final answer:

Each friend will get 4 apples.

Applied rules:

• Equal sharing: Total amount ÷ Number of groups = Amount per group

• Keywords: "share equally," "divided among," "each," "per"

• Verification: Always check by multiplying the answer by the number of groups

2 Grouping Problem
Exercise 2
A teacher has 35 markers. She wants to put them in boxes with 5 markers in each box. How many boxes will she need?
Definition:

Grouping: A type of division problem where a total amount is divided into groups of a specific size.

Total Markers
35
Markers per Box
5
Number of Boxes
?
Step 1: Identify the problem type

This is a grouping problem: 35 markers in groups of 5 per box

Step 2: Set up the division

35 ÷ 5 = ?

Step 3: Solve using known facts

I know that 5 × 7 = 35, so 35 ÷ 5 = 7

Step 4: Verify the answer

Check: 7 × 5 = 35 ✓

Step 5: Answer in context

The teacher will need 7 boxes.

35 ÷ 5 = 7
Final answer:

The teacher will need 7 boxes.

Applied rules:

• Grouping: Total amount ÷ Group size = Number of groups

• Keywords: "groups of," "sets of," "boxes with," "in each"

• Verification: Always check by multiplying the answer by the group size

3 Division with Remainder
Exercise 3
A bakery has 47 cupcakes. They want to pack them in boxes that hold 6 cupcakes each. How many full boxes can they fill, and how many cupcakes will be left over?
Definition:

Division with remainder: When the total amount cannot be divided evenly into groups of the specified size, there will be some left over.

Total Cupcakes
47
Cupcakes per Box
6
Full Boxes & Remainder
?
Step 1: Identify the problem type

This is a grouping problem with remainder: 47 cupcakes in groups of 6 per box

Step 2: Set up the division

47 ÷ 6 = ?

Step 3: Find how many times 6 goes into 47

6 × 7 = 42 (less than 47)
6 × 8 = 48 (more than 47)
So 6 goes into 47 seven times.

Step 4: Calculate the remainder

47 - (6 × 7) = 47 - 42 = 5

Step 5: Express the answer

47 ÷ 6 = 7 R5 (read as "7 remainder 5")

Step 6: Verify the answer

Check: (6 × 7) + 5 = 42 + 5 = 47 ✓

Step 7: Answer in context

They can fill 7 full boxes and will have 5 cupcakes left over.

47 ÷ 6 = 7 R5
Final answer:

They can fill 7 full boxes and will have 5 cupcakes left over.

Applied rules:

• Remainder rule: The remainder is always less than the divisor

• Verification: Dividend = (Divisor × Quotient) + Remainder

• Contextual answer: Include both the quotient and remainder in the answer

Division Word Problems: Keywords, Types, and Strategies
Total ÷ Number of Groups = Amount per Group
Equal Sharing Formula
Equal Sharing
24 ÷ 6 = 4
24 apples shared among 6 friends = 4 each
Grouping
35 ÷ 5 = 7
35 markers in groups of 5 = 7 groups
With Remainder
47 ÷ 6 = 7 R5
47 cupcakes in boxes of 6 = 7 boxes + 5 left
Key definitions:

Division word problems: Real-world scenarios that require division to solve.

Equal sharing: Distributing a total amount equally among recipients.

Grouping: Organizing a total amount into groups of a specific size.

Remainder: The amount left over when division is not exact.

Word problem solving methods:
  1. Read carefully: Understand what the problem is asking
  2. Identify key information: What numbers are involved and what operation is needed
  3. Look for keywords: Words that indicate division is needed
  4. Set up the problem: Write the division equation
  5. Solve: Perform the division calculation
  6. Check: Verify the answer makes sense in the context
Tip 1: Look for keywords like "each," "per," "shared among," "divided equally," "groups of."
Tip 2: Always check that your answer makes sense in the problem context.
Tip 3: When there's a remainder, make sure to address what it means in the context of the problem.
Tip 4: Draw a picture or use objects to help visualize the problem if needed.
Word problem types: Equal sharing (dividing total among groups) and grouping (making groups of specific size).
Remainder interpretation: Sometimes remainders represent "left over" items, other times they mean you need one more group.
Important division word problem rules:

• Keywords for equal sharing: "each," "per," "shared among," "divided equally"

• Keywords for grouping: "groups of," "sets of," "packs of," "in each"

• Always verify your answer by multiplying and adding remainder if needed

• Remainder must always be less than the divisor

• Answer should address the specific question asked in the problem

Word Problem Keywords and Strategies
Keyword Recognition
Visualizing the frequency and importance of keywords in division word problems.

Analysis: The chart shows how keywords help identify division word problems.

  • "Each" and "per" strongly indicate equal sharing
    • "Groups of" suggests grouping problems
  • Keywords help determine the operation needed
Solution: Exercises 4 to 5
4 Multi-Step Problem
Exercise 4
A school has 120 students going on a field trip. The school has 4 buses. If the students are distributed equally among the buses, how many students will be on each bus? If each bus can hold 35 students, how many extra seats are there in total?
Definition:

Multi-step word problems: Problems that require multiple operations to solve, often involving division followed by addition, subtraction, or multiplication.

Total Students
120
Number of Buses
4
Students per Bus
?
Step 1: Identify the first question

How many students will be on each bus? This is equal sharing: 120 ÷ 4

Step 2: Solve the first part

120 ÷ 4 = 30 students per bus

Step 3: Identify the second question

How many extra seats are there in total?

Step 4: Calculate capacity vs. actual

Each bus holds 35 students, but only 30 are on each bus
Extra seats per bus = 35 - 30 = 5

Step 5: Calculate total extra seats

Extra seats per bus × Number of buses = 5 × 4 = 20

Step 6: Verify the answer

Check: 30 students × 4 buses = 120 students ✓
Total capacity = 35 × 4 = 140
140 - 120 = 20 extra seats ✓

120 ÷ 4 = 30, (35-30) × 4 = 20
Final answer:

There will be 30 students on each bus, and there will be 20 extra seats in total.

Applied rules:

• Multi-step problems: Solve one part at a time in logical order

• Equal sharing: Total ÷ Number of groups = Amount per group

• Verification: Check that all parts of the problem are addressed

5 Division with Remainder - Contextual Problem
Exercise 5
A party planner has 58 balloons to arrange in bunches of 7. How many complete bunches can be made? If each bunch is tied with a ribbon, how many ribbons are needed? How many balloons will be left over?
Definition:

Contextual remainders: Problems where the remainder has practical significance in the real-world situation.

Total Balloons
58
Balloons per Bunch
7
Complete Bunches
?
Step 1: Identify the problem type

This is a grouping problem: 58 balloons in groups of 7 per bunch

Step 2: Set up the division

58 ÷ 7 = ?

Step 3: Find how many times 7 goes into 58

7 × 8 = 56 (less than 58)
7 × 9 = 63 (more than 58)
So 7 goes into 58 eight times.

Step 4: Calculate the remainder

58 - (7 × 8) = 58 - 56 = 2

Step 5: Answer the first question

8 complete bunches can be made.

Step 6: Answer the second question

One ribbon is needed for each complete bunch, so 8 ribbons are needed.

Step 7: Answer the third question

There will be 2 balloons left over.

Step 8: Verify the answer

Check: (7 × 8) + 2 = 56 + 2 = 58 ✓

58 ÷ 7 = 8 R2
Final answer:

8 complete bunches can be made, 8 ribbons are needed, and 2 balloons will be left over.

Applied rules:

• Grouping: Total amount ÷ Group size = Number of groups

• Contextual interpretation: Apply the mathematical result to the real-world scenario

• Multiple questions: Address each question separately using the same division result

Complete Summary: Division Word Problems
Total ÷ Number of Groups = Amount per Group
Equal Sharing Formula
Key definitions:

Division word problems: Real-world scenarios that require division to solve.

Equal sharing: Distributing a total amount equally among recipients.

Grouping: Organizing a total amount into groups of a specific size.

Remainder: The amount left over when division is not exact.

Multi-step problems: Problems requiring multiple operations to solve.

Complete methodology:
  1. Read the problem carefully: Understand what is being asked.
  2. Identify key information: Find the numbers and what they represent.
  3. Look for keywords: Identify words that suggest division is needed.
  4. Determine the problem type: Equal sharing or grouping?
  5. Set up the division: Write the equation based on the problem.
  6. Solve: Perform the division calculation.
  7. Interpret the answer: Make sure it makes sense in context.
  8. Check: Verify your answer using multiplication.
Tip 1: Circle or underline important numbers and keywords in the problem.
Tip 2: Ask yourself: "Am I sharing equally?" or "Am I making groups?"
Tip 3: Always include units in your answer (apples, boxes, students, etc.).
Tip 4: When there's a remainder, think about what it means in the real-world context.
Common errors: Misidentifying the problem type, forgetting to check if answer makes sense, not addressing all parts of multi-step problems.
Key keywords: Equal sharing: "each," "per," "shared among," "divided equally." Grouping: "groups of," "sets of," "in each," "packs of."
Division word problem rules:

• Equal sharing: Total ÷ Number of groups = Amount per group

• Grouping: Total ÷ Group size = Number of groups

• Remainder is always less than the divisor

• Always verify by multiplying: (Divisor × Quotient) + Remainder = Dividend

• Answer should address the specific question asked in the problem

Exercise with Visualization: Problem Type Distribution
Exercise 6: Problem Classification
Distribution of division word problem types in typical grade 4 curriculum:
f₁(x) = Equal sharing problems (percentage)
f₂(x) = Grouping problems (percentage)
f₃(x) = Problems with remainders (percentage)

Analysis: The chart shows the distribution of different types of division word problems.

  • Equal sharing and grouping are the most common types
  • Many problems include remainders
  • Multi-step problems combine different concepts

Questions & Answers

Question: How do I know if a word problem is about equal sharing or grouping?

Answer: Look for these clues:

  • Equal sharing: The total is divided among a number of recipients. Keywords: "shared among," "divided equally," "each," "per," "between."
  • Grouping: You're making groups of a specific size. Keywords: "groups of," "sets of," "packs of," "in each," "bunches of."

Example: "24 apples shared among 6 friends" (equal sharing) vs. "24 apples in bags of 6" (grouping).

Question: What should I do when a word problem has a remainder? Sometimes I don't know what to do with it.

Answer: The remainder's meaning depends on the context:

  • Leftover items: "35 cupcakes in boxes of 6 = 5 full boxes with 5 left over"
  • Rounding up: "If you need to transport 35 people in cars that hold 6 each, you need 6 cars (round up from 5 R5)"
  • Partial group: "You can make 5 complete groups with 5 items remaining"

Always read the problem carefully to see how the remainder relates to the question.

Question: My child has trouble identifying what operation to use in word problems. Any suggestions?

Answer: Teach your child to look for key words and phrases:

  • Division: "each," "per," "shared among," "divided equally," "groups of," "sets of," "in each," "out of"
  • Have them circle or underline important numbers and keywords
  • Ask: "Am I splitting something up?" (division) or "Am I putting things together?" (addition/multiplication)
  • Practice with simple problems first, then gradually increase difficulty

Creating a keyword reference sheet can be very helpful!

Question: Why do I need to check my answer in word problems? Isn't solving it enough?

Answer: Checking your answer is crucial for several reasons:

  • It helps catch calculation errors
  • It ensures your answer makes sense in the problem context
  • It verifies that you performed the correct operation
  • It confirms that you addressed all parts of multi-step problems

For division: multiply your answer by the divisor and add remainder to check!

Question: How do I solve word problems that have multiple questions in them?

Answer: Tackle multi-step problems systematically:

  • Read the entire problem carefully
  • Identify each separate question within the problem
  • Solve one question at a time, using previous answers if needed
  • Keep track of units (apples, students, boxes, etc.)
  • Check that each answer makes sense in context

Sometimes you'll use the same division result to answer different questions!