Solved Exercises on Division Word Problems in Grade 3

Master division word problems: sharing equally, grouping, and multi-step problems with visual representations through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Sharing Equally
Exercise 1
Maria has 20 candies. She wants to share them equally among her 4 friends. How many candies will each friend get?
Definition:

Sharing equally: Distributing a total amount into equal groups. This is the most common type of division word problem.

Problem-solving method:
  1. Identify the total amount (dividend)
  2. Identify the number of groups (divisor)
  3. Set up the division equation
  4. Solve the division
  5. Check the answer
Total Candies
20
Number of Friends
4
Candies per Friend
?
1
2
3
4
5
6
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16
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20
Step 1: Identify the total amount

Maria has 20 candies (dividend)

Step 2: Identify the number of groups

She wants to share among 4 friends (divisor)

Step 3: Set up the division

20 ÷ 4 = ?

Step 4: Solve the division

20 ÷ 4 = 5

Step 5: Check the answer

5 × 4 = 20 ✓

20 ÷ 4 = 5
Final answer:

Each friend will get 5 candies.

Applied rules:

• Sharing equally: Total amount divided by number of groups

• Division concept: How many items each group gets

• Verification: Multiply quotient by divisor to check

2 Grouping Problem
Exercise 2
There are 24 books on a shelf. The librarian wants to put them in boxes, with 6 books in each box. How many boxes will she need?
Definition:

Grouping problem: Determining how many equal groups can be made from a total amount. The total amount is divided by the size of each group.

Total Books
24
Books per Box
6
Number of Boxes
?
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5
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24
Step 1: Identify the total amount

There are 24 books (dividend)

Step 2: Identify the group size

Each box holds 6 books (divisor)

Step 3: Set up the division

24 ÷ 6 = ?

Step 4: Solve the division

24 ÷ 6 = 4

Step 5: Check the answer

4 × 6 = 24 ✓

24 ÷ 6 = 4
Final answer:

The librarian will need 4 boxes.

Applied rules:

• Grouping: Total amount divided by group size

• Division concept: How many equal groups can be made

• Verification: Multiply quotient by divisor to check

3 Multi-Step Problem
Exercise 3
A teacher has 36 markers. She gives 4 markers to each student. Then she divides the remaining markers equally among 4 classrooms. How many markers does each classroom get?
Definition:

Multi-step problem: A problem that requires multiple operations to solve. First, solve one part, then use that result to solve the next part.

Step 1: Find how many markers are given to students
Step 2: Calculate remaining markers
Step 3: Divide remaining markers among classrooms
Total Markers
36
Markers per Student
4
Classrooms
4
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16
17
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35
36
Step 1: Find how many markers are given to students

Assuming she gives markers to 4 students: 4 × 4 = 16 markers given

Step 2: Calculate remaining markers

36 - 16 = 20 markers remaining

Step 3: Divide remaining markers among classrooms

20 ÷ 4 = 5 markers per classroom

Step 4: Check the answer

Students get 16, classrooms get 20, total = 36 ✓

(36 - 16) ÷ 4 = 5
Final answer:

Each classroom gets 5 markers.

Applied rules:

• Multi-step solving: Break the problem into smaller parts

• Sequential operations: Use results from earlier steps

• Verification: Check that all parts add up correctly

Division Word Problem Types
Total ÷ Groups = Each Group
Sharing
Sharing
20 ÷ 4 = 5
Distribute equally
Grouping
24 ÷ 6 = 4
Form equal groups
Multi-Step
(36-16)÷4=5
Solve in parts
Key Rule: Identify whether you're sharing or grouping to set up the division correctly.
Problem Logic: Division word problems involve splitting a total into equal parts.
Tip 1: Look for keywords like "each," "per," "shared equally," or "divided among."
Tip 2: Draw pictures or use objects to visualize the problem.
Tip 3: Always check your answer by multiplying.
Key Rules to Remember:

• Identify the total: Find the dividend in the problem

• Identify the divisor: Find what you're dividing by (groups or size)

• Set up division: Total ÷ Divisor = Quotient

• Check answer: Multiply quotient by divisor to verify

Dividend ÷ Divisor = Quotient
Division Components
SHARING
20 ÷ 4 = 5
GROUPING
24 ÷ 6 = 4
Additional Practice
4 Mixed Practice
Exercise 4
Solve these division word problems:
a) 35 apples shared among 7 people
b) 48 cookies packed in bags of 8
c) 56 pencils divided equally among 8 students
Definition:

Mixed practice: Combining different types of division word problems to strengthen understanding.

Part a: Sharing problem

35 apples ÷ 7 people = 5 apples per person

Part b: Grouping problem

48 cookies ÷ 8 cookies per bag = 6 bags

Part c: Sharing problem

56 pencils ÷ 8 students = 7 pencils per student

Final answers:

a) Each person gets 5 apples

b) 6 bags are needed

c) Each student gets 7 pencils

Applied rules:

• Consistency: Apply the same method to all problems

• Problem identification: Determine if it's sharing or grouping

• Verification: Check each answer by multiplying

5 Advanced Word Problem
Exercise 5
A bakery made 45 cupcakes. They sold 27 cupcakes in the morning. Then they packed the remaining cupcakes into boxes, with 6 cupcakes in each box. How many boxes did they use?
Definition:

Advanced problem: A multi-step problem requiring both subtraction and division.

Step 1: Find remaining cupcakes
Step 2: Pack remaining cupcakes into boxes
Step 1: Find remaining cupcakes

45 - 27 = 18 cupcakes remaining

Step 2: Pack remaining cupcakes into boxes

18 ÷ 6 = 3 boxes needed

Step 3: Check the answer

27 sold + (3 boxes × 6 cupcakes) = 27 + 18 = 45 total ✓

(45 - 27) ÷ 6 = 3
Final answer:

They used 3 boxes.

Applied rules:

• Multi-step solving: Break the problem into smaller parts

• Sequential operations: Use results from earlier steps

• Verification: Check that all parts add up correctly

Comprehensive Summary: Division Word Problems
Total ÷ Groups = Each Group or Total ÷ Size = Number of Groups
Division Word Problems
Key Definitions:

Division word problem: A real-life situation that requires division to solve.

Sharing equally: Distributing a total amount into equal groups.

Grouping: Determining how many equal groups can be made.

Multi-step problem: A problem requiring multiple operations to solve.

Keywords: Words that indicate division (each, per, shared, divided, among).

Verification: Checking the answer by multiplying.

Complete Methodology:
  1. Read carefully: Understand what the problem is asking
  2. Identify components: Find the total amount and what to divide by
  3. Determine problem type: Is it sharing or grouping?
  4. Set up division: Write the division equation
  5. Solve: Calculate the answer
  6. Check: Verify by multiplying
Tip 1: Look for keywords like "each," "per," "shared equally," or "divided among."
Tip 2: Draw pictures or use objects to visualize the problem.
Tip 3: Always check your answer by multiplying.
Tip 4: For multi-step problems, solve one part at a time.
Common errors: Misidentifying the dividend/divisor, not reading carefully, forgetting to check.
Key insights: Word problems connect math to real-world situations.
Core Rules and Principles:

• Problem identification: Determine if it's sharing or grouping

• Component recognition: Identify the total amount and divisor

• Equation setup: Write the correct division equation

• Verification: Always check by multiplying quotient by divisor

• Multi-step approach: Solve complex problems one step at a time

Examples: 20÷4=5 (sharing), 24÷6=4 (grouping), (45-27)÷6=3 (multi-step)
Problem Examples
Memory aid: "Total divided by groups gives each group, total divided by size gives number of groups."
Success check: If 20÷4=5, then 5×4 should equal 20. ✓

Questions & Answers

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

Answer: Here's how to tell the difference:

Sharing (equal distribution):

  • Keywords: "shared among," "given to each," "divided equally," "split between"
  • Example: "20 candies shared among 4 friends" → 20 ÷ 4 = 5 each
  • You know the number of groups, find how many in each group

Grouping (making equal groups):

  • Keywords: "groups of," "boxes of," "packs of," "sets of"
  • Example: "24 books in boxes of 6" → 24 ÷ 6 = 4 boxes
  • You know the size of each group, find how many groups

Both use division, but the question being asked is different!

Question: My child is struggling with multi-step word problems. How can I help them break these down?

Answer: Here are effective strategies for multi-step problems:

Step-by-step approach:

  • Read the problem completely first
  • Identify what the question is asking
  • Highlight or underline important information
  • Solve one piece at a time

Visual organization:

  • Create a chart or table for each step
  • Draw diagrams to represent each part
  • Use different colored pencils for each step

Example breakdown:

  • Step 1: What do you need to find first?
  • Step 2: What operation solves that part?
  • Step 3: How does that answer help with the next step?

Practice with simpler multi-step problems first, then gradually increase difficulty.

Question: What if my answer doesn't come out to a whole number? Like if I divide 17 by 5?

Answer: Great question! When division doesn't result in a whole number, you have a remainder:

Example with 17 ÷ 5:

  • 17 ÷ 5 = 3 remainder 2 (written as 3 R2)
  • Each group gets 3, and 2 are left over
  • Check: 3 × 5 + 2 = 15 + 2 = 17 ✓

In word problems:

  • Sometimes you need to interpret the remainder
  • Example: If 17 candies are shared among 5 kids, each gets 3 and 2 candies remain
  • For grouping: You can make 3 complete groups of 5, with 2 left over

Don't worry if the answer isn't a whole number - that's part of real math!