Solved Exercises on Multiplication and Division Problem Solving in Grade 4

Master multiplication and division problem solving: multi-step problems, real-world applications, and strategic approaches through these 5 detailed exercises.

Problem Solving Strategies: Complete Guide
Core Concepts & Definitions

Problem Solving: The process of finding solutions to mathematical challenges using logical thinking and appropriate strategies.

Multiplication Problems: Problems that require finding totals of equal groups, repeated addition, or scaling up.

Division Problems: Problems that involve sharing equally, finding group size, or splitting into equal parts.

Multi-Step Problems: Problems that require more than one operation to solve.

📖
Read
🤔
Plan
⚙️
Solve
✅
Check
Multiplication Keywords

• Total

• Times

• Product

• Each

• Per

• Groups of

Division Keywords

• Share

• Split

• Each

• Equal groups

• Per

• Distributed

Problem Types

• Equal groups

• Area problems

• Rate problems

• Sharing problems

• Comparison problems

Draw a Picture
Visualize the problem by creating diagrams or models to understand the situation.
Make a Table
Organize information in a table to identify patterns or relationships.
Work Backwards
Start with the end result and work backwards to find the solution.
Guess and Check
Make an educated guess and verify if it solves the problem.
Step-by-Step Problem Solving Process
  1. Read and Understand: Carefully read the problem and identify what is being asked
  2. Identify Information: Circle or highlight important numbers and key words
  3. Choose Strategy: Decide which problem-solving strategy to use
  4. Set Up Equation: Write the mathematical expression or plan the steps
  5. Solve: Perform calculations carefully
  6. Check: Verify your answer makes sense in the context
  7. Answer: Write a complete sentence with the answer
Multiplication Patterns

• Finding totals

• Area of rectangles

• Comparing quantities

• Scaling up

Division Patterns

• Sharing equally

• Finding group size

• Finding number of groups

• Scaling down

Tips for Problem Solving Success
  • Read the problem multiple times before starting
  • Identify what the question is asking for
  • Look for key words that indicate operations
  • Draw pictures or diagrams to visualize
  • Estimate your answer first
  • Check if your answer makes sense
  • Always include units in your answer
  • Try different strategies if one doesn't work
Problem Solving Exercises: 1 to 3
1 Multi-step multiplication problem
Exercise 1
A school has 4 classrooms. Each classroom has 6 rows of desks with 5 desks in each row. How many desks are there in total?
Definition:

Multi-step multiplication problem: A problem requiring multiple multiplication operations to find the total

Solution method:
  1. First, find how many desks are in one classroom (rows × desks per row)
  2. Then, multiply by the number of classrooms
  3. Calculate: (6 × 5) × 4
  4. Include the appropriate units in your answer
Problem
4 classrooms × (6 rows × 5 desks)
Solution
120 desks
Step 1: Find desks in one classroom

6 rows × 5 desks per row = 30 desks per classroom

Step 2: Find total desks in all classrooms

4 classrooms × 30 desks per classroom = 120 desks

Step 3: Alternative approach

4 × 6 × 5 = 24 × 5 = 120

Step 4: Check the answer

Estimate: 4 × 30 = 120, so answer is reasonable

4 × (6 × 5) = 120
Final answer:

There are 120 desks in total.

Applied rules:

• Associative property: Order of multiplication doesn't matter

• Multi-step problem: Requires multiple operations

• Verification: 120 ÷ 4 = 30, 30 ÷ 6 = 5 ✓

🏫
Classrooms
4
➡️
Multiply by
→
🪑
Desks per Room
30
🟰
Total Desks
120
2 Division word problem
Exercise 2
A restaurant has 144 chairs to arrange equally in 8 sections. Then, each section is divided into 4 tables. How many chairs are at each table?
Definition:

Multi-step division problem: A problem requiring multiple division operations to find the final answer

Problem
144 ÷ 8 ÷ 4
Solution
4.5 chairs/table
Step 1: Find chairs per section

144 chairs ÷ 8 sections = 18 chairs per section

Step 2: Find chairs per table

18 chairs per section ÷ 4 tables per section = 4.5 chairs per table

Step 3: Alternative approach

144 ÷ (8 × 4) = 144 ÷ 32 = 4.5

Step 4: Check the answer

4.5 × 4 × 8 = 144 ✓

144 ÷ 8 ÷ 4 = 4.5
Final answer:

There are 4.5 chairs at each table.

Applied rules:

• Sequential division: Divide in steps

• Multi-step problem: Requires multiple operations

• Verification: 4.5 × 32 = 144 ✓

🪑
Total Chairs
144
➡️
Divide by Sections
→ 8
➡️
Divide by Tables
→ 4
🟰
Chairs per Table
4.5
3 Multi-step multiplication and division problem
Exercise 3
A store sells notebooks in packages of 6. If they sold 42 packages and want to redistribute them into packages of 3, how many new packages can they make?
Definition:

Multi-step multiplication and division problem: A problem requiring both operations to solve

Problem
(42 × 6) ÷ 3
Solution
84 packages
Step 1: Find total notebooks

42 packages × 6 notebooks per package = 252 notebooks

Step 2: Find new packages

252 notebooks ÷ 3 notebooks per new package = 84 packages

Step 3: Alternative approach

(42 × 6) ÷ 3 = 252 ÷ 3 = 84

Step 4: Check the answer

84 × 3 = 252, and 252 ÷ 6 = 42 ✓

(42 × 6) ÷ 3 = 84
Final answer:

They can make 84 new packages.

Applied rules:

• Combination of operations: Both multiplication and division needed

• Multi-step problem: Requires multiple calculations

• Verification: 84 × 3 = 252, 252 ÷ 6 = 42 ✓

📝
Original Packages
42
➡️
× 6
→ 252
➡️
÷ 3
→ 84
🟰
New Packages
84
Problem Solving Strategies & Methods
Total = Rate × Time
Rate Problems
Multiplication
Total = Rate × Quantity
Equal groups
Division
Rate = Total ÷ Quantity
Equal sharing
Multi-Step
Multiple Operations
Complex problems
Key definitions:

Multiplication: Repeated addition of equal groups

Division: Sharing equally or finding group size

Rate: Amount per unit (per hour, per day, per item)

Unit: The measurement used (dollars, hours, items)

Complete methodology:
  1. Read and understand: What is being asked?
  2. Identify key information: Circle numbers and important words
  3. Choose strategy: Which approach works best?
  4. Plan the solution: What operations are needed?
  5. Solve: Perform calculations carefully
  6. Check: Does the answer make sense?
Tip 1: Draw a picture to visualize the problem.
Tip 2: Make a table to organize information.
Tip 3: Estimate your answer first to check reasonableness.
Tip 4: Always include units in your final answer.
Common errors: Misreading the question, choosing wrong operations, forgetting units.
Key notes: Multi-step problems require careful planning and organization.
Important rules to remember:

• Multiplication: Use when finding totals of equal groups

• Division: Use when sharing equally or finding group size

• Keywords: Look for "each," "total," "share," "split"

• Units: Always include appropriate units in your answer

🔍
Read
Understand the problem
⚙️
Plan
Choose operations
✅
Check
Verify solution
Problem Solving Exercises: 4 to 5
4 Real-world rate problem
Exercise 4
A delivery truck can carry 24 packages per trip and makes 7 trips per day. If it operates for 5 days, how many packages does it deliver in total?
Definition:

Rate problem: A problem involving rates of production, delivery, or consumption over time

Problem
24 × 7 × 5
Solution
840 packages
Step 1: Find packages per day

24 packages per trip × 7 trips per day = 168 packages per day

Step 2: Find total packages over 5 days

168 packages per day × 5 days = 840 packages

Step 3: Alternative approach

24 × 7 × 5 = 24 × 35 = 840

Step 4: Check the answer

840 ÷ 5 = 168, and 168 ÷ 7 = 24 ✓

24 × 7 × 5 = 840
Final answer:

The truck delivers 840 packages in total.

Applied rules:

• Rate calculation: Packages per trip × trips per day × days

• Multi-step multiplication: Three numbers multiplied

• Verification: 840 ÷ (24 × 7) = 5 ✓

📦
Per Trip
24
➡️
× Trips/Day
× 7
➡️
× Days
× 5
🟰
Total
840
5 Multi-step sharing problem
Exercise 5
Emma bought 8 boxes of crayons. Each box contains 24 crayons. She wants to share them equally among her 6 friends. How many crayons does each friend get?
Definition:

Multi-step sharing problem: A problem requiring multiplication to find total, then division to share equally

Problem
(8 × 24) ÷ 6
Solution
32 crayons each
Step 1: Find total crayons

8 boxes × 24 crayons per box = 192 crayons

Step 2: Share equally among friends

192 crayons ÷ 6 friends = 32 crayons per friend

Step 3: Alternative approach

(8 × 24) ÷ 6 = 192 ÷ 6 = 32

Step 4: Check the answer

32 × 6 = 192, and 192 ÷ 24 = 8 ✓

(8 × 24) ÷ 6 = 32
Final answer:

Each friend gets 32 crayons.

Applied rules:

• Combination of operations: Both multiplication and division needed

• Equal sharing: Total divided by number of recipients

• Verification: 32 × 6 = 192, 192 ÷ 8 = 24 ✓

🎨
Boxes
8
➡️
× Per Box
× 24
➡️
÷ Friends
÷ 6
🟰
Per Friend
32

Questions & Answers

Question: How do I know if I need to multiply or divide in a word problem?

Answer: Look for key words and think about what the problem is asking:

  • Multiply when: You need to find a total of equal groups ("each," "times," "product," "area")
  • Divide when: You need to share equally or find how many groups ("share," "split," "each," "per," "distribute")

For example: "There are 4 apples in each basket and 5 baskets" → Multiply (4 × 5)

"Share 20 apples equally among 4 children" → Divide (20 ÷ 4)

Question: My child has trouble with multi-step problems. How can I help them break them down?

Answer: Here are strategies to help with multi-step problems:

  • Have your child read the problem multiple times
  • Circle or highlight important numbers and words
  • Break the problem into smaller parts
  • Ask: "What do I know?" and "What do I need to find?"
  • Look for key operation words (multiply/divide words)
  • Draw a simple picture or diagram for each step

Encourage them to solve one step at a time!

Question: How do I check if my answer makes sense?

Answer: Here are several ways to check your answer:

  • Estimate first - does your exact answer match your estimate?
  • Use the opposite operation (multiply to check division, divide to check multiplication)
  • Plug your answer back into the original problem
  • Ask yourself: "Does this make sense in the real world?"
  • Check that your units are correct

For example, if you found 500 apples in a problem about 5 kids sharing 20 apples, you know something went wrong!