Solved Exercises on Multiplication and Division Problems with Answers in Grade 4

Master multiplication and division problems with complete answers: multi-step problems, real-world applications, and detailed solutions through these 5 exercises.

Multiplication and Division Problems: Complete Guide with Answers
Core Concepts & Definitions

Multiplication Problems: Mathematical challenges requiring finding totals of equal groups, repeated addition, or scaling up.

Division Problems: Mathematical challenges involving sharing equally, finding group size, or splitting into equal parts.

Problem with Answers: Mathematical problems presented with complete solutions and explanations.

Multi-Step Problems: Problems requiring more than one operation to reach the solution.

📖
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
Answer Key Principles
  • Every answer should be verified using the inverse operation
  • Answers should include appropriate units
  • All steps should be clearly explained
  • Final answers should address the original question
  • Alternative methods should be shown when applicable
Problems with Answers: 1 to 3
1 Multi-step multiplication problem with complete answer
Problem 1
A school has 5 classrooms. Each classroom has 8 rows of desks with 4 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: (8 × 4) × 5
  4. Include the appropriate units in your answer
Problem
5 classrooms × (8 rows × 4 desks)
Solution
160 desks
Step 1: Find desks in one classroom

8 rows × 4 desks per row = 32 desks per classroom

Step 2: Find total desks in all classrooms

5 classrooms × 32 desks per classroom = 160 desks

Step 3: Alternative approach

5 × 8 × 4 = 40 × 4 = 160

Step 4: Check the answer

Estimate: 5 × 30 = 150, so 160 is reasonable

5 × (8 × 4) = 160
Final answer:

There are 160 desks in total.

Applied rules:

• Associative property: Order of multiplication doesn't matter

• Multi-step problem: Requires multiple operations

• Verification: 160 ÷ 5 = 32, 32 ÷ 8 = 4 ✓

🏫
Classrooms
5
➡️
Multiply by
→
🪑
Desks per Room
32
🟰
Total Desks
160
2 Division word problem with complete answer
Problem 2
A restaurant has 180 chairs to arrange equally in 9 sections. Then, each section is divided into 5 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
180 ÷ 9 ÷ 5
Solution
4 chairs/table
Step 1: Find chairs per section

180 chairs ÷ 9 sections = 20 chairs per section

Step 2: Find chairs per table

20 chairs per section ÷ 5 tables per section = 4 chairs per table

Step 3: Alternative approach

180 ÷ (9 × 5) = 180 ÷ 45 = 4

Step 4: Check the answer

4 × 5 × 9 = 180 ✓

180 ÷ 9 ÷ 5 = 4
Final answer:

There are 4 chairs at each table.

Applied rules:

• Sequential division: Divide in steps

• Multi-step problem: Requires multiple operations

• Verification: 4 × 45 = 180 ✓

🪑
Total Chairs
180
➡️
Divide by Sections
→ 9
➡️
Divide by Tables
→ 5
🟰
Chairs per Table
4
3 Multi-step multiplication and division problem with complete answer
Problem 3
A store sells notebooks in packages of 8. If they sold 35 packages and want to redistribute them into packages of 4, how many new packages can they make?
Definition:

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

Problem
(35 × 8) ÷ 4
Solution
70 packages
Step 1: Find total notebooks

35 packages × 8 notebooks per package = 280 notebooks

Step 2: Find new packages

280 notebooks ÷ 4 notebooks per new package = 70 packages

Step 3: Alternative approach

(35 × 8) ÷ 4 = 280 ÷ 4 = 70

Step 4: Check the answer

70 × 4 = 280, and 280 ÷ 8 = 35 ✓

(35 × 8) ÷ 4 = 70
Final answer:

They can make 70 new packages.

Applied rules:

• Combination of operations: Both multiplication and division needed

• Multi-step problem: Requires multiple calculations

• Verification: 70 × 4 = 280, 280 ÷ 8 = 35 ✓

📝
Original Packages
35
➡️
× 8
→ 280
➡️
÷ 4
→ 70
🟰
New Packages
70
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?
  7. Answer: Include units and complete sentence
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
Problems with Answers: 4 to 5
4 Real-world rate problem with complete answer
Problem 4
A delivery truck can carry 30 packages per trip and makes 6 trips per day. If it operates for 4 days, how many packages does it deliver in total?
Definition:

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

Problem
30 × 6 × 4
Solution
720 packages
Step 1: Find packages per day

30 packages per trip × 6 trips per day = 180 packages per day

Step 2: Find total packages over 4 days

180 packages per day × 4 days = 720 packages

Step 3: Alternative approach

30 × 6 × 4 = 30 × 24 = 720

Step 4: Check the answer

720 ÷ 4 = 180, and 180 ÷ 6 = 30 ✓

30 × 6 × 4 = 720
Final answer:

The truck delivers 720 packages in total.

Applied rules:

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

• Multi-step multiplication: Three numbers multiplied

• Verification: 720 ÷ (30 × 6) = 4 ✓

📦
Per Trip
30
➡️
× Trips/Day
× 6
➡️
× Days
× 4
🟰
Total
720
5 Multi-step sharing problem with complete answer
Problem 5
Lucas bought 6 boxes of markers. Each box contains 28 markers. He wants to share them equally among his 8 friends. How many markers does each friend get?
Definition:

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

Problem
(6 × 28) ÷ 8
Solution
21 markers each
Step 1: Find total markers

6 boxes × 28 markers per box = 168 markers

Step 2: Share equally among friends

168 markers ÷ 8 friends = 21 markers per friend

Step 3: Alternative approach

(6 × 28) ÷ 8 = 168 ÷ 8 = 21

Step 4: Check the answer

21 × 8 = 168, and 168 ÷ 28 = 6 ✓

(6 × 28) ÷ 8 = 21
Final answer:

Each friend gets 21 markers.

Applied rules:

• Combination of operations: Both multiplication and division needed

• Equal sharing: Total divided by number of recipients

• Verification: 21 × 8 = 168, 168 ÷ 6 = 28 ✓

🎨
Boxes
6
➡️
× Per Box
× 28
➡️
÷ Friends
÷ 8
🟰
Per Friend
21

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!