Solved Exercises on Multiplication and Division in Word Problems in Grade 4

Master multiplication and division in word problems: solving real-world scenarios through these 5 detailed exercises.

Multiplication and Division in Word Problems: Complete Guide
Core Concepts & Definitions

Word Problems: Mathematical problems presented in a real-world context using words instead of just numbers.

Multiplication in Word Problems: Used when finding totals of equal groups, repeated addition, or area.

Division in Word Problems: Used when sharing equally, finding the number of groups, or splitting into equal parts.

Key Words: Words that indicate which operation to use (more, total, times for multiplication; share, split, each for division).

🔍
Read
❓
Question
🔢
Numbers
⚙️
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

• Array problems

Multiplication
Use when you need to find a total of equal groups or repeated addition.
Division
Use when you need to share equally or find how many groups.
Step-by-Step Problem Solving Process
  1. Read the problem carefully: Understand what is being asked
  2. Identify key information: Circle important numbers and words
  3. Determine the operation: Decide if you need multiplication or division
  4. Set up the equation: Write the mathematical expression
  5. Solve the problem: Perform the calculation
  6. Check your answer: Does it make sense in the context?
  7. Write your answer: Include units and answer the question
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 Word Problem Success
  • Read the entire problem before starting
  • Identify what the question is asking for
  • Circle or highlight important numbers
  • Look for key words that indicate the operation
  • Draw pictures or diagrams if it helps
  • Estimate your answer first
  • Check if your answer makes sense
  • Always include units in your answer
Word Problem Exercises: 1 to 3
1 Multiplication word problem
Exercise 1
A bakery makes 24 loaves of bread each day. How many loaves does the bakery make in 15 days?
Definition:

Multiplication word problem: A problem that requires finding the total when there are equal groups or repeated addition

Solution method:
  1. Identify what is being multiplied (loaves per day × number of days)
  2. Set up the multiplication: 24 × 15
  3. Calculate using multi-digit multiplication
  4. Include the appropriate units in your answer
Problem
24 loaves/day × 15 days
Solution
360 loaves
Step 1: Identify the problem

We need to find total loaves made in 15 days

Step 2: Identify the operation

Key words: "each day" and "in 15 days" suggest multiplication

Step 3: Set up the equation

24 loaves per day × 15 days = ? total loaves

Step 4: Calculate 24 × 15

24 × 15 = (20 × 15) + (4 × 15) = 300 + 60 = 360

Step 5: Check the answer

Estimate: 25 × 15 = 375, so 360 is reasonable

24 × 15 = 360
Final answer:

The bakery makes 360 loaves in 15 days.

Applied rules:

• Repeated addition: 24 loaves added 15 times

• Unit conversion: Days cancel out, leaving loaves

• Verification: 360 ÷ 15 = 24 ✓

🍞
Per Day
24
📅
Days
15
🟰
Total
360
2 Division word problem
Exercise 2
A school has 324 students who need to be divided equally into 6 classrooms. How many students will be in each classroom?
Definition:

Division word problem: A problem that requires sharing a total amount equally among groups

Problem
324 students ÷ 6 classrooms
Solution
54 students/classroom
Step 1: Identify the problem

We need to find how many students per classroom

Step 2: Identify the operation

Key words: "divided equally" suggests division

Step 3: Set up the equation

324 students ÷ 6 classrooms = ? students per classroom

Step 4: Calculate 324 ÷ 6

324 ÷ 6 = 54

Step 5: Check the answer

54 × 6 = 324 ✓

324 ÷ 6 = 54
Final answer:

There will be 54 students in each classroom.

Applied rules:

• Equal sharing: Total divided by number of groups

• Unit conversion: Students divided by classrooms

• Verification: 54 × 6 = 324 ✓

👤
Total Students
324
🏫
Classrooms
6
🟰
Per Classroom
54
3 Multiplication word problem
Exercise 3
A factory packs 18 toys in each box. If they need to pack 45 boxes, how many toys will they need in total?
Definition:

Multiplication word problem: A problem that requires finding the total when there are equal groups

Problem
18 toys/box × 45 boxes
Solution
810 toys
Step 1: Identify the problem

We need to find total toys needed for 45 boxes

Step 2: Identify the operation

Key words: "each box" and "45 boxes" suggest multiplication

Step 3: Set up the equation

18 toys per box × 45 boxes = ? total toys

Step 4: Calculate 18 × 45

18 × 45 = (10 × 45) + (8 × 45) = 450 + 360 = 810

Step 5: Check the answer

Estimate: 20 × 45 = 900, so 810 is reasonable

18 × 45 = 810
Final answer:

The factory will need 810 toys in total.

Applied rules:

• Equal groups: 18 toys in each of 45 boxes

• Unit conversion: Boxes cancel out, leaving toys

• Verification: 810 ÷ 45 = 18 ✓

🧸
Per Box
18
📦
Boxes
45
🟰
Total Toys
810
Word Problem Rules & Methods
Total = Rate × Time
Rate Problems
Multiplication
Total = Rate × Quantity
Equal groups
Division
Rate = Total ÷ Quantity
Equal sharing
Area
Area = Length × Width
Rectangular arrays
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 the problem: Understand what is being asked
  2. Identify key information: Circle numbers and important words
  3. Determine operation: Look for multiplication or division keywords
  4. Set up equation: Write the mathematical expression
  5. Solve: Perform the calculation
  6. Check: Verify the answer makes sense
Tip 1: Look for key words that indicate multiplication or division.
Tip 2: Draw a picture or diagram to visualize the problem.
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 operation, forgetting units.
Key notes: Multiplication makes numbers bigger, division makes them smaller.
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

✖️
Multiplication
Finding totals, rates, area
➗
Division
Sharing, grouping, rates
❓
Keywords
Each, total, share, split
Word Problem Exercises: 4 to 5
4 Division word problem
Exercise 4
A bus company has 528 passengers to transport and each bus can hold 44 passengers. How many buses are needed?
Definition:

Division word problem: A problem that requires finding how many groups are needed to accommodate everyone

Problem
528 passengers ÷ 44 passengers/bus
Solution
12 buses
Step 1: Identify the problem

We need to find how many buses are required

Step 2: Identify the operation

Key words: "each bus can hold" suggests division

Step 3: Set up the equation

528 passengers ÷ 44 passengers per bus = ? buses

Step 4: Calculate 528 ÷ 44

528 ÷ 44 = 12

Step 5: Check the answer

12 × 44 = 528 ✓

528 ÷ 44 = 12
Final answer:

The bus company needs 12 buses.

Applied rules:

• Grouping: Total divided by capacity per group

• Unit conversion: Passengers divided by passengers per bus

• Verification: 12 × 44 = 528 ✓

👤
Total Passengers
528
🚌
Capacity
44
🟰
Buses Needed
12
5 Multiplication word problem
Exercise 5
A library receives 35 new books each month. How many books will they receive in 8 months?
Definition:

Multiplication word problem: A problem that requires finding the total when there are equal amounts over time

Problem
35 books/month × 8 months
Solution
280 books
Step 1: Identify the problem

We need to find total books received in 8 months

Step 2: Identify the operation

Key words: "each month" and "in 8 months" suggest multiplication

Step 3: Set up the equation

35 books per month × 8 months = ? total books

Step 4: Calculate 35 × 8

35 × 8 = 280

Step 5: Check the answer

Estimate: 40 × 8 = 320, so 280 is reasonable

35 × 8 = 280
Final answer:

The library will receive 280 books in 8 months.

Applied rules:

• Rate over time: Books per month × number of months

• Unit conversion: Months cancel out, leaving books

• Verification: 280 ÷ 8 = 35 ✓

📚
Per Month
35
📅
Months
8
🟰
Total Books
280

Questions & Answers

Question: How do I know if I should 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 understanding what the question is asking. How can I help them identify the important information?

Answer: Here are strategies to help identify important information:

  • Have your child read the problem twice before starting
  • Circle or highlight numbers in the problem
  • Underline the question being asked
  • 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

Encourage them to slow down and think before calculating!

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!