Solved Exercises on Multiplication and Division Word Problems in Grade 4

Master multiplication and division word problems: multi-digit calculations, problem-solving strategies, and mathematical reasoning through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Multi-digit multiplication
Exercise 1
Sarah has 24 boxes of crayons. Each box contains 15 crayons. How many crayons does Sarah have in total?
Definition:

Multiplication word problems: Problems that require finding the total when you have equal groups of items.

Problem-solving method:
  1. Identify what you're looking for (total number of crayons)
  2. Find the number of groups (24 boxes)
  3. Find how many in each group (15 crayons per box)
  4. Multiply: groups × items per group = total items
Problem
24 boxes × 15 crayons per box
Calculation
24 × 15
Result
360
Step 1: Set up the multiplication

24 × 15

Step 2: Break down using distributive property

24 × 15 = 24 × (10 + 5) = (24 × 10) + (24 × 5)

Step 3: Calculate partial products

24 × 10 = 240 and 24 × 5 = 120

Step 4: Add partial products

240 + 120 = 360

24 × 15 = 360
Final answer:

Sarah has 360 crayons in total.

Applied rules:

• Multiplication: Finding total when you have equal groups

• Distributive property: Breaking down multi-digit multiplication

• Place value: Understanding tens and ones in multiplication

2 Multi-digit division
Exercise 2
A school has 288 students going on a field trip. They need to divide the students equally among 8 buses. How many students will be on each bus?
Definition:

Division word problems: Problems that require sharing a total amount equally among groups.

Problem
288 ÷ 8
Division
36
Step 1: Identify the division problem

Total students ÷ Number of buses = Students per bus

288 ÷ 8 = ?

Step 2: Use long division method

8 goes into 28 three times (8 × 3 = 24), remainder 4

Bring down 8 to make 48

8 goes into 48 six times (8 × 6 = 48), remainder 0

Step 3: Verify the answer

36 × 8 = 288 ✓

288 ÷ 8 = 36
Final answer:

Each bus will have 36 students.

Applied rules:

• Division: Sharing equally among groups

• Long division: Systematic method for multi-digit division

• Verification: Check by multiplying quotient × divisor

3 Mixed operations
Exercise 3
Emma bought 12 packs of stickers. Each pack costs $4. She paid with a $50 bill. How much change did she receive?
Definition:

Mixed operation problems: Problems requiring multiple steps with different operations.

Cost calculation
12 × $4
Change
$50 - $48
Result
$2
Step 1: Calculate total cost

Number of packs × Cost per pack = Total cost

12 × $4 = $48

Step 2: Calculate change

Amount paid - Total cost = Change

$50 - $48 = $2

Step 3: Verify the calculation

Cost + Change = Amount paid: $48 + $2 = $50 ✓

Emma received $2 in change.
Final answer:

Emma received $2 in change.

Applied rules:

• Order of operations: Solve multiplication first, then subtraction

• Problem breakdown: Identify separate operations needed

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

Rules and methods, laws,...
\(a \times b = \text{total when you have } a \text{ groups of } b\)
Multiplication in Word Problems
Multiplication Keywords
each, per, every, times, product, total
Look for these words to identify multiplication
Division Keywords
shared equally, divided among, per, each, split, quotient
Look for these words to identify division
Mixed Operations
multiple steps, more than one operation
Solve step by step in order
Key definitions:

Multiplication: Repeated addition of equal groups

Division: Sharing equally or finding how many groups

Word problems: Real-life situations requiring mathematical operations

Complete methodology:
  1. Read carefully: Understand what the problem is asking
  2. Identify key information: Numbers and relationships
  3. Find keywords: Determine which operation to use
  4. Set up equation: Write the mathematical expression
  5. Solve: Calculate the answer
  6. Check: Make sure the answer makes sense
Tip 1: Draw pictures or make tables to visualize the problem.
Tip 2: Always check if your answer is reasonable in the context of the problem.
Tip 3: For division, multiply your answer by the divisor to check.
Common errors: Misreading keywords, forgetting to carry over in multiplication, incorrect subtraction in long division.
Success strategies: Circle important numbers, underline the question, check your work step by step.
Formulas to know by heart:

• Multiplication: Total = Groups × Items per group

• Division: Items per group = Total ÷ Number of groups

• Verification: Quotient × Divisor = Dividend

Solution: Exercises 4 to 5
4 Multi-step problem
Exercise 4
A farmer has 15 fields. Each field has 24 apple trees. If each tree produces 18 apples, how many apples does the farmer harvest in total?
Definition:

Multi-step problems: Problems requiring more than one operation to solve.

Step 1
Fields × Trees per field
Step 2
Total trees × Apples per tree
Result
6,480
Step 1: Calculate total number of trees

Number of fields × Trees per field = Total trees

15 × 24 = 360 trees

Step 2: Calculate total number of apples

Total trees × Apples per tree = Total apples

360 × 18 = 6,480 apples

Step 3: Alternative method (multiply all together)

15 × 24 × 18 = 6,480 apples

15 × 24 × 18 = 6,480
Final answer:

The farmer harvests 6,480 apples in total.

Applied rules:

• Associative property: (a × b) × c = a × (b × c)

• Multi-step problem solving: Break complex problems into smaller steps

• Verification: Check calculations at each step

5 Division with remainder
Exercise 5
A teacher has 137 pencils to distribute equally among 6 students. How many pencils does each student get? How many pencils are left over?
Definition:

Division with remainder: When a number doesn't divide evenly, the leftover amount is called the remainder.

Division
137 ÷ 6
Quotient
22
Remainder
5
Step 1: Set up the division problem

137 ÷ 6 = ? R ?

Step 2: Use long division

6 goes into 13 twice (6 × 2 = 12), remainder 1

Bring down 7 to make 17

6 goes into 17 twice (6 × 2 = 12), remainder 5

Step 3: Interpret the result

Quotient = 22 (pencils per student)

Remainder = 5 (pencils left over)

Step 4: Verify the answer

(22 × 6) + 5 = 132 + 5 = 137 ✓

137 ÷ 6 = 22 R 5
Final answer:

Each student gets 22 pencils, and 5 pencils are left over.

Applied rules:

• Division algorithm: Dividend = (Divisor × Quotient) + Remainder

• Remainder interpretation: Leftover items that can't be distributed equally

• Verification: Always check with the division algorithm

Key Concepts and Strategies for Word Problems
\(\text{Total} = \text{Groups} \times \text{Items per group}\)
Multiplication Relationship
Key definitions:

Multiplication: Finding totals when you have equal groups

Division: Sharing equally or finding how many groups

Remainder: The amount left over when division isn't exact

Word problem: A real-world situation requiring mathematical solution

Complete methodology:
  1. Read the problem completely: Don't rush to calculate
  2. Identify what you need to find: Circle or underline the question
  3. Find the given information: List numbers and their meanings
  4. Look for clue words: Identify operation needed
  5. Draw a picture or model: Visualize the problem
  6. Write the equation: Set up the mathematical expression
  7. Solve step by step: Show all work
  8. Check your answer: Does it make sense in context?
Tip 1: Clue words for multiplication: each, per, every, times, product, total, area, rows of, columns of.
Tip 2: Clue words for division: shared equally, divided among, per, each, split, separated into, quotient.
Tip 3: For multi-step problems, solve one step at a time and write down each answer.
Tip 4: Always include units in your final answer (apples, dollars, students, etc.).
Common errors: Misreading numbers, using wrong operation, forgetting to carry in multiplication, incorrect subtraction in division.
Success strategies: Read twice, circle important numbers, draw models, check work systematically.
Formulas to know by heart:

• Multiplication: Total = Groups × Items per group

• Division: Items per group = Total ÷ Number of groups

• Division algorithm: Dividend = (Divisor × Quotient) + Remainder

• Verification: Quotient × Divisor + Remainder = Dividend

Visualization: Problem-Solving Patterns
Understanding Multiplication vs Division
Compare these scenarios:
• Multiplication: Equal groups → Total
• Division: Total → Equal groups
• Mixed: Multiple operations needed

Analysis: The chart shows the relationship between known and unknown quantities in different problem types.

  • Multiplication: Known: Groups and items per group → Find: Total
  • Division: Known: Total and number of groups → Find: Items per group
  • Mixed: Multiple steps combining operations

Questions & Answers

Question: I sometimes get confused between multiplication and division in word problems. How can I tell which one to use?

Answer: Great question! Here are the key differences:

  • Multiplication: You know the number of groups AND how many in each group → You find the TOTAL
  • Division: You know the TOTAL AND the number of groups → You find how many in each group

Think of it this way:

  • Multiplication: "I have 5 bags with 8 apples each. How many apples altogether?" (5 groups of 8 = 40 total)
  • Division: "I have 40 apples to share equally among 5 friends. How many does each friend get?" (40 total shared among 5 = 8 each)

Also look for clue words: "each," "per," "every" often indicate multiplication, while "shared equally," "divided among," "split" suggest division.

Question: When I divide and get a remainder, how do I know what the remainder means in the word problem?

Answer: The remainder represents what's left over that can't be distributed equally. Here's how to interpret it:

  • If the question asks about equal sharing: The remainder is the extra amount that can't be shared equally
  • If the question asks how many full groups: The quotient is the number of full groups, remainder is what's left over
  • If the question asks if everything fits: A remainder means something won't fit or won't be distributed

Example: If you have 17 cookies to share among 4 children (17 ÷ 4 = 4 R 1), each child gets 4 cookies and 1 cookie remains that can't be shared equally.

Always connect the remainder back to the story in the problem!

Question: How can I check if my answer to a word problem makes sense?

Answer: Here are several ways to verify your answer:

  1. Estimation: Round numbers and do mental math to see if your answer is close
  2. Reverse operation: For multiplication, divide your answer to check. For division, multiply.
  3. Context check: Does the answer make sense in the real-world situation?
  4. Unit check: Are your units correct? (apples, dollars, students, etc.)

For example, if you calculated that 100 students need 5 buses, each bus should hold about 20 students, which seems reasonable. If you got 500 buses, that wouldn't make sense!

Always take a moment to ask yourself: "Does this answer make sense in the story?"