Complete Exercises with Answers for Multiplication and Division Word Problems in Grade 4

Complete exercises with answers for multiplication and division word problems: comprehensive solved examples, problem-solving strategies, and mathematical reasoning for 4th grade students.

Complete Solutions: Exercises 1 to 3
1 Basic Multiplication Problem
Exercise 1
📚 Sarah has 5 boxes of books. Each box contains 8 books. How many books does Sarah have in total?
Definition:

Multiplication Word Problem: A mathematical problem that uses real-world situations to practice multiplication skills. It involves combining equal groups to find a total amount.

Problem-Solving Method:
  1. 📚 Read the problem completely to understand the situation
  2. 📚 Identify what you're looking for (total number of books)
  3. 📚 Find the number of groups (5 boxes)
  4. 📚 Find how many in each group (8 books per box)
  5. 📚 Multiply: groups × items per group = total items
Groups
5 boxes
Each group
8 books
Total
40 books
Step 1: Identify the groups

Sarah has 5 boxes

Step 2: Identify items per group

Each box contains 8 books

Step 3: Set up the multiplication

5 groups × 8 items per group = 40 total items

Step 4: Calculate and verify

5 × 8 = 40 ✓

5 × 8 = 40
Final answer:

Sarah has 40 books in total.

Rule:

📚 Multiplication: Groups × Items per group = Total items

2 Basic Division Problem
Exercise 2
🍪 Tom has 24 cookies. He wants to share them equally among 6 friends. How many cookies will each friend get?
Definition:

Division Word Problem: A mathematical problem that uses real-world situations to practice division skills. It involves sharing a total amount equally among groups or finding how many groups can be formed.

Total
24 cookies
Groups
6 friends
Each group
4 cookies
Step 1: Identify the total amount

Tom has 24 cookies in total

Step 2: Identify the number of groups

He wants to share among 6 friends

Step 3: Set up the division

Total ÷ Groups = Items per group

24 ÷ 6 = 4

Step 4: Calculate and verify

24 ÷ 6 = 4, and 4 × 6 = 24 ✓

24 ÷ 6 = 4
Final answer:

Each friend will get 4 cookies.

Rule:

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

3 Mixed Operations Problem
Exercise 3
💰 Lisa buys 3 packs of markers. Each pack costs $4. If she pays with a $20 bill, how much change will she get?
Definition:

Mixed Operations Word Problem: A mathematical problem that requires multiple operations (addition, subtraction, multiplication, division) to solve. These problems often involve real-life scenarios with multiple steps.

Step 1
3 × $4 = $12
Step 2
$20 - $12 = $8
Step 1: Calculate the total cost

Number of packs × Cost per pack = Total cost

3 × $4 = $12

Step 2: Calculate the change

Money given - Total cost = Change

$20 - $12 = $8

Step 3: Verify your answer

Total cost + Change = Money given: $12 + $8 = $20 ✓

Total cost: $12, Change: $8
Final answer:

Lisa will get $8 in change.

Rules:

📚 Multi-step problems: Solve one operation at a time in the correct order

📚 Verification: Always check if your answer makes sense in the context

Answer Concepts & Key Ideas
\(a \times b = \text{total when you have } a \text{ groups of } b\)
Multiplication Formula
📚 Multiplication
Groups × Items per group = Total
Example: 5 × 8 = 40
📚 Division
Total ÷ Groups = Items per group
Example: 24 ÷ 6 = 4
📚 Key Words
Multiplication: each, per, times, total
Division: share, divide, equally, among
Answer Definitions:

📚 Multiplication: A mathematical operation that combines equal groups to find a total amount. It's repeated addition of the same number.

📚 Division: A mathematical operation that splits a total amount into equal groups or finds how many groups can be formed.

📚 Word Problems: Mathematical problems presented in real-world contexts that require translation into mathematical operations.

📚 Remainder: The amount left over when a division doesn't result in a whole number.

Answer Verification Method:
  1. 📚 Understand: Read the problem carefully and identify what is being asked
  2. 📚 Plan: Determine what information is given and what operation(s) to use
  3. 📚 Solve: Carry out the mathematical operations
  4. 📚 Check: Verify that your answer makes sense in the context of the problem
💡 Tip 1: Draw pictures or make tables to visualize the problem.
💡 Tip 2: Always check if your answer is reasonable in the context.
💡 Tip 3: Look for clue words that indicate which operation to use.
📚 Common Mistakes: Misreading numbers, using wrong operation, forgetting to carry in multiplication.
📚 Success Strategy: Circle important numbers, underline the question, check your work systematically.
Essential Answer Rules:

📚 Multiplication: Total = Groups × Items per group

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

📚 Verification: Quotient × Divisor = Dividend

Advanced Solutions: Exercises 4 to 5
4 Two-Step Problem
Exercise 4
🍎 A farmer has 6 baskets. Each basket has 9 apples. If he sells 25 apples at the market, how many apples does he have left?
Definition:

Multi-Step Word Problem: A problem that requires more than one mathematical operation to solve. These problems often involve real-life scenarios with multiple phases.

Step 1
6 × 9 = 54
Step 2
54 - 25 = 29
Step 1: Find the total number of apples

Number of baskets × Apples per basket = Total apples

6 × 9 = 54 apples

Step 2: Subtract the apples sold

Total apples - Sold apples = Apples left

54 - 25 = 29 apples

Step 3: Verify your answer

Apples left + Sold = Total: 29 + 25 = 54 ✓

First: 6 × 9 = 54, Then: 54 - 25 = 29
Final answer:

The farmer has 29 apples left.

Multi-Step Rule:

📚 First: Complete the multiplication to find the total

📚 Then: Complete the subtraction to find what remains

5 Division with Remainder
Exercise 5
🍕 There are 31 pizza slices to share equally among 5 children. How many slices does each child get? Are there any slices left over?
Definition:

Division with Remainder: When a division doesn't result in equal groups, the leftover amount is called the remainder. Understanding remainders is crucial for real-world applications.

Division
31 ÷ 5
Quotient
6
Remainder
1
Step 1: Set up the division

31 ÷ 5 = ?

Step 2: Find how many times 5 goes into 31

5 × 6 = 30, which is less than 31

5 × 7 = 35, which is more than 31

So 5 goes into 31 six times

Step 3: Find the remainder

31 - 30 = 1 slice left over

Step 4: Verify your answer

(5 × 6) + 1 = 30 + 1 = 31 ✓

31 ÷ 5 = 6 R 1
Final answer:

Each child gets 6 slices, and 1 slice is left over.

Remainder Rule:

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

📚 Remainder interpretation: The amount left over that cannot be distributed equally

Complete Answer Summary: Key Concepts and Strategies
\(\text{Total} = \text{Groups} \times \text{Items per group}\)
Multiplication Formula
Comprehensive Answer Definitions:

📚 Multiplication: Combining equal groups to find a total amount. Example: 6 groups of 9 = 6 × 9 = 54.

📚 Division: Sharing a total equally among groups or finding how many groups. Example: 54 shared among 6 = 54 ÷ 6 = 9.

📚 Word Problems: Real-world situations that require mathematical operations to solve. They help connect math to everyday life.

📚 Remainder: The amount left over when division doesn't result in equal groups. Example: 31 ÷ 5 = 6 R 1.

Complete Problem-Solving Process:
  1. 📚 Read carefully: Understand the full context of the problem
  2. 📚 Identify the question: What are you trying to find?
  3. 📚 Find key information: Identify numbers and their relationships
  4. 📚 Look for clue words: Help determine which operation to use
  5. 📚 Plan your solution: Decide on the sequence of operations
  6. 📚 Solve step by step: Show all work clearly
  7. 📚 Check your answer: Does it make sense in the context?
💡 Tip 1: Clue words for multiplication: each, per, every, times, product, total, altogether.
💡 Tip 2: Clue words for division: share, divide, equally, per, each, among, distributed.
💡 Tip 3: Always check your division by multiplying: Quotient × Divisor = Dividend.
💡 Tip 4: For multi-step problems, solve one step at a time and write down each answer.
📚 Common Patterns: Most problems follow the format: Groups × Items per group = Total OR Total ÷ Groups = Items per group.
📚 Building Blocks: Master these fundamental concepts before advancing to more complex problems.
Essential Answer Formulas:

📚 Multiplication: Total = Groups × Items per group

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

📚 Remainder check: Dividend = (Divisor × Quotient) + Remainder

📚 Verification: Always check your work by reversing the operation

Answer Verification Visualization
Understanding Problem Types
Compare these problem categories:
• Multiplication: Groups → Total
• Division: Total → Groups
• Mixed: Multiple steps 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

Answer Questions & Solutions

❓ Question: How do I know when to use multiplication or division in word problems?

📚 Answer: Here's how to distinguish between them:

  • 📚 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

Look for these clue words:

  • 📚 Multiplication: "each," "per," "times," "product," "total," "groups of"
  • 📚 Division: "share," "divide," "equally," "per," "split," "among"

For example:

  • "5 boxes with 8 items each" → 5 × 8 = 40 (multiplication)
  • "40 items shared among 5 groups" → 40 ÷ 5 = 8 (division)

❓ Question: What does "remainder" mean in division problems?

📚 Answer: A remainder is what's left over when numbers don't divide evenly:

  • When you divide 31 by 5, you get 6 with a remainder of 1
  • This means 5 goes into 31 six times (5 × 6 = 30) with 1 left over
  • You write it as: 31 ÷ 5 = 6 R 1

In real life, remainders mean there are some items left over that can't be shared equally. For example, if you have 31 pizza slices to share among 5 children, each gets 6 slices and 1 slice remains.

Always check: (Divisor × Quotient) + Remainder = Dividend

Check: (5 × 6) + 1 = 30 + 1 = 31 ✓

❓ Question: How can I check if my answer to a word problem is correct?

📚 Answer: Here are several ways to verify your answers:

  1. 📚 Estimate: Round numbers and do quick 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. 📚 Add up parts: In mixed problems, make sure all parts add up correctly

Examples:

  • Multiplication check: If 5 × 8 = 40, then 40 ÷ 8 = 5 ✓
  • Division check: If 24 ÷ 6 = 4, then 4 × 6 = 24 ✓
  • Mixed problem check: Cost + Change = Money given

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