Solving Word Problems: Multiplication and Division - Practice Exercises

Master multiplication and division word problems: identify operations, set up equations, and find solutions with these 10 detailed exercises.

Exercises 1 to 5
1 Apples in baskets (Multiplication)
Exercise 1
Sarah has 4 baskets. Each basket contains 6 apples. How many apples does Sarah have in total?
Definition:

Multiplication word problem: A math problem presented in a real-world context requiring multiplication to solve.

Problem-solving method:
  1. Read the problem carefully
  2. Identify the number of groups (baskets)
  3. Identify the number in each group (apples per basket)
  4. Multiply the number of groups by the number in each group
Number of groups
4 baskets
Items per group
6 apples
Total
4 × 6
Step 1: Identify what we're looking for

We need to find the total number of apples

Step 2: Identify the number of groups

Sarah has 4 baskets (groups)

Step 3: Identify the number in each group

Each basket has 6 apples

Step 4: Set up the multiplication

Total apples = Number of baskets × Apples per basket

Total apples = 4 × 6

Step 5: Calculate

4 × 6 = 24

Sarah has 24 apples in total.
Final answer:

Sarah has 24 apples in total.

Applied rules:

• Grouping concept: Multiplication represents equal groups

• Problem identification: Look for keywords like "each", "per", "total"

• Equation setup: Groups × Items per group = Total items

2 Students in groups (Division)
Exercise 2
There are 24 students in a class. The teacher wants to divide them into 4 equal groups. How many students will be in each group?
Definition:

Division word problem: A math problem requiring equal sharing or grouping.

Total items
24 students
Number of groups
4 groups
Per group
24 ÷ 4
Step 1: Identify what we're looking for

We need to find how many students in each group

Step 2: Identify the total amount

There are 24 students total

Step 3: Identify the number of groups

We want 4 equal groups

Step 4: Set up the division

Students per group = Total students ÷ Number of groups

Students per group = 24 ÷ 4

Step 5: Calculate

24 ÷ 4 = 6

There will be 6 students in each group.
Final answer:

There will be 6 students in each group.

Applied rules:

• Equal sharing: Total ÷ Number of groups = Amount per group

• Keyword recognition: "Divide", "share equally", "each group" indicate division

• Verification: 6 × 4 = 24 ✓

3 Cars and wheels (Multiplication)
Exercise 3
A car dealership has 7 cars. Each car has 4 wheels. How many wheels are there in total?
Definition:

Unit rate problems: Finding the total when you know the number of units and the quantity per unit.

Number of cars
7 cars
Wheels per car
4 wheels
Total wheels
7 × 4
Step 1: Identify what we're looking for

We need to find the total number of wheels

Step 2: Identify the number of groups

There are 7 cars (groups)

Step 3: Identify the number in each group

Each car has 4 wheels

Step 4: Set up the multiplication

Total wheels = Number of cars × Wheels per car

Total wheels = 7 × 4

Step 5: Calculate

7 × 4 = 28

There are 28 wheels in total.
Final answer:

There are 28 wheels in total.

Applied rules:

• Unit rate: Quantity per unit × Number of units = Total quantity

• Real-world connection: Relate to familiar objects

• Checking reasonableness: 28 wheels for 7 cars makes sense

4 Pizza slices (Division)
Exercise 4
A pizza was cut into 12 slices. If 4 friends share the pizza equally, how many slices will each friend get?
Definition:

Equal sharing: Distributing a total amount equally among a certain number of people or groups.

Total slices
12 slices
Number of friends
4 friends
Slices per friend
12 ÷ 4
Step 1: Identify what we're looking for

We need to find how many slices each friend gets

Step 2: Identify the total amount

There are 12 slices total

Step 3: Identify the number of people

4 friends will share equally

Step 4: Set up the division

Slices per friend = Total slices ÷ Number of friends

Slices per friend = 12 ÷ 4

Step 5: Calculate

12 ÷ 4 = 3

Each friend will get 3 slices.
Final answer:

Each friend will get 3 slices.

Applied rules:

• Equal sharing: Total ÷ Number of people = Amount per person

• Verification: 3 × 4 = 12 ✓

• Real-world context: Sharing food equally

5 Pages in books (Multiplication)
Exercise 5
Tom has 5 books. Each book has 15 pages. How many pages are there in all the books?
Definition:

Repeated addition: Multiplication is a shortcut for adding the same number multiple times.

Number of books
5 books
Pages per book
15 pages
Total pages
5 × 15
Step 1: Identify what we're looking for

We need to find the total number of pages

Step 2: Identify the number of groups

Tom has 5 books (groups)

Step 3: Identify the number in each group

Each book has 15 pages

Step 4: Set up the multiplication

Total pages = Number of books × Pages per book

Total pages = 5 × 15

Step 5: Calculate

5 × 15 = 75

There are 75 pages in all the books.
Final answer:

There are 75 pages in all the books.

Applied rules:

• Repeated addition: 5 × 15 = 15 + 15 + 15 + 15 + 15

• Place value: Break down larger numbers (5 × 10 + 5 × 5)

• Verification: Check that 75 is reasonable for 5 books

Exercises 6 to 10
6 Cookies in bags (Division)
Exercise 6
Maria baked 24 cookies and put them into 6 bags equally. How many cookies are in each bag?
Definition:

Equal distribution: Dividing a total amount into equal parts.

Total cookies
24 cookies
Number of bags
6 bags
Cookies per bag
24 ÷ 6
Step 1: Identify what we're looking for

We need to find how many cookies are in each bag

Step 2: Identify the total amount

Maria baked 24 cookies total

Step 3: Identify the number of containers

She used 6 bags

Step 4: Set up the division

Cookies per bag = Total cookies ÷ Number of bags

Cookies per bag = 24 ÷ 6

Step 5: Calculate

24 ÷ 6 = 4

There are 4 cookies in each bag.
Final answer:

There are 4 cookies in each bag.

Applied rules:

• Equal distribution: Total ÷ Number of containers = Amount per container

• Verification: 4 × 6 = 24 ✓

• Contextual check: 4 cookies per bag is reasonable

7 Fish in tanks (Multiplication)
Exercise 7
The pet store has 8 fish tanks. Each tank has 7 fish. How many fish are there in total?
Definition:

Real-world multiplication: Applying multiplication to everyday situations.

Number of tanks
8 tanks
Fish per tank
7 fish
Total fish
8 × 7
Step 1: Identify what we're looking for

We need to find the total number of fish

Step 2: Identify the number of groups

There are 8 tanks (groups)

Step 3: Identify the number in each group

Each tank has 7 fish

Step 4: Set up the multiplication

Total fish = Number of tanks × Fish per tank

Total fish = 8 × 7

Step 5: Calculate

8 × 7 = 56

There are 56 fish in total.
Final answer:

There are 56 fish in total.

Applied rules:

• Context understanding: Tanks contain equal numbers of fish

• Problem structure: Groups × Items per group = Total

• Reasonableness: 56 fish in 8 tanks is realistic

8 Spoons in sets (Division)
Exercise 8
A restaurant received 36 spoons. They want to put them into sets of 4 spoons each. How many sets can they make?
Definition:

Grouping problems: Determining how many equal groups can be formed from a total amount.

Total spoons
36 spoons
Spoons per set
4 spoons
Number of sets
36 ÷ 4
Step 1: Identify what we're looking for

We need to find how many sets of 4 spoons can be made

Step 2: Identify the total amount

There are 36 spoons total

Step 3: Identify the group size

Each set has 4 spoons

Step 4: Set up the division

Number of sets = Total spoons ÷ Spoons per set

Number of sets = 36 ÷ 4

Step 5: Calculate

36 ÷ 4 = 9

They can make 9 sets of spoons.
Final answer:

They can make 9 sets of spoons.

Applied rules:

• Grouping: Total ÷ Size of each group = Number of groups

• Verification: 9 × 4 = 36 ✓

• Contextual understanding: Sets of 4 spoons for restaurant use

9 Seeds in packets (Multiplication)
Exercise 9
A gardener bought 6 packets of seeds. Each packet contains 8 seeds. How many seeds did he buy?
Definition:

Quantity problems: Finding totals when items come in packages or sets.

Number of packets
6 packets
Seeds per packet
8 seeds
Total seeds
6 × 8
Step 1: Identify what we're looking for

We need to find the total number of seeds

Step 2: Identify the number of groups

The gardener bought 6 packets (groups)

Step 3: Identify the number in each group

Each packet contains 8 seeds

Step 4: Set up the multiplication

Total seeds = Number of packets × Seeds per packet

Total seeds = 6 × 8

Step 5: Calculate

6 × 8 = 48

He bought 48 seeds.
Final answer:

He bought 48 seeds.

Applied rules:

• Packaging concept: Items sold in equal quantities per package

• Multiplier identification: Number of packages × items per package

• Context verification: 48 seeds from 6 packets is reasonable

10 Chairs in rows (Division)
Exercise 10
There are 45 chairs in the auditorium. They want to arrange them in 5 equal rows. How many chairs will be in each row?
Definition:

Arrangement problems: Distributing items equally in rows or groups.

Total chairs
45 chairs
Number of rows
5 rows
Chairs per row
45 ÷ 5
Step 1: Identify what we're looking for

We need to find how many chairs are in each row

Step 2: Identify the total amount

There are 45 chairs total

Step 3: Identify the number of groups

They want 5 equal rows

Step 4: Set up the division

Chairs per row = Total chairs ÷ Number of rows

Chairs per row = 45 ÷ 5

Step 5: Calculate

45 ÷ 5 = 9

There will be 9 chairs in each row.
Final answer:

There will be 9 chairs in each row.

Applied rules:

• Equal arrangement: Total ÷ Number of rows = Items per row

• Verification: 9 × 5 = 45 ✓

• Practical verification: 9 chairs per row in 5 rows is reasonable

Complete Summary: Multiplication & Division Word Problems

Operation Selection 🧮

📊
Multiplication Clues
each, per, every, times, product, groups of, sets of, rows of, columns of
Division Clues
shared equally, divided, split, per group, each group, how many in each, how many groups
Problem Steps
1. Read carefully 2. Find clue words 3. Choose operation 4. Solve 5. Check
Multiplication Formula
Groups × Items per group = Total
Division Formula
Total ÷ Number of groups = Items per group
Multiplication vs Division
M
Groups × Each = Total
D
Total ÷ Groups = Each
Visual Example
🍎🍎🍎🍎🍎🍎
🍎🍎🍎🍎🍎🍎
🍎🍎🍎🍎🍎🍎
🍎🍎🍎🍎🍎🍎
4 rows × 6 = 24 apples (Multiplication)
24 apples ÷ 4 rows = 6 per row (Division)
Practice Both Operations! 🌟
Multiplication: a × b = c
Division: c ÷ a = b
Inverse Operations
Key Definitions:

Word Problem: A math problem presented in a real-world context

Multiplication: Repeated addition of equal groups

Division: Splitting a total into equal groups or finding group size

Clue Words: Words that indicate which operation to use

Problem-Solving Strategy:
  1. Read: Understand the story situation
  2. Identify: Find clue words and important numbers
  3. Choose: Select multiplication or division
  4. Solve: Set up and calculate the equation
  5. Check: Verify if the answer makes sense
Tip 1: Draw pictures to visualize the problem.
Tip 2: Look for clue words like "each", "per", "shared equally".
Tip 3: Always check if your answer makes sense in the story.
Tip 4: Use inverse operations to verify: 6×4=24, so 24÷4=6.
Common Errors: Confusing multiplication and division, misreading clue words, calculation mistakes.
Success Strategy: Practice identifying clue words, draw models, check answers with inverse operations.
Multiplication & Division Concepts & Strategies
a × b = c
c ÷ a = b
c ÷ b = a
Inverse Relationship
Operation Relationships:

Multiplication & Division: Inverse operations that undo each other

Equal Groups: Same number of items in each group

Arrays: Objects arranged in rows and columns

Visualization Techniques:
  1. Draw pictures: Sketch the groups
  2. Make arrays: Arrange items in rows/columns
  3. Use manipulatives: Count with physical objects
  4. Write equations: Translate words to math
Strategy 1: Use skip counting for multiplication (3×4: 4,8,12).
Strategy 2: Break apart numbers (6×8 = 6×5 + 6×3).
Strategy 3: Use known facts to find unknown facts.
Strategy 4: Estimate first, then calculate precisely.
Key Concepts: Multiplication is repeated addition of equal groups, division splits into equal groups.
Real World: These operations help solve everyday problems efficiently.
Problem Recognition Patterns:

• Multiplication: "Each container has X items", "Rows of X items"

• Division: "Share equally", "Split into groups", "How many in each"

• Time: "X times per day for Y days" (multiplication)

• Money: "X items at Y dollars each" (multiplication)

Questions & Answers

Question: I always get confused when reading word problems. How do I know if I should multiply or divide?

Answer: Great question! Here's how to tell the difference:

  • Multiplication: Look for words like "each", "per", "every", "times", "product", "groups of", or "sets of". These suggest equal groups.
  • Division: Look for words like "divide", "share equally", "split", "per group", "how many in each", or "arrange in rows". These suggest splitting into equal groups.

For example: "Sarah has 4 bags with 6 apples each" → 4 groups of 6 → 4×6

But: "24 apples shared equally among 4 friends" → 24÷4 → Division

Ask yourself: "Am I finding a total?" (multiply) or "Am I sharing/splitting?" (divide)?

Question: My child struggles with drawing models for multiplication and division word problems. Are there other ways to help visualize?

Answer: Yes, there are several visualization techniques beyond drawing:

  • Physical objects: Use coins, blocks, or counters to represent groups
  • Finger counting: Skip count using fingers (2, 4, 6, 8...)
  • Tally marks: Draw groups of tally marks
  • Arrays: Arrange objects in rows and columns
  • Number lines: Skip count on a number line

For example, for 4×6: arrange 4 rows of 6 objects, or count by 6s four times: 6, 12, 18, 24.

For 24÷4: arrange 24 objects into 4 equal groups to see how many in each.

Let your child try different methods to see which works best for their learning style.

Question: How can I help my students check if their answers to multiplication and division word problems make sense?

Answer: Teaching estimation and reasonableness checks is crucial:

  • Round numbers: Round factors to nearest ten and estimate (4×6 ≈ 4×5 = 20)
  • Context check: Does the answer fit the story? (24 apples in 4 baskets is reasonable)
  • Inverse operation: For multiplication, divide to verify (24÷4=6); for division, multiply (6×4=24)
  • Alternative method: Solve using addition to verify (6+6+6+6 = 24)

Encourage students to ask: "Is my answer bigger or smaller than expected?" and "Does it make sense in the story?"

This builds mathematical reasoning skills beyond just computation.