Solved Exercises on 3 Digit Multiplication Word Problems in Grade 4

Master 3 digit multiplication word problems: strategies, methods, and step-by-step solutions through these 10 detailed exercises.

Solution: Exercises 1 to 3
1 Basic multiplication word problem
Exercise 1
A school has 324 students in grade 4. Each student needs 3 notebooks for the year. How many notebooks does the school need to order?
Definition:

3-digit multiplication: Multiplying a 3-digit number by a 1-digit number using place value understanding

Multiplication method:
  1. Multiply each digit in the 3-digit number by the 1-digit number
  2. Start from the ones place and work left
  3. Regroup when necessary
Problem
324 × 3
Solution
972
Step 1: Set up the problem

We need to multiply 324 by 3 to find total notebooks

Step 2: Multiply ones place

4 × 3 = 12 → Write 2, carry 1

Step 3: Multiply tens place

2 × 3 = 6, plus carried 1 = 7

Step 4: Multiply hundreds place

3 × 3 = 9

324 × 3 = 972
Final answer:

The school needs to order 972 notebooks.

Applied rules:

• Place value: Each digit represents hundreds, tens, or ones

• Carrying: When product exceeds 9, carry to next place value

• Multiplication algorithm: Multiply each digit starting from right

2 Money word problem
Exercise 2
A store sells 456 bottles of juice each day. If each bottle costs $4, how much money does the store make in one day?
Definition:

Word problem solving: Understanding context, identifying numbers, and applying mathematical operations

Problem
456 × 4
Solution
1,824
Step 1: Identify the operation

We need to multiply the number of bottles by the cost per bottle

Step 2: Multiply ones place

6 × 4 = 24 → Write 4, carry 2

Step 3: Multiply tens place

5 × 4 = 20, plus carried 2 = 22 → Write 2, carry 2

Step 4: Multiply hundreds place

4 × 4 = 16, plus carried 2 = 18

456 × 4 = 1,824
Final answer:

The store makes $1,824 in one day.

Applied rules:

• Word problem strategy: Identify key information and operation needed

• Multiplication with regrouping: Carry digits when product exceeds 9

• Money notation: Include dollar sign in final answer

3 Grouping word problem
Exercise 3
A factory produces 573 toy cars each week. How many toy cars will it produce in 6 weeks?
Definition:

Repeated addition: Multiplication as repeated addition of equal groups

Problem
573 × 6
Solution
3,438
Step 1: Understand the problem

We need to find the total production over 6 weeks

Step 2: Multiply ones place

3 × 6 = 18 → Write 8, carry 1

Step 3: Multiply tens place

7 × 6 = 42, plus carried 1 = 43 → Write 3, carry 4

Step 4: Multiply hundreds place

5 × 6 = 30, plus carried 4 = 34

573 × 6 = 3,438
Final answer:

The factory will produce 3,438 toy cars in 6 weeks.

Applied rules:

• Place value understanding: Each digit has a specific value

• Regrouping strategy: Carry digits when necessary

• Problem solving: Connect mathematical operation to real-world context

Solution: Exercises 4 to 5
4 Books word problem
Exercise 4
A library has 689 books on each shelf. If there are 7 shelves, how many books are in the library?
Definition:

Area model concept: Multiplication as finding the total in rectangular arrays

Problem
689 × 7
Solution
4,823
Step 1: Identify the numbers

Books per shelf = 689, Number of shelves = 7

Step 2: Multiply ones place

9 × 7 = 63 → Write 3, carry 6

Step 3: Multiply tens place

8 × 7 = 56, plus carried 6 = 62 → Write 2, carry 6

Step 4: Multiply hundreds place

6 × 7 = 42, plus carried 6 = 48

689 × 7 = 4,823
Final answer:

The library has 4,823 books in total.

Applied rules:

• Regrouping process: Carefully carry digits to maintain accuracy

• Place value alignment: Keep digits in correct columns

• Word problem comprehension: Identify what is being asked

5 Distance word problem
Exercise 5
A delivery truck travels 247 miles each day for 8 days. How many miles does the truck travel in total?
Definition:

Total distance calculation: Finding cumulative distance over multiple periods

Problem
247 × 8
Solution
1,976
Step 1: Understand the problem

We need to find total distance traveled over 8 days

Step 2: Multiply ones place

7 × 8 = 56 → Write 6, carry 5

Step 3: Multiply tens place

4 × 8 = 32, plus carried 5 = 37 → Write 7, carry 3

Step 4: Multiply hundreds place

2 × 8 = 16, plus carried 3 = 19

247 × 8 = 1,976
Final answer:

The truck travels 1,976 miles in total.

Applied rules:

• Accurate carrying: Track all carried digits carefully

• Contextual interpretation: Relate computation to the problem situation

• Unit consistency: Include units in final answer

Multiplication Strategies and Methods
ABC × D = ?
3-Digit by 1-Digit Multiplication
Strategy 1
Standard Algorithm
Multiply each digit, carry when needed
Strategy 2
Partial Products
Break apart by place value
Strategy 3
Area Model
Visual representation of multiplication

3-Digit Multiplication Steps

🔢
Step 1: Multiply Ones
Multiply the ones digit of the top number by the bottom number
Step 2: Multiply Tens
Multiply the tens digit of the top number by the bottom number
Step 3: Multiply Hundreds
Multiply the hundreds digit of the top number by the bottom number
Step 4: Regroup
Carry digits when products exceed 9
Multiplication Laws, Rules, and Properties
324 × 5 = (300 × 5) + (20 × 5) + (4 × 5)
Distributive Property
Key definitions:

3-digit multiplication: Multiplying a number with hundreds, tens, and ones places

Place value: Each digit's value depends on its position (hundreds, tens, ones)

Regrouping: Carrying when a product exceeds 9 in any place value

Complete methodology:
  1. Read the problem carefully: Identify what is being asked
  2. Identify the numbers: Find the 3-digit and 1-digit numbers
  3. Set up multiplication: Align numbers properly
  4. Multiply each place value: Start with ones, then tens, then hundreds
  5. Regroup when needed: Carry digits to the next place value
  6. Check your work: Estimate to verify reasonableness
Tip 1: Always start multiplying from the ones place and move left.
Tip 2: Remember to add any carried digits to the next multiplication.
Tip 3: Estimate first to check if your answer is reasonable.
Tip 4: Draw lines under each partial product to stay organized.
Common errors: Forgetting to carry digits, misaligning numbers, computational mistakes.
Exam preparation: Practice with various 3-digit by 1-digit combinations, focus on place value understanding.
Properties to remember:

• Commutative Property: a × b = b × a (though order matters for organization)

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

• Distributive Property: a × (b + c) = (a × b) + (a × c)

• Identity Property: a × 1 = a

• Zero Property: a × 0 = 0

Questions & Answers

Question: I get confused about when to carry digits in 3-digit multiplication. Can you explain when and how to do it?

Answer: Carrying happens whenever the product of your multiplication is greater than 9:

  • When multiplying any digit, if your answer is 10 or more, you need to carry
  • Write down only the ones digit of your product
  • Carry the tens digit to the next column to the left
  • Add the carried digit to your next multiplication

Example: In 456 × 7, when multiplying 5 × 7 = 35, write down 5 and carry 3 to the hundreds place. Then calculate 4 × 7 = 28, plus the carried 3 = 31.

Think of carrying as "moving extra tens" to the next place value. This keeps your answer accurate!

Question: How can I check if my answer to a 3-digit multiplication word problem is reasonable?

Answer: Estimation is your best tool for checking reasonableness:

  • Round the 3-digit number to the nearest hundred or ten
  • Multiply the rounded number by the 1-digit number
  • Compare your exact answer to your estimate

Example: For 324 × 6, round 324 to 300. Then 300 × 6 = 1,800. Your exact answer should be close to 1,800. If you got 180 or 18,000, you likely made an error.

You can also perform the multiplication a second time or use inverse operations (division) to verify your answer.

Question: What's the best way to organize my work when solving 3-digit multiplication word problems?

Answer: Good organization prevents errors and helps you track your thinking:

  1. Read the problem completely and underline important numbers
  2. Write down what you're solving for
  3. Set up the multiplication vertically with proper alignment
  4. Draw small lines or boxes to separate place values
  5. Work systematically from right to left
  6. Circle or box your final answer with the correct units

Example format:
Problem: 456 × 8
456
× 8
_______
3,648

Keep your work neat and aligned in columns. This helps prevent place value errors!