Solved Exercises on Multiplication Word Problems with 2-Digit Numbers in Grade 4

Master multiplication word problems with 2-digit numbers: step-by-step solutions, rules, methods, and practice exercises.

Solution: Exercises 1 to 3
1 Apples in boxes
Exercise 1
A farmer has 24 boxes of apples. Each box contains 35 apples. How many apples does the farmer have in total?
Definition:

Word Problem: A mathematical problem presented in everyday language requiring identification of operation and numbers.

Solution method:
  1. Identify what is being asked (total number of apples)
  2. Identify the numbers involved (24 boxes, 35 apples per box)
  3. Identify the operation needed (multiplication)
  4. Set up the multiplication: 24 × 35
  5. Solve using standard algorithm
Problem
24 boxes × 35 apples
Setup
24 × 35
Solution
840 apples
Step 1: Set up the multiplication

24 × 35

Step 2: Multiply by ones place

24 × 5 = 120

Step 3: Multiply by tens place

24 × 30 = 720

Step 4: Add the partial products

120 + 720 = 840

24 × 35 = 840 apples
Final answer:

The farmer has 840 apples in total.

Applied rules:

• Standard Algorithm: Multiply each digit, carrying over as needed

• Place Value: Remember that 3 in 35 represents 30

• Word Problem Strategy: Identify, organize, solve, and verify

2 Students in rows
Exercise 2
In a school auditorium, there are 18 rows of seats. Each row has 26 seats. How many seats are there in total?
Definition:

Arrays Model: A rectangular arrangement showing multiplication as rows × columns.

Problem
18 rows × 26 seats
Setup
18 × 26
Solution
468 seats
Step 1: Set up the multiplication

18 × 26

Step 2: Multiply by ones place (6)

18 × 6 = 108

Step 3: Multiply by tens place (20)

18 × 20 = 360

Step 4: Add the partial products

108 + 360 = 468

18 × 26 = 468 seats
Final answer:

There are 468 seats in total.

Applied rules:

• Array Model: Multiplication represents equal groups arranged in rows and columns

• Partial Products: Break down multiplication into simpler parts

• Addition: Combine partial products to get final answer

3 Days in weeks
Exercise 3
There are 42 weeks in a school year. How many days are there in the school year? (Assume 7 days per week)
Definition:

Repeated Addition: Multiplication is repeated addition of equal groups.

Problem
42 weeks × 7 days
Setup
42 × 7
Solution
294 days
Step 1: Set up the multiplication

42 × 7

Step 2: Multiply ones place

2 × 7 = 14, write 4, carry 1

Step 3: Multiply tens place

4 × 7 = 28, add carried 1 = 29

Step 4: Write the result

294 days

42 × 7 = 294 days
Final answer:

There are 294 days in the school year.

Applied rules:

• Carrying: When product exceeds 9, carry the tens digit

• Place Value: Align digits correctly when adding partial products

• Unit Understanding: Keep track of units in word problems

Multiplication Rules and Methods
\(a \times b = c\)
Multiplication Formula
Commutative Property
\(a \times b = b \times a\)
Order doesn't matter
Associative Property
\((a \times b) \times c = a \times (b \times c)\)
Grouping doesn't matter
Distributive Property
\(a \times (b + c) = a \times b + a \times c\)
Break apart numbers
Key definitions:

Multiplicand: The number being multiplied

Multiplier: The number that tells how many times to multiply

Product: The result of multiplication

Standard Algorithm Steps:
  1. Line up numbers by place value
  2. Multiply bottom number's ones by top number
  3. Multiply bottom number's tens by top number
  4. Add partial products together
Tip 1: Always estimate first to check reasonableness of your answer.
Tip 2: Draw arrays or area models to visualize the multiplication.
Tip 3: Check your work by dividing the product by one factor.
Tip 4: Line up digits properly to avoid calculation errors.
Solution: Exercises 4 to 5
4 Earnings
Exercise 4
Sarah earns $36 per day working at a bookstore. If she works for 28 days, how much money will she earn?
Definition:

Rate Problem: Problems involving amount per unit (dollars per day, miles per hour, etc.)

Problem
$36/day × 28 days
Setup
36 × 28
Solution
$1,008
Step 1: Set up the multiplication

36 × 28

Step 2: Multiply by ones place (8)

36 × 8 = 288

Step 3: Multiply by tens place (20)

36 × 20 = 720

Step 4: Add partial products

288 + 720 = 1,008

36 × 28 = $1,008
Final answer:

Sarah will earn $1,008 in 28 days.

Applied rules:

• Rate × Time = Total: Unit rate problems follow this pattern

• Partial Products: Multiply by each digit separately

• Money Notation: Include currency symbol in final answer

5 Pages in books
Exercise 5
A library has 56 bookshelves. Each shelf holds 43 books. How many books are there in total?
Definition:

Area Model: Visual representation of multiplication as length × width.

Problem
56 shelves × 43 books
Setup
56 × 43
Solution
2,408 books
Step 1: Set up the multiplication

56 × 43

Step 2: Multiply by ones place (3)

56 × 3 = 168

Step 3: Multiply by tens place (40)

56 × 40 = 2,240

Step 4: Add partial products

168 + 2,240 = 2,408

56 × 43 = 2,408 books
Final answer:

There are 2,408 books in total.

Applied rules:

• Place Value: Remember that 4 in 43 represents 40

• Regrouping: Carry over when necessary

• Verification: Estimate to check reasonableness (50 × 40 = 2,000)

Multiplication Laws, Methods, and Key Concepts
\(a \times b = c\)
Basic Multiplication
Key definitions:

2-Digit Number: A number with a tens and ones place (10-99)

Partial Product: Result of multiplying one digit by the entire other number

Standard Algorithm: Traditional method of multiplication with carrying

Complete methodology:
  1. Read Carefully: Understand what the problem is asking
  2. Identify Numbers: Find the multiplicand and multiplier
  3. Set Up: Write the multiplication vertically
  4. Multiply: Follow standard algorithm steps
  5. Check: Verify with estimation or division
Tip 1: Always align numbers by place value when setting up multiplication.
Tip 2: When multiplying by tens digit, remember to shift one place left.
Tip 3: Use zeros as placeholders when multiplying by tens, hundreds, etc.
Tip 4: Practice mental math shortcuts like 25 × 4 = 100.
Common errors: Misaligning digits, forgetting to carry, skipping zeros in partial products.
Key strategies: Break apart numbers, use area models, estimate first.
Properties to remember:

• Commutative: Order doesn't change the product

• Associative: Grouping doesn't change the product

• Distributive: Helps break apart larger numbers

• Identity: Any number × 1 = itself

• Zero Property: Any number × 0 = 0

Word Problem Strategies and Visualization
Multiplication Word Problem Patterns
Common word problem structures for 2-digit multiplication:
• Equal groups (boxes of items)
• Arrays (seats in rows/columns)
• Rate problems (earnings per day)
• Area problems (length × width)

Strategy Framework: Read → Identify → Plan → Solve → Check

  • Read: Understand the context and what's being asked
  • Identify: Find numbers and operation needed
  • Plan: Set up the multiplication
  • Solve: Use standard algorithm
  • Check: Verify reasonableness

Questions & Answers

Question: I keep getting confused about when to carry over numbers in multiplication. How do I know when to carry?

Answer: Great question! You carry when the product of multiplying two digits is 10 or greater.

  • When multiplying single digits, if the result is 10 or more, you have to carry the tens digit.
  • For example: 7 × 8 = 56. Write the 6 in the current place and carry the 5 to the next column.
  • When multiplying by the tens digit of the bottom number, remember to shift one place to the left.

Memory trick: "If it's 10 or bigger, carry the first digit!"

Example: 43 × 27
43 × 7 = 301 (carry the 2 when 3×7=21, and 4×7=28+2=30)
43 × 20 = 860 (shift one place left)
Total: 301 + 860 = 1,161

Question: My child struggles with word problems. How can I help them identify when to use multiplication?

Answer: Look for clue words that suggest multiplication:

  • Equal groups: "each," "per," "every," "times"
  • Arrays: "rows of," "columns of," "arranged in"
  • Rate problems: "per day," "per hour," "at a rate of"
  • Total amounts: "altogether," "in all," "total"

Teach your child to ask: "Am I finding how many in equal groups?" If yes, it's likely multiplication.

Practice with simple examples: "If 5 friends each get 3 cookies, how many cookies total?" (5 groups of 3 = 5 × 3)

Question: Are there any shortcuts for multiplying 2-digit numbers faster?

Answer: Yes! Here are some helpful shortcuts:

  • Round and adjust: For 24 × 19, think 24 × 20 = 480, then subtract 24 to get 456
  • Break apart numbers: 36 × 15 = 36 × (10 + 5) = 360 + 180 = 540
  • Use friendly numbers: Numbers ending in 5 or 0 are easier to multiply
  • Look for patterns: 25 × 4 = 100, so 25 × 16 = 25 × 4 × 4 = 400

However, make sure you master the standard algorithm first - it works for ALL problems!

Example: 42 × 25
Think: 42 × 100 ÷ 4 = 4,200 ÷ 4 = 1,050