Solved Exercises on Expanded Form Word Problems in Grade 4

Master expanded form word problems: place value decomposition, digit representation, and number composition through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic place value word problem
Exercise 1
A school library has 4,725 books. Write the number of books in expanded form and explain what each part represents.
Definition:

Expanded form: Writing a number to show the value of each digit based on its place value.

Problem-Solving Method:
  1. Read the word problem carefully and identify the number
  2. Identify the place value of each digit
  3. Multiply each digit by its place value
  4. Add all the products together
  5. Interpret what each part means in context
Number
4,725
Expanded
4,000 + 700 + 20 + 5
Step 1: Identify the number from the problem

The problem states: "4,725 books"

Step 2: Identify place values

4 is in thousands place (4 × 1,000 = 4,000)

7 is in hundreds place (7 × 100 = 700)

2 is in tens place (2 × 10 = 20)

5 is in ones place (5 × 1 = 5)

Step 3: Write as addition of place values

4,725 = 4,000 + 700 + 20 + 5

Step 4: Interpret in context

4,000: Four thousand books

700: Seven hundred books

20: Twenty books

5: Five books

4,725 = 4,000 + 700 + 20 + 5
Final answer:

4,725 = 4,000 + 700 + 20 + 5

The library has 4 thousand books, 7 hundred books, 2 tens of books, and 5 single books.

Applied rules:

• Place Value: Each digit has a specific value based on position

• Problem Context: Connect math to the real-world situation

• Decomposition: Break down into parts that sum to original number

2 Word problem with zeros
Exercise 2
A town has 6,043 residents. Write this number in expanded form and explain what each part means.
Definition:

Zero in expanded form: Even zeros represent their place value (e.g., 0 hundreds = 0)

Number
6,043
Expanded
6,000 + 0 + 40 + 3
Simplified
6,000 + 40 + 3
Step 1: Identify the number from the problem

The problem states: "6,043 residents"

Step 2: Identify place values

6 is in thousands place (6 × 1,000 = 6,000)

0 is in hundreds place (0 × 100 = 0)

4 is in tens place (4 × 10 = 40)

3 is in ones place (3 × 1 = 3)

Step 3: Write as addition of place values

6,043 = 6,000 + 0 + 40 + 3

Step 4: Simplify by removing zero term

6,043 = 6,000 + 40 + 3

Step 5: Interpret in context

6,000: Six thousand residents

40: Forty residents

3: Three residents

6,043 = 6,000 + 40 + 3
Final answer:

6,043 = 6,000 + 40 + 3

The town has 6 thousand residents and 4 tens of residents and 3 single residents.

Applied rules:

• Zero Place Value: Zeros still represent their position's value

• Simplification: Adding zero doesn't change the sum

• Problem Context: Connect math to the real-world situation

3 Converting expanded to standard form in word problem
Exercise 3
A farmer harvested crops that can be represented as 8,000 + 300 + 0 + 7. How many crops did the farmer harvest?
Definition:

Standard form: The regular way we write numbers without showing place values

Expanded
8,000 + 300 + 0 + 7
Standard
8,307
Step 1: Identify each place value from the expanded form

8,000 → 8 in thousands place

300 → 3 in hundreds place

0 → 0 in tens place

7 → 7 in ones place

Step 2: Combine the digits in order

Thousands: 8, Hundreds: 3, Tens: 0, Ones: 7

So we get 8,307

Step 3: Answer the question in context

The farmer harvested 8,307 crops.

Step 4: Verify by converting back to expanded form

8,307 = 8,000 + 300 + 0 + 7 ✓

8,000 + 300 + 0 + 7 = 8,307
Final answer:

The farmer harvested 8,307 crops.

Applied rules:

• Place Value Addition: Sum all expanded parts to get standard form

• Digit Placement: Each part corresponds to a specific place

• Problem Context: Answer the question asked in the word problem

Word Problem Strategy and Expanded Form Rules
\(4,725 = 4,000 + 700 + 20 + 5\)
Expanded Form Example
Ones Place
\(d \times 1\)
Digit × 1
Tens Place
\(d \times 10\)
Digit × 10
Hundreds Place
\(d \times 100\)
Digit × 100
Thousands Place
\(d \times 1,000\)
Digit × 1,000
Key definitions:

Place Value: The value of a digit based on its position in a number

Expanded Form: Writing a number as the sum of the value of each digit

Standard Form: The regular way we write numbers

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

Context: The real-world situation described in the problem

Interpretation: Explaining what the math means in the real world

Complete word problem methodology:
  1. Read carefully: Identify the number and what is being asked
  2. Extract information: Find the relevant number from the context
  3. Identify positions: Recognize thousands, hundreds, tens, ones
  4. Determine values: Multiply each digit by its place value
  5. Express as sum: Write the addition of all place values
  6. Interpret: Explain what each part means in the context
  7. Verify: Check that the sum equals the original number
Tip 1: Underline or circle the number in the word problem to focus on it.
Tip 2: Always relate your answer back to the context of the problem.
Tip 3: Remember the order: Thousands, Hundreds, Tens, Ones (THOUS).
Tip 4: Use base-10 blocks to visualize place values for better understanding.
Common errors: Misreading the number, forgetting place values, not connecting to context.
Memory aid: Use "THOUS" (Thousands, Hundreds, Tens, Ones) to remember the order.
Formulas to know by heart:

• Place value: Digit × Position value (1, 10, 100, 1000...)

• Expanded form: Sum of all place values

• Standard form: Regular number notation

• Verification: Sum of expanded parts = Original number

Solution: Exercises 4 to 5
4 Multi-step word problem
Exercise 4
A company made 7,280 sales in January and 3,056 sales in February. Write the total sales for both months in expanded form.
Definition:

Multi-step problem: A problem requiring multiple operations to solve

January
7,280
February
3,056
Total
10,336
Step 1: Add the sales from both months

7,280 + 3,056 = 10,336 total sales

Step 2: Identify each digit's place value in the total

1 is in ten-thousands place (1 × 10,000 = 10,000)

0 is in thousands place (0 × 1,000 = 0)

3 is in hundreds place (3 × 100 = 300)

3 is in tens place (3 × 10 = 30)

6 is in ones place (6 × 1 = 6)

Step 3: Write in expanded form

10,336 = 10,000 + 0 + 300 + 30 + 6

Step 4: Simplify by removing zero term

10,336 = 10,000 + 300 + 30 + 6

Step 5: Interpret in context

10,000: Ten thousand sales

300: Three hundred sales

30: Thirty sales

6: Six sales

10,336 = 10,000 + 300 + 30 + 6
Final answer:

The total sales of 10,336 can be written in expanded form as: 10,000 + 300 + 30 + 6

The company made 10 thousand sales, 3 hundred sales, 3 tens of sales, and 6 single sales over both months.

Applied rules:

• Multi-step approach: Solve step by step

• Place value understanding: Each digit represents a specific quantity

• Context interpretation: Explain what each part means

5 Comparison word problem
Exercise 5
City A has a population of 45,672 people. City B has a population of 30,089 people. Write the population of each city in expanded form and compare which has more people.
Definition:

Comparison problem: A problem requiring comparison of two or more quantities

City A
45,672
Expanded A
40,000 + 5,000 + 600 + 70 + 2
City B
30,089
Expanded B
30,000 + 0 + 80 + 9
Step 1: Write City A's population in expanded form

45,672 = 40,000 + 5,000 + 600 + 70 + 2

Step 2: Write City B's population in expanded form

30,089 = 30,000 + 0 + 80 + 9

Step 3: Compare the populations

City A: 45,672 people

City B: 30,089 people

Since 45,672 > 30,089, City A has more people.

Step 4: Interpret the results

City A has 4 ten-thousands of people plus more, while City B has only 3 ten-thousands.

City A: 45,672 = 40,000 + 5,000 + 600 + 70 + 2
City B: 30,089 = 30,000 + 80 + 9
City A has more people.
Final answer:

City A: 45,672 = 40,000 + 5,000 + 600 + 70 + 2

City B: 30,089 = 30,000 + 80 + 9

City A has more people because 45,672 > 30,089.

Applied rules:

• Multiple representations: Work with both cities separately

• Comparison skills: Compare numbers using place value

• Verification: Confirm the comparison is correct

Complete Summary: Expanded Form Word Problems
\(d_n \times 10^n + d_{n-1} \times 10^{n-1} + ... + d_1 \times 10^1 + d_0 \times 10^0\)
General Expanded Form Formula
Key definitions:

Place Value: The value of a digit based on its position in a number (ones, tens, hundreds, thousands, etc.)

Expanded Form: A number expressed as the sum of the value of each digit multiplied by its place value

Standard Form: The usual way we write numbers (e.g., 4,725)

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

Context: The real-world situation described in the problem that gives meaning to the numbers

Interpretation: Explaining what the mathematical solution means in the real-world situation

Complete word problem methodology:
  1. Read carefully: Identify the number and what is being asked
  2. Extract information: Find the relevant number from the context
  3. Identify positions: Recognize the place value of each digit
  4. Multiplication: Multiply each digit by its corresponding power of 10
  5. Addition: Express the number as the sum of all place values
  6. Interpretation: Explain what each part means in the context
  7. Verification: Add the expanded parts to confirm they equal the original number
Tip 1: Use the acronym THOUS (Thousands, Hundreds, Tens, Ones) to remember place value order.
Tip 2: Draw a place value chart to organize digits before expanding.
Tip 3: Always connect your answer back to the context of the word problem.
Tip 4: Practice reading numbers aloud to reinforce place value understanding.
Common errors: Misreading the number, forgetting zeros, confusing place values, not connecting to context.
Memory aids: Use base-10 blocks, draw charts, underline numbers in problems.
Formulas and Rules to Know:

• Place Value Pattern: ..., 10,000, 1,000, 100, 10, 1

• Expanded Form: Sum of (digit × place value)

• Zero Rule: Zeros contribute 0 to the sum but indicate position

• Verification: Expanded parts must sum to original number

• Context Rule: Always relate math back to the real-world situation

Word Problem Visualization: Population Comparison
Exercise 6: Understanding Place Values in Context
Consider the populations of two cities:
City A: 45,672 = 40,000 + 5,000 + 600 + 70 + 2
City B: 30,089 = 30,000 + 0 + 80 + 9
Compare their populations using expanded form.

Analysis: The chart shows how expanded form helps compare large numbers.

  • City A: 4×10,000 + 5×1,000 + 6×100 + 7×10 + 2×1 (Forty-five thousand six hundred seventy-two)
  • City B: 3×10,000 + 0×1,000 + 8×10 + 9×1 (Thirty thousand eighty-nine)
  • By comparing place values, City A clearly has more people.

Questions & Answers

Question: I don't understand why we need to learn expanded form in word problems. Why can't we just work with the regular numbers?

Answer: Great question! Expanded form in word problems is especially valuable because:

  • It helps you understand what each digit means in the context of the problem
  • It builds stronger place value understanding which is essential for larger numbers
  • It helps with estimation and checking if your answer makes sense
  • It connects abstract math to real-world understanding

For example, if a word problem says "The school has 4,725 books," expanded form (4,000 + 700 + 20 + 5) helps you understand that this is 4 thousand books plus 7 hundred books plus 20 books plus 5 books. This makes the magnitude of the number more meaningful!

Question: My child gets confused when word problems have zeros in the middle of a number like 6,043. How do I help them understand the expanded form?

Answer: Here's a helpful approach for word problems with zeros:

  • Use a place value chart to show every position: Ten-Thousands | Thousands | Hundreds | Tens | Ones
  • Write 6,043 in the chart: 6 in thousands, 0 in hundreds, 4 in tens, 3 in ones
  • Even though the hundreds digit is 0, it still represents 0 hundreds = 0
  • So: 6,043 = 6,000 + 0 + 40 + 3, which simplifies to 6,000 + 40 + 3
  • In the context of "6,043 residents," this means 6 thousand residents, 0 hundred residents, 4 tens of residents, and 3 single residents

You can also use manipulatives like base-10 blocks: 6 thousand blocks, 0 hundred blocks, 4 ten sticks, 3 unit cubes. The absence of hundred blocks still represents 0 hundreds!

The zero keeps the other digits in their correct places!

Question: What's the best way to check if my expanded form answer is correct in a word problem?

Answer: Here are effective verification methods for word problems:

  • Add up the expanded parts: If you wrote 4,725 as 4,000 + 700 + 20 + 5, add them: 4,000 + 700 + 20 + 5 = 4,725 ✓
  • Count the digits: Make sure you have one term for each digit in the original number
  • Check place values: Ensure each digit is multiplied by the correct power of 10
  • Context check: Does your answer make sense in the real-world situation?
  • Estimation: The largest term should be close to the original number

For example, with 4,725 books: The largest term (4,000) is close to 4,725, which makes sense. The sum 4,000 + 700 + 20 + 5 = 4,725 confirms the answer is correct. Also, having 4 thousand books makes sense for a school library!