Solved Exercises on Word Problems with Decimals in Grade 4

Master word problems with decimals: addition, subtraction, and real-world applications of decimal operations through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Shopping problem (addition)
Exercise 1
Maria bought a book for $12.75, a notebook for $3.25, and a pen for $1.50. How much did she spend in total?
Definition:

Word problem: A real-life situation described in words that requires mathematical operations to solve

Problem-solving method:
  1. Read the problem carefully
  2. Identify the important information
  3. Determine what operation to use
  4. Set up the equation
  5. Solve the equation
  6. Check if the answer makes sense
Given
$12.75 + $3.25 + $1.50
Total
$17.50
Context: Maria bought a book ($12.75), notebook ($3.25), and pen ($1.50). Need to find total cost.
Key Information:
  • Book: $12.75
  • Notebook: $3.25
  • Pen: $1.50
  • Operation: Addition (total cost)
Step 1: Identify the operation

We need to find the total amount spent, so we add all costs.

Step 2: Set up the addition
$12.75 + $3.25 + $1.50
Step 3: Align decimal points and add
$12.75
+
$3.25
+
$1.50
Step 4: Perform the addition
$12.75 + $3.25 + $1.50 = $17.50
Step 5: Verify the answer

Estimate: $13 + $3 + $2 = $18. Our answer of $17.50 is close to our estimate.

Item Price Book $12.75 Notebook $3.25 Pen $1.50 Total $17.50
Maria spent $17.50 in total
Final answer:

Maria spent $17.50 in total for all items.

Applied rules:

• Identify operation: "Total" suggests addition

• Align decimals: Keep decimal points aligned

• Estimation check: Verify answer is reasonable

2 Money problem (subtraction)
Exercise 2
James had $25.00. He spent $8.75 on lunch and $3.25 on snacks. How much money does he have left?
Definition:

Subtraction word problem: A problem that requires taking away one or more amounts from an initial amount

Given
$25.00 - $8.75 - $3.25
Remaining
$12.00
Context: James starts with $25.00 and spends money on lunch and snacks. Need to find remaining amount.
Key Information:
  • Starting amount: $25.00
  • Lunch: $8.75
  • Snacks: $3.25
  • Operation: Subtraction (money left)
Step 1: Identify the operation

We need to find what's left after spending, so we subtract expenses from the starting amount.

Step 2: Calculate total expenses

$8.75 + $3.25 = $12.00

Step 3: Subtract total expenses from starting amount
$25.00 - $12.00 = $13.00
Step 4: Alternative method - subtract one by one

$25.00 - $8.75 = $16.25

$16.25 - $3.25 = $13.00

Step 5: Verify the answer

Estimate: $25 - $9 - $3 = $13. Our answer of $13.00 matches our estimate.

Starting: $25.00
-
Lunch: $8.75
-
Snacks: $3.25
↓
Remaining: $13.00
James has $13.00 left
Final answer:

James has $13.00 left after his purchases.

Applied rules:

• Identify operation: "Left" suggests subtraction

• Multiple subtractions: Can subtract all expenses at once or one by one

• Estimation check: Verify answer is reasonable

3 Measurement problem (addition)
Exercise 3
A recipe calls for 2.5 cups of flour, 1.75 cups of sugar, and 0.25 cups of cocoa powder. How many cups of ingredients are needed in total?
Definition:

Measurement word problem: A problem involving quantities measured in specific units

Given
2.5 + 1.75 + 0.25
Total
4.5
Context: A recipe requires different amounts of ingredients. Need to find the total amount of ingredients needed.
Key Information:
  • Flour: 2.5 cups
  • Sugar: 1.75 cups
  • Cocoa powder: 0.25 cups
  • Unit: cups
  • Operation: Addition (total amount)
Step 1: Identify the operation

We need to find the total amount of ingredients, so we add all measurements.

Step 2: Equalize decimal places

2.5 = 2.50 (to match other measurements with 2 decimal places)

Step 3: Align decimal points and add
2.50 + 1.75 + 0.25
Step 4: Perform the addition
2.50 + 1.75 + 0.25 = 4.50
Step 5: Include the unit in the answer

4.50 cups = 4.5 cups (can remove trailing zero)

Ingredient Amount (cups) Flour 2.50 Sugar 1.75 Cocoa powder 0.25 Total 4.50
4.5 cups of ingredients needed
Final answer:

The recipe requires 4.5 cups of ingredients in total.

Applied rules:

• Identify operation: "Total" suggests addition

• Unit consistency: Include units in final answer

• Decimal alignment: Equalize decimal places for clarity

Rules and methods, laws,...
\text{Word Problem Solution} = \text{Identify} + \text{Operate} + \text{Verify}
Word Problem Solving Formula
Key definitions:

Word Problem: A real-life situation described in words that requires mathematical operations to solve

Context: The real-world situation described in the problem

Operation: The mathematical action needed (addition, subtraction, etc.)

Key Information: The important numbers and facts in the problem

Unit: The measurement system used (dollars, pounds, cups, etc.)

Complete methodology:
  1. Read carefully: Understand the situation described
  2. Identify key information: Find important numbers and facts
  3. Determine the operation: Decide if you need to add, subtract, etc.
  4. Set up the equation: Write the mathematical expression
  5. Solve the equation: Perform the calculation
  6. Include units: Add the appropriate measurement unit
  7. Verify: Check if the answer makes sense in context
Tip 1: Look for keywords that indicate operations: "total," "sum," "altogether" (addition); "left," "remaining," "less" (subtraction).
Tip 2: Always include the appropriate unit in your final answer.
Tip 3: Estimate your answer first to check if your final answer is reasonable.
Tip 4: Draw a picture or diagram if it helps you understand the problem.
Common errors: Misreading the question, using the wrong operation, forgetting units, not checking reasonableness of answer.
Key concepts: Context understanding, operation identification, decimal alignment, unit inclusion.
Rules to remember:

• Keywords: "Total," "sum," "altogether" → Addition

• Keywords: "Left," "remaining," "less," "difference" → Subtraction

• Units: Always include appropriate units in final answer

• Alignment: Keep decimal points aligned when adding/subtracting

• Verification: Estimate to check if answer is reasonable

\text{Estimate} \approx \text{Actual Answer}
Verification Principle
Key Notes to Remember:

• Read the problem multiple times to understand it

• Circle or highlight important numbers

• Always include units in your final answer

• Check if your answer makes sense in the real-world context

Solution: Exercises 4 to 5
4 Length problem (subtraction)
Exercise 4
A piece of rope was 10.5 meters long. After cutting off 3.75 meters, how much rope remains?
Definition:

Length word problem: A problem involving measurements of distance or length

Given
10.5 - 3.75
Remaining
6.75
Context: Starting with a long rope, cutting off a piece. Need to find remaining length.
Key Information:
  • Original length: 10.5 meters
  • Cut off: 3.75 meters
  • Unit: meters
  • Operation: Subtraction (what remains)
Step 1: Identify the operation

We need to find what remains after cutting, so we subtract.

Step 2: Equalize decimal places

10.5 = 10.50 (to match 2 decimal places)

Step 3: Align decimal points and subtract
10.50 - 3.75
Step 4: Perform the subtraction
10.50 - 3.75 = 6.75
Step 5: Include the unit

6.75 meters

Step 6: Verify the answer

Estimate: 11 - 4 = 7. Our answer of 6.75 is close to our estimate.

Original: 10.50m
-
Cut off: 3.75m
↓
Remaining: 6.75m
6.75 meters of rope remain
Final answer:

There are 6.75 meters of rope remaining.

Applied rules:

• Identify operation: "Remains" suggests subtraction

• Decimal alignment: Equalize decimal places for clarity

• Unit inclusion: Include "meters" in final answer

5 Multi-step shopping problem
Exercise 5
Sarah started shopping with $50.00. She bought groceries for $24.75, paid $8.50 for gas, and received $3.25 in change from a purchase. How much money does she have now?
Definition:

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

Given
$50.00 - $24.75 - $8.50 + $3.25
Final amount
$20.00
Context: Sarah starts with money, spends on groceries and gas, receives change. Need to track all transactions.
Key Information:
  • Starting amount: $50.00
  • Spent on groceries: $24.75 (subtract)
  • Spent on gas: $8.50 (subtract)
  • Received change: $3.25 (add)
  • Operation: Mixed operations
Step 1: Identify all operations

Start with $50.00

Subtract $24.75 (groceries)

Subtract $8.50 (gas)

Add $3.25 (change received)

Step 2: Perform operations in order

$50.00 - $24.75 = $25.25

$25.25 - $8.50 = $16.75

$16.75 + $3.25 = $20.00

Step 3: Alternative approach

Total spent: $24.75 + $8.50 = $33.25

Total received: $3.25

Net spent: $33.25 - $3.25 = $30.00

Final amount: $50.00 - $30.00 = $20.00

Step 4: Verify the answer

Estimate: $50 - $25 - $9 + $3 = $19. Our answer of $20 is close to our estimate.

Transaction Type Amount Running Total Start Initial $50.00 $50.00 Groceries Expense $24.75 $25.25 Gas Expense $8.50 $16.75 Change Income $3.25 $20.00
Sarah has $20.00 remaining
Final answer:

Sarah has $20.00 remaining after all transactions.

Applied rules:

• Multi-step tracking: Handle each transaction separately

• Operation identification: Expenses subtract, income adds

• Alternative methods: Can solve in different ways to verify

Word Problems with Decimals Fundamentals and Practice
\text{Word Problem Solution} = \text{Identify} + \text{Operate} + \text{Verify}
Word Problem Solving Formula
Key definitions:

Word Problem: A real-life situation described in words that requires mathematical operations to solve

Context: The real-world situation described in the problem

Operation: The mathematical action needed (addition, subtraction, etc.)

Key Information: The important numbers and facts in the problem

Unit: The measurement system used (dollars, pounds, cups, etc.)

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

Estimation: Approximating the answer to check reasonableness

Complete methodology:
  1. Read carefully: Understand the situation described
  2. Identify key information: Find important numbers and facts
  3. Determine the operation: Decide if you need to add, subtract, etc.
  4. Set up the equation: Write the mathematical expression
  5. Solve the equation: Perform the calculation
  6. Include units: Add the appropriate measurement unit
  7. Verify: Check if the answer makes sense in context
Tip 1: Look for keywords that indicate operations: "total," "sum," "altogether" (addition); "left," "remaining," "less" (subtraction).
Tip 2: Always include the appropriate unit in your final answer.
Tip 3: Estimate your answer first to check if your final answer is reasonable.
Tip 4: Draw a picture or diagram if it helps you understand the problem.
Tip 5: For multi-step problems, solve one step at a time and keep track of your progress.
Common errors: Misreading the question, using the wrong operation, forgetting units, not checking reasonableness of answer, losing track in multi-step problems.
Success strategies: Reading carefully, highlighting important information, using estimation, checking work, organizing steps clearly.
Essential formulas and rules:

• Keywords for Addition: "Total," "sum," "altogether," "combined," "in all"

• Keywords for Subtraction: "Left," "remaining," "less," "difference," "spent," "cut off"

• Decimal Alignment: Keep decimal points aligned when adding/subtracting

• Unit Consistency: Always include appropriate units in final answer

• Verification: Estimate to check if answer is reasonable

\text{Estimate} \approx \text{Actual Answer}
Verification Principle
Memory Aids:

• "Total" means Add: When you see "total," think addition

• "Left" means Subtract: When you see "left," think subtraction

• Units Matter: Always include units in your final answer

• Check Reasonableness: Your answer should make sense in the real world

Word Problem Solving Process
1
Read
2
Identify
3
Operate
4
Solve
5
Verify

Questions & Answers

Question: How do I know whether to add or subtract in a word problem?

Answer: Look for keywords that indicate the operation:

Addition keywords:

  • "Total" - "What is the total?"
  • "Sum" - "Find the sum"
  • "Altogether" - "How many altogether?"
  • "Combined" - "What is the combined amount?"
  • "In all" - "How many in all?"

Subtraction keywords:

  • "Left" - "How much is left?"
  • "Remaining" - "What remains?"
  • "Less" - "How much less?"
  • "Spent" - "How much did you spend?"
  • "Difference" - "What is the difference?"

Also think about the situation: if you're combining things, you add. If you're taking away, you subtract.

Question: Do I always need to include the unit (like dollars or meters) in my answer?

Answer: Yes, you should always include the appropriate unit in your final answer:

  • It makes your answer complete and meaningful
  • It shows you understand what the numbers represent
  • It helps you catch errors (if your unit doesn't match the problem)
  • Teachers expect it and often require it for full credit

Examples:

  • If the problem is about money: include "$" and specify dollars
  • If the problem is about length: include "meters," "feet," or "inches"
  • If the problem is about weight: include "kilograms," "pounds," or "ounces"

Think of it this way: "25" isn't as meaningful as "$25" or "25 meters."

Question: What should I do if a word problem has more than one step?

Answer: For multi-step word problems, follow these strategies:

  • Break it down: Solve one step at a time
  • Keep track: Write down intermediate results
  • Organize: Use a table or list to organize information
  • Check each step: Make sure each calculation makes sense

Example: If Sarah starts with $50, spends $25, and then gets $5 back:

  • Step 1: $50 - $25 = $25 remaining
  • Step 2: $25 + $5 = $30 final amount

You can also look for alternative approaches - sometimes solving differently can help verify your answer!

The key is to stay organized and tackle one piece at a time.