Solved Exercises on Money Word Problems Mixed Operations in Grade 3

Master money word problems with mixed operations: addition, subtraction, multiplication, and division through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Addition and Subtraction
Exercise 1
Mia had $12.50. She spent $3.75 on lunch and then earned $5.25 from helping her neighbor. How much money does she have now?
Definition:

Mixed Operations: Problems requiring multiple arithmetic operations (addition, subtraction, multiplication, division)

Order of Operations:
  1. Perform operations from left to right
  2. Align decimal points when adding/subtracting
  3. Keep track of positive (earned) and negative (spent) amounts
Starting Amount
$12.50
Subtract Lunch
-$3.75
Add Earnings
+$5.25
Final Amount
$14.00
Step 1: Start with initial amount

Mia starts with $12.50

Step 2: Subtract money spent

$12.50 - $3.75 = $8.75

Step 3: Add money earned

$8.75 + $5.25 = $14.00

Step 4: State the final answer

Mia has $14.00

Mia has $14.00
Final answer:

Mia has $14.00

Applied rules:

• Left to right: Solve operations in order they appear

• Decimal alignment: Keep decimal points aligned during calculations

• Positive/negative: Spending decreases, earning increases amount

💰
$12.50
Start
🍽️
-$3.75
Lunch
👨‍👩‍👧‍👦
+$5.25
Help
✅
$14.00
End
2 Multiplication and Addition
Exercise 2
David bought 4 notebooks for $1.25 each and 2 pens for $0.75 each. How much did he spend in total?
Definition:

Unit Price: Cost of one item; Total cost = Unit price × Quantity

Notebooks
4 × $1.25 = $5.00
Pens
2 × $0.75 = $1.50
Total
$6.50
Step 1: Calculate cost of notebooks

4 notebooks × $1.25 each = $5.00

Step 2: Calculate cost of pens

2 pens × $0.75 each = $1.50

Step 3: Add both amounts

$5.00 + $1.50 = $6.50

Step 4: State the total

David spent $6.50 in total

David spent $6.50 in total
Final answer:

David spent $6.50 in total

Applied rules:

• Multiplication: Find total cost per item type

• Addition: Combine costs of different items

• Unit pricing: Multiply quantity by unit price

$1.25
×
4
=
$5.00
3 Division and Subtraction
Exercise 3
Emma had $20.00. She bought 5 identical toys and received $2.50 in change. How much did each toy cost?
Definition:

Division: Sharing equally; Cost per item = Total spent ÷ Number of items

Started With
$20.00
Received Change
-$2.50
Amount Spent
$17.50
Per Toy
$3.50
Step 1: Find total amount spent

$20.00 - $2.50 = $17.50

Step 2: Divide by number of toys

$17.50 ÷ 5 toys = $3.50 per toy

Step 3: Verify the answer

5 toys × $3.50 = $17.50; $17.50 + $2.50 = $20.00 ✓

Step 4: State the answer

Each toy cost $3.50

Each toy cost $3.50
Final answer:

Each toy cost $3.50

Applied rules:

• Subtraction: Find amount spent by subtracting change

• Division: Divide total spent by number of items

• Verification: Multiply back to check answer

💰
$20.00
Start
🪆
5 toys
Bought
🪙
$2.50
Change
🏷️
$3.50
Each
Mixed Operations Concepts and Rules
Total = (Price × Quantity) + Other Costs
Multiplication Plus Addition
Operation
Addition (+)
Total, combine, increase
Operation
Subtraction (-)
Take away, decrease, difference
Operation
Multiplication (×)
Groups, rate, per unit
Operation
Division (÷)
Share, divide, per person
Key definitions:

Mixed Operations: Problems requiring multiple arithmetic operations

Unit Price: Cost of one item (e.g., $2.50 per apple)

Total Cost: Sum of all expenses

Complete methodology:
  1. Read the problem: Identify what you need to find
  2. Find key information: Note all numbers and operations needed
  3. Determine sequence: Decide which operations to perform first
  4. Solve step by step: Follow proper order of operations
  5. Check your work: Verify with estimation or inverse operations
Tip 1: Look for clue words: "total" (add), "each" (multiply/divide), "left" (subtract).
Tip 2: Break complex problems into smaller parts.
Tip 3: Always align decimal points when adding or subtracting money.
Tip 4: Estimate your answer first to catch major errors.
Common errors: Misaligning decimals, doing operations in wrong order, forgetting to carry.
Practice areas: Multi-step problems, unit pricing, making change.
Order of Operations for Money:

• Parentheses first

• Multiplication/Division (left to right)

• Addition/Subtraction (left to right)

Cost per Item = Total Spent ÷ Number of Items
Finding Unit Price
Solution: Exercises 4 to 5
4 Complex Mixed Operations
Exercise 4
James earned $15.00 from mowing lawns. He spent $4.50 on snacks, saved half of the remaining money, and gave the rest to charity. How much did he give to charity?
Definition:

Fraction of Amount: Half means divide by 2, or multiply by 1/2

Earned
$15.00
Spent
-$4.50
Remaining
$10.50
Saved
$5.25
Charity
$5.25
Step 1: Calculate remaining after spending

$15.00 - $4.50 = $10.50

Step 2: Calculate amount saved (half)

$10.50 ÷ 2 = $5.25

Step 3: Calculate amount given to charity

$10.50 - $5.25 = $5.25

Step 4: Verify the answer

$4.50 + $5.25 + $5.25 = $15.00 ✓

James gave $5.25 to charity
Final answer:

James gave $5.25 to charity

Applied rules:

• Sequential operations: Perform operations in logical order

• Division for fractions: Half means divide by 2

• Verification: All parts should add up to original amount

💼
$15.00
Earned
🍔
$4.50
Spent
🏦
$5.25
Saved
❤️
$5.25
Charity
5 Multi-step Shopping Problem
Exercise 5
Sarah had $30.00. She bought 3 shirts at $4.95 each, 2 pairs of socks at $1.50 each, and then spent half of what was left on a hat. How much money did she have remaining?
Definition:

Multi-step problems: Require several calculations in sequence

Shirts
3 × $4.95 = $14.85
Socks
2 × $1.50 = $3.00
Total Spent
$17.85
Remaining
$12.15
Hat
$6.08
Final
$6.07
Step 1: Calculate cost of shirts

3 shirts × $4.95 = $14.85

Step 2: Calculate cost of socks

2 pairs × $1.50 = $3.00

Step 3: Find total spent on clothes

$14.85 + $3.00 = $17.85

Step 4: Find remaining after clothes

$30.00 - $17.85 = $12.15

Step 5: Calculate hat cost (half remaining)

$12.15 ÷ 2 = $6.075 ≈ $6.08

Step 6: Find final amount

$12.15 - $6.08 = $6.07

Sarah had $6.07 remaining
Final answer:

Sarah had $6.07 remaining

Applied rules:

• Multiple multiplications: Calculate each item type separately

• Sequential subtraction: Work through each expense

• Rounding: Money typically rounds to nearest cent

💰
$30.00
Start
👕
$14.85
Shirts
🧦
$3.00
Socks
👒
$6.08
Hat
✅
$6.07
End
Money Word Problems Mixed Operations Summary
Comprehensive Summary of Mixed Operations
Definitions of Key Concepts:

Mixed Operations: Problems that require more than one arithmetic operation to solve (addition, subtraction, multiplication, division).

Unit Price: The cost of one item. Example: $2.50 per apple.

Total Cost: The sum of all individual costs. Example: 3 apples at $2.50 each = $7.50 total.

Rate Problems: Problems involving cost per unit time or quantity. Example: $5 per hour of work.

Core Rules and Principles:

• Order of Operations: Perform operations from left to right unless parentheses indicate otherwise.

• Decimal Alignment: Always align decimal points when adding or subtracting money.

• Multiplication First: When calculating total cost, multiply quantity by unit price first.

• Verification: Always check that your answer makes sense in the context of the problem.

Step-by-Step Methods:

1. Read Carefully: Identify what the problem is asking for.

2. Highlight Key Information: Note all numbers and operations mentioned.

3. Determine Sequence: Decide which operations to perform first.

4. Solve Systematically: Perform calculations step by step.

5. Check Answer: Verify your answer is reasonable and accurate.

Examples from Simple to Advanced:

Simple: $5.00 + $2.00 = $7.00

Medium: 3 items × $1.50 each + $0.75 tax = $5.25

Advanced: $20.00 - (4 × $2.25) ÷ 2 = $11.00 remaining

Tips and Tricks:

• Clue Words: "Total" means add, "each" often means multiply or divide, "left" means subtract.

• Estimate First: Round numbers to estimate your answer before calculating precisely.

• Draw Diagrams: Visual representations can help organize complex problems.

• Check Units: Make sure your answer is in the correct monetary unit.

Common Pitfalls to Avoid:

• Misaligning decimal points during addition/subtraction

• Performing operations in the wrong order

• Forgetting to convert fractions to decimals when necessary

• Not rounding money to the nearest cent

Key Takeaways for Memorization:

• Always align decimal points when adding or subtracting money

• "Per" or "each" usually indicates multiplication or division

• Break complex problems into smaller, manageable steps

• Verify your answer by checking if it's reasonable in the problem's context

Total = Σ(Unit Price × Quantity)
Calculating Total Cost
➕
Addition
Combine amounts
➖
Subtraction
Remove amounts
✖️
Multiplication
Groups/rates
➗
Division
Share equally

Questions & Answers

Question: How do I know which operation to do first in a mixed operations problem?

Answer: In money word problems, follow the story chronologically:

  • Look for clue words: "total" suggests addition, "each" suggests multiplication/division
  • Follow the sequence of events described in the problem
  • Calculate unit costs first (multiplication), then combine amounts (addition)
  • When dividing, ensure you're sharing or splitting appropriately

Example: "I bought 3 items at $2 each, then spent $1 more" → (3 × $2) + $1

Question: When I have to divide money, how do I handle cents that don't divide evenly?

Answer: When money doesn't divide evenly:

  • Round to the nearest cent (hundredth of a dollar)
  • Look for context clues in the problem
  • If sharing money, some people might get slightly more or less
  • When calculating unit price, round to make the answer practical

Example: $10.00 ÷ 3 people = $3.333... ≈ $3.33 per person, with $0.01 left over

Always consider what makes sense in the real-world scenario!

Question: What if I get confused about whether to add or subtract in a problem?

Answer: Think about the situation:

  • Addition: When money comes IN (earnings, gifts, combining amounts)
  • Subtraction: When money goes OUT (spending, paying, losing)
  • Keywords: Earned, received, total, combined vs. spent, paid, left, remaining

Example: "I earned $5 and then spent $2" → $5 + (not spent) then $5 - $2

Draw a simple picture showing money coming in and going out!