Solved Exercises on Practice Change Process

Master making change: calculating correct amounts, giving proper change, and solving real-world transaction problems through these 3 detailed exercises.

Solution: Change Process Exercises 1 to 3
1 Simple Change
Exercise 1
Emma buys a toy that costs $2.35. She gives the cashier $5.00. How much change should she receive?
Definition:

Change calculation: Change = Amount Paid - Cost of Item

Change process method:
  1. Identify the cost of the item
  2. Identify the amount paid
  3. Subtract the cost from the amount paid
  4. Express the change in dollars and cents
Amount Paid
$5.00
Cost
$2.35
Change
$2.65
1 Identify: Cost = $2.35, Paid = $5.00
2 Calculate: $5.00 - $2.35
3 Subtract: Since 0 < 5, borrow from dollars
4 Result: $2.65 in change
Step 1: Set up the subtraction

$5.00 - $2.35

$5.00 - $2.35
Step 2: Subtract cents

Since 0 < 5, borrow from dollars: 100¢ - 35¢ = 65¢

Step 3: Subtract dollars

$4 - $2 = $2

Step 4: Combine results

$2 + $0.65 = $2.65

Emma should receive $2.65 in change
Final answer:

Emma should receive $2.65 in change

Applied rules:

• Change formula: Change = Amount Paid - Cost

• Borrowing: When subtracting decimals, borrow from higher place value

• Money operations: Align decimal points during calculations

2 Complex Change
Exercise 2
Tom buys a book for $4.75 and a pencil for $0.65. He gives the cashier $10.00. How much change should he receive?
Definition:

Multi-item purchase: First calculate total cost, then subtract from amount paid

Items
$4.75 + $0.65 = $5.40
Paid
$10.00
Change
$10.00 - $5.40 = $4.60
1 Calculate total cost: $4.75 + $0.65 = $5.40
2 Identify amount paid: $10.00
3 Calculate change: $10.00 - $5.40
4 Result: $4.60 in change
Step 1: Calculate total cost

$4.75 + $0.65 = $5.40

Step 2: Set up the subtraction

$10.00 - $5.40

Step 3: Subtract dollars

$10 - $5 = $5

Step 4: Subtract cents

$0.00 - $0.40, so borrow: $5.00 becomes $4.60

Step 5: Final result

Tom should receive $4.60 in change

Tom should receive $4.60 in change
Final answer:

Tom should receive $4.60 in change

Applied rules:

• Multi-step process: Add items first, then subtract from payment

• Decimal alignment: Align decimal points during addition and subtraction

• Money operations: Borrow when necessary during subtraction

3 Coin Change
Exercise 3
Lisa buys candy for $1.85. She pays with a $2.00 bill. What coins should the cashier give her as change?
Definition:

Coin change: Calculate the exact amount of change and express it using appropriate coins

Amount Paid
$2.00
Cost
$1.85
Change
$2.00 - $1.85 = $0.15
1 Calculate change: $2.00 - $1.85 = $0.15
2 Convert to cents: $0.15 = 15¢
3 Select appropriate coins: 1 dime + 1 nickel
4 Alternative: 3 nickels or 15 pennies
Step 1: Calculate the exact change

$2.00 - $1.85 = $0.15

Step 2: Convert to cents

$0.15 = 15¢

Step 3: Select appropriate coins

Option 1: 1 dime (10¢) + 1 nickel (5¢) = 15¢

Option 2: 3 nickels (5¢ each) = 15¢

Option 3: 15 pennies (1¢ each) = 15¢

Step 4: Choose the most efficient option

Best option: 1 dime + 1 nickel (uses fewest coins)

Cashier should give: 1 dime and 1 nickel
Final answer:

The cashier should give Lisa 1 dime and 1 nickel (or equivalent combination)

Applied rules:

• Coin optimization: Use fewest coins possible to make change

• Value matching: Ensure coin combination equals the exact change amount

• Practical consideration: Choose coins that are commonly available

Complete Summary: Practice Change Process

Definitions of Key Concepts

Change: The money returned to a customer when they pay more than the cost of an item.

Change process: The systematic method of calculating and providing correct change.

Money transaction: The exchange of goods/services for money, including handling change.

Coin combination: Using different coins to make up a specific amount of money.

Core Rules and Principles

• Change formula: Change = Amount Paid - Total Cost

• Decimal subtraction: Align decimal points when subtracting money amounts

• Coin values: Penny = 1¢, Nickel = 5¢, Dime = 10¢, Quarter = 25¢

• Optimization principle: Use the fewest coins possible to make exact change

• Verification rule: Always check that change + cost = amount paid

Step-by-Step Methods

Method 1: Simple Change Calculation

  1. Identify the cost of the item(s)
  2. Identify the amount paid by the customer
  3. Subtract the cost from the amount paid (Change = Paid - Cost)
  4. Express the result in dollars and cents
  5. Verify by adding change back to cost

Method 2: Multi-Item Change Process

  1. Calculate the total cost of all items
  2. Identify the amount paid by the customer
  3. Subtract the total cost from the amount paid
  4. Express the change in dollars and cents
  5. Provide the change to the customer

Method 3: Coin Change Selection

  1. Calculate the exact amount of change needed
  2. Convert the change amount to cents
  3. Select the combination of coins that adds up to the exact amount
  4. Choose the combination that uses the fewest coins possible
  5. Give the coins to the customer
Examples (Simple → Advanced)

Simple Example: Buy a $0.50 apple with $1.00. Change = $1.00 - $0.50 = $0.50 (2 quarters)

Moderate Example: Buy a $3.25 book with $5.00. Change = $5.00 - $3.25 = $1.75 (7 quarters or equivalent)

Advanced Example: Buy items totaling $4.87 with $10.00. Change = $10.00 - $4.87 = $5.13 (5 dollars, 1 dime, 3 pennies)

Tips, Tricks, and Common Pitfalls

Tips:

  • Always double-check your subtraction by adding change back to the cost
  • For coin change, start with the largest denomination possible
  • Count change out loud when giving it to the customer
  • Practice with real coins to build muscle memory

Common Pitfalls:

  • Subtracting the wrong way (cost - paid instead of paid - cost)
  • Forgetting to align decimal points during subtraction
  • Using too many small coins instead of larger denominations
  • Not verifying that change + cost equals amount paid
Key Notes for Memorization

• Change formula: "Paid minus cost equals change"

• Coin values: "Penny = 1¢, Nickel = 5¢, Dime = 10¢, Quarter = 25¢"

• Verification: "Always check: Change + Cost = Amount Paid"

• Efficiency: "Fewer coins is better for making change"

• Practice: "More practice leads to faster, more accurate change-making"

Change Process Rules
Change = Amount\ Paid - Cost
Change Formula
Penny
1¢ = $0.01
Smallest coin
Nickel
5¢ = $0.05
Worth 5 pennies
Dime
10¢ = $0.10
Worth 10 pennies
Quarter
25¢ = $0.25
Worth 25 pennies
Total\ Cost = Item_1 + Item_2 + ... + Item_n
Multi-Item Total
Verification: Change + Cost = Amount\ Paid
Check Your Work
Subtraction Rule: Always subtract cost from amount paid
Coin Optimization: Use fewest coins possible for exact change
Key Concepts, Methods, and Memory Aids
100¢ = \$1
Money Conversion
Key definitions:

Change calculation: Determining the difference between payment and cost

Coin combination: Using different coins to make up exact amounts

Transaction verification: Checking that all amounts add up correctly

Complete methodology:
  1. Identify amounts: Determine cost and amount paid
  2. Apply formula: Change = Amount Paid - Cost
  3. Calculate result: Perform the subtraction carefully
  4. Verify accuracy: Check that change + cost = amount paid
  5. Provide change: Give the correct amount to the customer
Tip 1: Always verify your change calculation by adding it back to the cost.
Tip 2: For coin change, start with the largest coins first (quarters, then dimes, etc.).
Tip 3: Count change out loud when giving it to others to avoid mistakes.
Tip 4: Remember: Change is always positive (amount paid must be greater than cost).
Common errors: Subtracting in wrong order, misaligning decimals, giving wrong coins.
Memory aids: "Paid minus cost gives change," "Check with: Change + Cost = Paid."
Essential facts to remember:

• Change = Amount Paid - Cost

• Always align decimal points during subtraction

• 100 cents = $1.00

• Verify: Change + Cost should equal Amount Paid

• Use fewest coins possible for coin change

Visual Learning Infographic
Change Process Infographic
💰
Change Formula
Change = Amount Paid - Cost
$5.00 - $2.35 = $2.65
Transaction Process
Steps to Calculate Change
1
Note cost
2
Note payment
3
Subtract
4
Verify
Coin Combinations

For $0.15: 1 dime + 1 nickel

For $0.25: 1 quarter

For $0.50: 2 quarters

Always use fewest coins possible!

Common Mistakes
  • Subtracting in wrong order
  • Not aligning decimal points
  • Using too many small coins
  • Not verifying the calculation
Memory Tricks

• "Paid minus cost gives change"

• "Check: Change + Cost = Paid"

  • • Start with largest coins first
  • • Fewer coins is better
    • Success Checklist
    • Did I subtract correctly (Paid - Cost)?
    • Are decimal points aligned?
    • Is the change amount positive?
    • Does Change + Cost = Amount Paid?
    Change Process Flow

    Cost → Payment → Subtraction → Change → Verification

    Practice Makes Perfect!

    Questions & Answers

    Question: I sometimes forget whether to add or subtract when making change. How do I remember?

    Answer: Great question! Here's a simple way to remember:

    • Change is what you get back: You start with more money than the cost, so you subtract to find the difference
    • Think of it this way: If something costs $2 and you give $5, you get back $3 ($5 - $2 = $3)
    • Memory phrase: "What I gave minus what it cost equals what I get back"

    Example: Item costs $1.50, you pay $2.00

    • Change = $2.00 - $1.50 = $0.50
    • You get 50¢ back because you paid more than the cost

    Remember: The customer pays MORE than the cost, so you subtract to find the difference!

    Question: When making change with coins, how do I know which coins to use?

    Answer: Here's the best strategy for selecting coins:

    • Start with the largest coins first: Quarters (25¢), then dimes (10¢), then nickels (5¢), then pennies (1¢)
    • Use as many of each large coin as possible: Before moving to smaller coins
    • Goal: Use the fewest coins possible to make the exact amount

    Example: Making $0.67 in change

    • Quarters: 2 quarters = 50¢ (leaves 17¢)
    • Dimes: 1 dime = 10¢ (leaves 7¢)
    • Nickels: 1 nickel = 5¢ (leaves 2¢)
    • Pennies: 2 pennies = 2¢ (equals 0¢ remaining)
    • Total: 2 quarters + 1 dime + 1 nickel + 2 pennies = $0.67

    This uses 6 coins total, which is efficient!

    Question: How can I check if my change calculation is correct?

    Answer: There are two excellent ways to verify your change calculation:

    • Addition check: Add the change to the cost and see if it equals the amount paid
    • Subtraction check: Subtract your change from the amount paid and see if it equals the cost

    Example: Item costs $3.45, paid $5.00, calculated change as $1.55

    • Addition check: $3.45 + $1.55 = $5.00 ✓
    • Subtraction check: $5.00 - $1.55 = $3.45 ✓

    If both checks work, your calculation is correct! This is a crucial step in making change.