Solved Exercises on Making Changes in Money and Time

Master making changes: counting coins, calculating change, telling time, and solving real-world problems through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Counting Coins
Exercise 1
Sarah has 3 quarters, 2 dimes, 1 nickel, and 4 pennies. How much money does she have?
Definition:

Coin values: Penny = $0.01, Nickel = $0.05, Dime = $0.10, Quarter = $0.25

Coin counting method:
  1. Identify the number of each type of coin
  2. Multiply the count by the value of each coin
  3. Add all amounts together
Coins
3Q + 2D + 1N + 4P
Values
$0.75 + $0.20 + $0.05 + $0.04
Total
$1.04
Step 1: Count quarters

3 quarters × $0.25 = $0.75

25¢ 25¢ 25¢ = $0.75
Step 2: Count dimes

2 dimes × $0.10 = $0.20

10¢ 10¢ = $0.20
Step 3: Count nickels

1 nickel × $0.05 = $0.05

5¢ = $0.05
Step 4: Count pennies

4 pennies × $0.01 = $0.04

1¢ 1¢ 1¢ 1¢ = $0.04
Step 5: Add all amounts

$0.75 + $0.20 + $0.05 + $0.04 = $1.04

Sarah has $1.04
Final answer:

Sarah has $1.04

Applied rules:

• Counting coins: Multiply quantity by value

• Decimal addition: Align decimal points when adding

• Money notation: Use dollar sign and decimal for amounts

2 Calculating Change
Exercise 2
Tom buys a toy for $3.45 and pays with a $5 bill. How much change should he receive?
Definition:

Change calculation: Change = Amount Paid - Cost of Item

Amount Paid
$5.00
Cost
$3.45
Change
$1.55
Step 1: Set up the subtraction

$5.00 - $3.45

$5.00 - $3.45
Step 2: Subtract cents

Since 0 < 5, borrow from dollars: 100¢ - 45¢ = 55¢

Step 3: Subtract dollars

$4 - $3 = $1

Step 4: Combine results

$1 + $0.55 = $1.55

Tom should receive $1.55 in change
Final answer:

Tom should receive $1.55 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

3 Time Calculation
Exercise 3
A movie starts at 2:30 PM and lasts for 1 hour and 45 minutes. What time does it end?
Definition:

Time calculation: Add hours and minutes separately, adjusting for overflow

Start Time
2:30 PM
Duration
1h 45m
End Time
4:15 PM
Step 1: Add hours

2:30 PM + 1 hour = 3:30 PM

Step 2: Add minutes

3:30 PM + 45 minutes = 3:75 PM

Step 3: Adjust for overflow

Since 75 minutes > 60, convert: 75 minutes = 1 hour 15 minutes

So 3:75 PM = 4:15 PM

Step 4: Final time

The movie ends at 4:15 PM

The movie ends at 4:15 PM
Final answer:

The movie ends at 4:15 PM

Applied rules:

• Time addition: Add hours and minutes separately

• Overflow adjustment: Convert minutes > 60 to hours

• AM/PM: Keep track of AM/PM when crossing noon/midnight

Coin Values and Time Rules
$0.01 + $0.05 + $0.10 + $0.25 = $0.41$
One of Each Coin
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
Change = Amount\ Paid - Cost
Change Formula
End\ Time = Start\ Time + Duration
Time Addition
Time Conversion: 60 minutes = 1 hour, 12 hours = half day
Money Conversion: 100 cents = $1, 4 quarters = $1
Key Concepts, Methods, and Memory Aids
100¢ = \$1
Money Conversion
Key definitions:

Counting coins: Adding the value of multiple coins together

Calculating change: Finding the difference between payment and cost

Time calculation: Adding duration to start time to find end time

Complete methodology:
  1. Identify the problem type: Is it counting coins, calculating change, or time?
  2. Organize the information: List all known values
  3. Apply the appropriate formula: Use coin values, change formula, or time addition
  4. Perform the calculation: Add, subtract, or convert as needed
  5. Verify the result: Check if the answer makes sense
Tip 1: Count largest coins first (quarters, then dimes, nickels, pennies).
Tip 2: To calculate change, think "what do I add to the cost to get the amount paid?"
Tip 3: When adding time, add hours first, then minutes, and adjust if over 60.
Tip 4: Remember: 4 quarters = 1 dollar, 2 half-dollars = 1 dollar.
Common errors: Miscounting coins, forgetting to convert 60+ minutes to hours, misaligning decimals in money calculations.
Memory aids: "Quarter" sounds like "four" (25 cents × 4 = $1), "Dime" is small but worth 10 cents.
Essential facts to remember:

• Penny = $0.01, Nickel = $0.05, Dime = $0.10, Quarter = $0.25

• Change = Amount Paid - Cost

• 60 minutes = 1 hour

• 100 cents = $1.00

• Time addition: Hours + Minutes, then adjust for overflow

Visual Learning Infographic
Making Changes Infographic
💰
Coin Recognition
1¢ Penny - Copper color
5¢ Nickel - Silver, thick
10¢ Dime - Small, silver
25¢ Quarter - Large, silver
Change Process
Steps to Calculate Change
1
Identify cost
2
Identify payment
3
Subtract
4
Check answer
Time Calculation
Start Time + Duration = End Time

If minutes ≥ 60, convert to hours

Example: 2:45 + 1:30 = 3:75 = 4:15

Common Mistakes
  • Confusing dime and penny values
  • Forgetting to convert 60+ minutes
  • Misaligning decimal points
  • Not checking if answer is reasonable
Memory Tricks

• "Quarter" has 4 letters = 4×25¢=$1

• Dime is small but worth 10¢

• Nickels are worth 5¢ each

• Pennies are worth 1¢ each

Success Checklist
  • Did I identify the coin values correctly?
  • Did I align decimal points when adding/subtracting?
  • Did I convert minutes to hours when necessary?
  • Does my answer make sense in context?
Money and Time Relationships

Counting coins → Adding values

Calculating change → Subtraction

Telling time → Addition with conversions

Practice Makes Perfect!

Questions & Answers

Question: I get confused when I have to count mixed coins. How can I keep track better?

Answer: Great question! Here's a systematic approach:

  • Sort first: Put all the same coins together
  • Count in order: Start with the highest value coins (quarters, then dimes, nickels, pennies)
  • Group by tens: Count pennies in groups of 10 to make it easier
  • Keep a running total: Add each coin value as you go

Example: If you have 2 quarters, 3 dimes, 1 nickel, and 6 pennies:

  • 2 quarters = $0.50
  • 3 dimes = $0.30 (total now: $0.80)
  • 1 nickel = $0.05 (total now: $0.85)
  • 6 pennies = $0.06 (final total: $0.91)

Practice with real coins to build muscle memory!

Question: When I subtract to find change, I sometimes get the wrong answer. How can I check my work?

Answer: Checking your subtraction is crucial! Here are two effective methods:

  • Addition check: Take your answer and add it to the cost. Does it equal the amount paid?
  • Counting up: Start with the cost and count up to the amount paid

Example: Item costs $2.35, paid with $5.00

  • Your answer: $2.65 in change
  • Check: $2.35 + $2.65 = $5.00 ✓
  • Or count up: $2.35 → $2.40 (+5¢) → $2.50 (+10¢) → $3.00 (+50¢) → $5.00 (+$2.00) = $2.65

Always double-check your work with one of these methods!

Question: I get confused when adding time and the minutes go over 60. Can you explain how to handle this?

Answer: Adding time with overflow is just like carrying in regular addition! Think of it this way:

  • Minutes work like a base-60 system (not base-10 like normal numbers)
  • When minutes reach 60 or more, convert every 60 minutes to 1 hour
  • Keep the remainder as minutes

Example: 1:45 + 2:30

  • Add hours: 1 + 2 = 3 hours
  • Add minutes: 45 + 30 = 75 minutes
  • Convert: 75 minutes = 60 + 15 = 1 hour and 15 minutes
  • Total: 3 hours + 1 hour and 15 minutes = 4 hours and 15 minutes

Think of it as: "Every 60 minutes becomes 1 hour, just like 10 ones become 1 ten!"