Making Change
Learn how to calculate the correct change when paying for items with cash.
Definition
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Worked Examples
You buy a book for 7 dollars and pay with a 10 dollar bill. How much change do you get?
Identify the amounts
Purchase price: 7 dollars. Amount paid: 10 dollars → 7 and 10
Subtract to find change
→ 3 dollars
Count the bills
Three 1 dollar bills make 3 dollars → 3 one-dollar bills
Answer: You get 3 dollars in change.
Common Mistakes
Forgetting to borrow when subtracting cents
Why it's wrong: When the cents you are subtracting is larger than the cents you have, you need to borrow from the dollars.
Correct: If subtracting 75 cents from 50 cents, borrow 1 dollar (100 cents) first: 150 - 75 = 75 cents, then subtract the borrowed dollar from the dollars.
Confusing the price and amount paid
Why it's wrong: Change should always be positive! If you get a negative answer, you probably subtracted in the wrong order.
Correct: Always subtract: Amount Paid - Purchase Price. The larger number (what you gave) minus the smaller (what it costs).
Giving wrong coin combinations
Why it's wrong: There are often multiple ways to make the same amount, but some are more efficient.
Correct: Use the fewest coins possible. For 75 cents, use 3 quarters instead of 7 dimes and 1 nickel.
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Practice Problems
17 problemsYou buy a pencil for 2 dollars and pay with a 5 dollar bill. How much change do you get?
Why It Matters
- Shopping: Verify that cashiers give you the correct change
- Working: Many jobs involve handling cash and making change for customers
- Selling: At garage sales, lemonade stands, or fundraisers
- Budgeting: Understanding exactly how much money you have left after purchases
Real World Applications
Working as a Cashier
Cashiers must quickly calculate change for every cash transaction to keep lines moving and customers happy.
Example:
A customer buys items totaling 23.47 dollars and pays with 30 dollars. The cashier gives back 6.53 dollars: one 5 dollar bill, one 1 dollar bill, two quarters, and 3 pennies.
A customer buys a meal for 8.75 dollars and pays with a 10 dollar bill.
What change should you give?
Step 1: Write the mathematical expression
Calculate:
Garage Sale
Running a garage sale means making change all day long for different items at various prices.
Example:
You sell a game for 4 dollars. The buyer gives you a 20 dollar bill. You need to count back 16 dollars in change.
Someone buys three items: a book for 2 dollars, a toy for 3.50 dollars, and a puzzle for 1.75 dollars. They pay with a 10 dollar bill.
How much change do you give?
Step 1: Write the mathematical expression
First add: , then subtract from 10
Checking Your Change
Always count your change to make sure you received the correct amount. Mistakes happen!
Example:
You buy a drink for 2.50 dollars and pay with a 5 dollar bill. You should get 2.50 dollars back. If the cashier only gives you 2 dollars, speak up politely!
You buy a sandwich for 6.25 dollars and pay with a 20 dollar bill. The cashier gives you 13.25 dollars in change.
Is this correct? If not, how much should you have received?
Step 1: Write the mathematical expression
Calculate:
Key Takeaways
- 1Change equals the amount paid minus the purchase price
- 2The counting up method: start at the price and count up to the amount paid
- 3Use the fewest bills and coins possible for efficient change
- 4Always double-check your change to catch any mistakes
Frequently Asked Questions
Glossary
- Change
- The money returned to you when you pay more than the purchase price
- Purchase price
- The cost of the item or items you are buying
- Counting up
- A method of finding change by adding from the price to the amount paid
- Denomination
- The value printed on a bill or coin (1 dollar, 5 dollars, 25 cents, etc.)