Making Change

Learn how to calculate the correct change when paying for items with cash.

Elementary20 minLesson

Definition

Making change means calculating how much money to give back when someone pays more than the purchase price.

The basic formula is:

\text{Change} = \text{Amount Paid} - \text{Purchase Price}

For example, if you buy something for 3 dollars and 50 cents and pay with a 5 dollar bill:

\text{Change} = 5.00 - 3.50 = 1.50

You should receive 1 dollar and 50 cents back!

Try it now

You buy a pencil for 2 dollars and pay with a 5 dollar bill. How much change do you get?

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

10.00 - 7.00 = 3.00

→ 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.

Interactive Visual

Money Counter

Score: 0/0

Item Price

$9.84

Paid With

$11.00

Change to give: $1.16

Drag coins and bills here (or tap them)

Bills

$100

$50

$20

$10

Coins

dollar coin

25¢

quarter

10¢

dime

5¢

nickel

1¢

penny

Total:$0.00

Range:to

Click on numbers to select them. Adjust the range to explore different values.

Interactive Sandbox

Expression Calculator

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History

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Practice Problems

17 problems

Problem 1 of 17

Easy

You buy a pencil for 2 dollars and pay with a 5 dollar bill. How much change do you get?

Practice Problems: Making Change

1. You buy a pencil for 2 dollars and pay with a 5 dollar bill. How much change do you get?
2. A cookie costs 1 dollar and 50 cents. You pay with 2 dollars. How many cents do you get back?
3. Which formula correctly shows how to calculate change?
4. You buy a toy for 6 dollars and pay with a 10 dollar bill. How much change do you receive?
5. A snack costs 3 dollars and 25 cents. You pay with 5 dollars. Find the change.
6. You buy items for 8 dollars and 47 cents. You pay with a 20 dollar bill. What is your change?
7. A book costs 14 dollars and 85 cents. You pay with a 20 dollar bill. What is your change in dollars and cents? (Write as X.XX)
8. Use the counting up method: A meal costs 7 dollars and 65 cents. You pay with 10 dollars. Find the change by counting up.
9. You buy items totaling 15 dollars and 63 cents. Which combination would be correct change from a 20 dollar bill?
10. You buy three items: a pen for 2 dollars and 50 cents, a notebook for 4 dollars and 25 cents, and an eraser for 1 dollar and 75 cents. You pay with a 20 dollar bill. What is your change?
11. A cashier gives you 3 dollars and 42 cents change. You paid with 10 dollars. What was the price of your purchase?
12. You have a 50 dollar bill. You buy groceries for 37 dollars and 84 cents. Calculate your change and determine how to give it using the fewest bills and coins.
13. A customer pays 23 dollars and 56 cents for items. The cashier accidentally enters 32 dollars and 56 cents. If the customer paid with 50 dollars, how much extra change did they incorrectly receive?
14. You pay for a 67 dollar and 89 cent purchase with a 100 dollar bill. How much change do you get?
15. You are a cashier. A customer buys items totaling 45 dollars and 73 cents and pays with three 20 dollar bills. Calculate the change and describe the bills and coins you would give.
16. What is the minimum number of coins needed to make exactly 87 cents in change? (Using US coins: pennies, nickels, dimes, quarters)
17. You buy candy for 75 cents. You pay with 1 dollar. What is your change?

Why It Matters

Making change is a life skill you will use almost every day:

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

Knowing how to make change helps you manage your money wisely and catch mistakes!

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.

1Try It Yourself

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: $10.00 - 8.75$

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.

2Try It Yourself

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: $2 + 3.50 + 1.75$ , 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!

3Try It Yourself

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: $20.00 - 6.25$

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

Instead of subtracting, you start at the purchase price and count up to the amount paid. For example, from 3.67 to 5.00 dollars: add 3 cents to get 3.70, add 30 cents to get 4.00, add 1 dollar to get 5.00. Your change is 1.33 dollars.

Counting change back helps both the cashier and customer verify the correct amount. It also helps catch mistakes before the customer leaves.

Pay with a larger bill or coin combination, and the cashier will give you the difference back. For example, pay for a 3.25 dollar item with a 5 dollar bill and get 1.75 dollars back.

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.)