Make correct change using currency

Ontario Grade 11 Mathematics

Earning and Purchasing

MEL3E study topic A3.7: Find the change owed and give it using suitable Canadian bills and coins.

At a store or workplace, correct change means returning the right amount of money to a customer. You need to know the total due, how much the customer gives you, and what amount to return.

The amount due is the total the customer must pay. The amount tendered is the money the customer gives the cashier. Change is the money returned when the customer pays more than the amount due. If the customer pays less, no change is owed yet.

You can find change by subtracting the amount due from the amount tendered. You can check by counting up from the amount due to the amount tendered. A calculator can check the arithmetic, but you must still make sure the bills and coins you hand over add to the change owed.

What you will learn

Find the change owed when a customer pays more than the amount due.
Check change by counting up or adding the change back to the amount due.
Choose bills and coins that add to the correct change amount.
Use cash rounding to the nearest five cents when the final cash total needs it.

1. Read the amounts carefully

Start by reading the final amount due on the receipt or register. Then check how much cash the customer gives you. If the customer gives exactly the amount due, the change is zero. If the customer gives less, they still owe money.

For a cash purchase in Canada, pennies are not used, so the final cash total is rounded to the nearest five cents. Totals ending in one or two cents round down to the nearest five-cent amount. Totals ending in three or four cents round up. The same pattern applies to six or seven cents (down) and eight or nine cents (up). Totals ending in zero or five cents stay as they are. Round only the final total, not each item on the receipt. Electronic payments use the exact total shown.

For example, if a cash total is CAD 12.32, the amount due becomes CAD 12.30. A cash total of CAD 12.34 becomes CAD 12.35. Once you know the correct amount due, use it to work out change.

\text{change} = \text{amount tendered} - \text{amount due}

Amount due is what the customer must pay.
Amount tendered is the money the customer gives.
Change is returned only when the amount tendered is greater than the amount due.
For cash, round the final total to the nearest five cents when needed.

2. Find change and check it

Subtract the amount due from the amount tendered. This works because the change is the part of the payment left after the amount due has been covered. The amount tendered should be larger; otherwise, stop and check whether the customer has paid enough.

You can check the result by counting up. Begin at the amount due and make small jumps until you reach the amount tendered. Add the jumps. Their total should match the change found by subtraction.

For example, to check CAD 5.65 in change from a CAD 10.00 payment when the amount due is CAD 4.35, count from CAD 4.35 to CAD 5.00, then from CAD 5.00 to CAD 10.00. The jumps are CAD 0.65 and CAD 5.00. Together, they make CAD 5.65.

A second check is to add the change to the amount due. The total should match the amount tendered. This catches errors before you hand over the money.

\text{amount due} + \text{change} = \text{amount tendered}

Subtract the amount due from the amount tendered.
Count up to check: the jumps must add to the change.
Adding the change to the amount due should give the amount tendered.

3. Choose bills and coins

After finding the change amount, choose bills and coins whose values add to it. Start with a large suitable value, then use smaller values for the remaining amount. Canadian everyday currency includes bills and coins such as five-cent, ten-cent, and twenty-five-cent coins, one-dollar and two-dollar coins, and bills. Check the value on each piece before giving it to the customer.

There can be more than one correct way to make an amount. What matters is that the values add exactly to the change owed. Keep the customer’s payment separate from the change as you count. This makes it easier to spot a mistake.

At work, follow the register display and your workplace’s cash-handling steps. If the register amount and your calculation do not match, pause and check before handing over cash. A calculator can help with subtraction. You can also practise transactions in a spreadsheet. Use technology to check your work, not to skip reading the amount due or counting the money.

Use bills and coins whose values add to the change owed.
Check each value and count the money as you hand it over.
Pause and recheck if your calculation and the register do not agree.

4. Use a steady routine

Use the same routine for each cash transaction: read the final amount due, apply cash rounding if needed, check the amount tendered, subtract to find the change, and check the result. Then choose bills and coins that add to the change amount and count them as you give them to the customer.

The final check is simple: the amount due plus the change should equal the amount tendered. If it does not, recount the money and check the figures before finishing the transaction. Taking a moment to check is better than giving the wrong amount.

\text{amount due} + \text{change} = \text{amount tendered}

Read, round if needed, subtract, check, and count out.
Make sure the bills and coins match the change amount.
Do not finish the transaction until the amounts agree.

Worked example

Cash purchase with a rounded total

A customer’s receipt total is CAD 18.72. They pay with a CAD 20 bill. Find the cash change and show one suitable way to give it.

Round the final cash total
The total ends in two cents, so round it down to CAD 18.70. The total is rounded once, after the items have been added.
$18.72 \rightarrow 18.70$
Subtract to find the change
Subtract the rounded amount due from the CAD 20 payment. The difference is the amount to return.
$20.00 - 18.70 = 1.30$
Choose suitable coins
A dollar coin, a quarter, and a nickel add to CAD 1.30. These are suitable Canadian coins for an everyday cash transaction.
$1.00 + 0.25 + 0.05 = 1.30$

Answer: The customer receives CAD 1.30 in change: one dollar coin, one quarter, and one nickel.

Check: Adding CAD 1.30 to the rounded amount due of CAD 18.70 gives CAD 20.00, the amount tendered.

Worked example

Check change by counting up

A customer buys an item for CAD 26.45 and pays with a CAD 50 bill. Find the change and check it by counting up.

Find the difference
The amount due ends in five cents, so cash rounding is not needed. Subtract the amount due from the amount tendered.
$50.00 - 26.45 = 23.55$
Count up to check
Count from CAD 26.45 to CAD 27.00, then to CAD 30.00, and finally to CAD 50.00. The jumps are CAD 0.55, CAD 3.00, and CAD 20.00. Their total confirms the change.
$0.55 + 3.00 + 20.00 = 23.55$
Give a matching amount
One suitable set is a twenty-dollar bill, a two-dollar coin, a one-dollar coin, a fifty-cent coin, and a five-cent coin. Their values make the change amount.
$20.00 + 2.00 + 1.00 + 0.50 + 0.05 = 23.55$

Answer: The customer receives CAD 23.55 in change.

Check: The amount due plus the change is CAD 26.45 plus CAD 23.55, which equals CAD 50.00.

Common mistakes and how to avoid them

Subtracting the amount tendered from the amount due.

Correction: When the customer has paid enough, subtract the smaller amount due from the larger amount tendered.

Rounding each item on a cash receipt.

Correction: Add the items first, then round only the final cash total when needed.

Forgetting the cents when choosing bills and coins.

Correction: Check the full change amount, including cents, and make sure the coins complete the total.

Counting bills but not checking the coins.

Correction: Count both bills and coins, then confirm their total matches the change owed.

Lesson summary

Identify the amount due and amount tendered.
For cash, round the final total to the nearest five cents when needed.
Subtract the amount due from the amount tendered to find change.
Check by counting up or adding the change back to the amount due.
Choose bills and coins whose values add to the change amount.

Check your understanding

Question 1

A cash total is CAD 9.68. The customer pays CAD 10. What change should they receive?

CAD 0.30
CAD 0.32
CAD 0.35
CAD 1.32

Show answer and explanation

CAD 0.30

A cash total ending in eight cents rounds up to CAD 9.70. Subtracting CAD 9.70 from CAD 10.00 gives CAD 0.30.

Question 2

A customer owes CAD 14.25 and pays CAD 20. Which check confirms CAD 5.75 in change?

Add CAD 5.75 to CAD 14.25 to get CAD 20.00.
Subtract CAD 5.75 from CAD 20.00 to get CAD 15.25.
Add CAD 14.25 to CAD 20.00 to get CAD 34.25.
Subtract CAD 14.25 from CAD 5.75 to get CAD 8.50.

Show answer and explanation

Add CAD 5.75 to CAD 14.25 to get CAD 20.00.

Add the change to the amount due. CAD 14.25 plus CAD 5.75 equals CAD 20.00, the amount tendered.

Key terms

Amount due: The total a customer must pay.
Amount tendered: The money a customer gives to pay.
Change: Money returned when a customer gives more than the amount due.
Cash rounding: Rounding the final cash total to the nearest five cents when needed, because pennies are not used in cash transactions.

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 11 Mathematics (MEL3E), expectation A3.7. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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