Calculate change
Theory
Calculating change is a Year 3 money skill: working out how much money you get back when you pay with more than something costs. The change is the amount paid minus the cost. This Year 3 maths page shows how to subtract, how to count on from the price up to the note, and how to add up the Australian coins that make the change. In the Australian Curriculum this is Year 4 content and in the Victorian Curriculum it is Level 4; it is taught in Year 3 in Western Australia. Curriculum: VC2M4N08 (Level 4) / AC9M4N07, AC9M4N08 (Year 4).
Change is the money you get back when you pay with more than something costs. If a drink costs \(\$3.00\) and you hand over a \(\$5\) note, you get \(\$2.00\) change.
To find the change, take the cost away from the money you paid: change = amount paid − cost. When the price has cents you can also count on from the cost: jump up to the next whole dollar first, then up to the note, and add the jumps.
The change is often handed back as coins and notes. In Australia the coins are \(5\)c, \(10\)c, \(20\)c, \(50\)c, \(\$1\) and \(\$2\). Because there are no \(1\)c or \(2\)c coins, a cash total is rounded to the nearest \(5\)c before the change is worked out.
There is one rule to remember for change, plus a handy way to check it.
How to work out change
- Find the amount paid. Add up the notes and coins handed over. Two \(\$5\) notes make \(\$10.00\).
- Find the cost. If there is more than one item, add the prices to get the total cost first.
- Take the cost away. Subtract, or count on from the cost up to the next dollar and then up to the amount paid.
- Write the change. Give the answer in dollars and cents, and check by adding it back onto the cost.
Handing back the change
- Fewest coins. Give the biggest note or coin that fits, then the biggest for what is left, until the change is made.
- Estimate first. Round the price to the nearest dollar to get a quick idea of the change, then work out the exact amount.
| \(\text{change}\) | \(=\) | \(\$5.00 - \$4.20\) |
| \(\text{change}\) | \(=\) | \(80\text{c}\) |
Count on: 80c makes \(\$4.20\) up to \(\$5.00\).
| \(\$6.15 \to \$6.20\) | \(:\) | \(5\text{c}\) |
| \(\$6.20 \to \$7.00\) | \(:\) | \(80\text{c}\) |
| \(\$7.00 \to \$10.00\) | \(:\) | \(\$3.00\) |
| \(5\text{c} + 80\text{c} + \$3.00\) | \(=\) | \(\$3.85\) |
The change is \(\$3.85\). Check: \(\$6.15 + \$3.85 = \$10.00\).
| \(\text{total}\) | \(=\) | \(\$2.60 + \$3.85 = \$6.45\) |
| \(\text{change}\) | \(=\) | \(\$10.00 - \$6.45\) |
| \(\text{change}\) | \(=\) | \(\$3.55\) |
Add the prices first, then subtract from \(\$10\).
| \(\$41.50 \to \$42.00\) | \(:\) | \(50\text{c}\) |
| \(\$42.00 \to \$50.00\) | \(:\) | \(\$8.00\) |
| \(50\text{c} + \$8.00\) | \(=\) | \(\$8.50\) |
The change is \(\$8.50\).
| \(\$19.85\) | \(\approx\) | \(\$20\) |
| \(\$50 - \$20\) | \(=\) | \(\$30\) |
| \(\$50.00 - \$19.85\) | \(=\) | \(\$30.15\) |
The change is about \(\$30\). The exact change is \(\$30.15\).
| \(\$1.65 - \$1\) | \(=\) | \(65\text{c}\) |
| \(65\text{c} - 50\text{c}\) | \(=\) | \(15\text{c}\) |
| \(15\text{c} - 10\text{c}\) | \(=\) | \(5\text{c}\) |
Give a \(\$1\) coin, a \(50\)c coin, a \(10\)c coin and a \(5\)c coin: \(4\) coins.
Common pitfalls
Frequently asked questions
How do you work out change?
Change equals the amount paid minus the cost. Take the price away from the money you hand over. For a \(\$4.20\) item paid with a \(\$5\) note, the change is \(\$5.00 - \$4.20 = 80\text{c}\).
How do you count on to find change?
Start at the cost and jump up to the next whole dollar, then up to the note. Add the jumps. From \(\$6.15\) you jump \(5\)c to \(\$6.20\), \(80\)c to \(\$7.00\), then \(\$3.00\) to \(\$10.00\), so the change is \(\$3.85\).
How do you find change when you buy two things?
Add the two prices first to get the total cost, then take that total away from the money paid. A \(\$2.60\) juice and a \(\$3.85\) muffin total \(\$6.45\), so the change from \(\$10\) is \(\$3.55\).
Why is cash rounded to the nearest 5 cents in Australia?
Australia no longer has 1c or 2c coins, so a cash total is rounded to the nearest 5c before the change is worked out. Paying by card does not round.
Is change the same as the total cost?
No. The total cost is what the items are worth. The change is the money left over and handed back after you pay, which is the amount paid minus the cost.
How do you check your change is correct?
Add the change back onto the cost. If it equals the amount you paid, the change is right. For a \(\$2.45\) toy paid with \(\$5\), \(\$2.45 + \$2.55 = \$5.00\), so \(\$2.55\) change is correct.
Why do some people pay with a note and a few coins?
It can make the change simpler. For a \(\$3.60\) item, paying \(\$5\) gives \(\$1.40\) change (three coins). Paying \(\$5.10\) gives \(\$1.50\) change, which is just a \(\$1\) coin and a \(50\)c coin.
How do you estimate change?
Round the price to the nearest dollar and subtract from the money paid. A \(\$19.85\) jacket is about \(\$20\), so the change from \(\$50\) is about \(\$30\).