Represent money amounts
In this Year 3 money topic (NSW Stage 2, outcomes MA2-AR-01 and MA2-MR-01) students name the Australian coins and notes, count a mixed handful of money and write the total in dollars and cents, using a point and two figures for the cents.
They swap between cents and dollars using 100 cents in a dollar, find different coin combinations for the same amount, make an amount with the fewest coins, add two simple prices, and put money amounts in order by comparing dollars first and then cents.
Theory
Representing money amounts is a Year 3 money skill: naming Australian coins and notes, using dollars-and-cents notation like \(\$4.65\), and changing between cents and dollars where \(100\) cents make \(\$1\). This page shows how to count a group of notes and coins, make an amount with the fewest coins, and compare and order money amounts.
Australian money is made from coins and notes. The coins are \(5\)c, \(10\)c, \(20\)c, \(50\)c, \(\$1\) and \(\$2\). The notes are \(\$5\), \(\$10\), \(\$20\), \(\$50\) and \(\$100\). There is no \(1\)c or \(2\)c coin, so the smallest coin is \(5\)c.
We write amounts in dollars and cents. In \(\$4.65\) the \(4\) is the dollars and the \(65\) is the cents. The dollars go before the point and the cents go after it. The cents part always has two figures, so five cents is \(\$0.05\) and fifty cents is \(\$0.50\).
Dollars and cents are linked: one dollar is one hundred cents, so \(\$1 = 100\) cents. To find a total, add the notes and coins together. To swap between cents and dollars, count in whole hundreds of cents.
The same amount can be made with different coins. Two \(10\)c coins have the same value as one \(20\)c coin. To use the fewest coins, start with the biggest coin that fits.
Money does not need formulas, but these facts help you build and change amounts.
| Coins | Notes |
|---|---|
| 5c, 10c, 20c, 50c | $5, $10 |
| $1, $2 | $20, $50, $100 |
How to represent a money amount
- Name the parts. Sort the money into dollars (notes and \(\$1\)/\(\$2\) coins) and cents (\(5\)c to \(50\)c coins).
- Add each part. Add the dollars together, then add the cents together. Remember \(100\) cents make \(\$1\).
- Write it in dollars and cents. Put the dollars before the point and the cents after, using two figures for the cents.
How to make an amount with the fewest coins
- Start big. Take the biggest coin that is not more than the amount.
- Find what is left. Take that coin away from the amount, then choose the biggest coin for what is left.
- Count the coins. Stop when nothing is left and count how many coins you used.
| \(\$1\) | \(=\) | \(100\text{c}\) |
| \(100 + 50 + 20 + 20 + 5\) | \(=\) | \(195\text{c}\) |
| \(195\text{c}\) | \(=\) | \(\$1.95\) |
The total is \(\$1.95\).
| \(305\text{c}\) | \(=\) | \(300\text{c} + 5\text{c}\) |
| \(300\text{c}\) | \(=\) | \(\$3\) |
| \(305\text{c}\) | \(=\) | \(\$3.05\) |
Write \(05\) so the cents have two figures.
| \(\$20 + \$10\) | \(=\) | \(\$30\) |
| \(\$2 + \$0.50\) | \(=\) | \(\$2.50\) |
| \(\$30 + \$2.50\) | \(=\) | \(\$32.50\) |
The total is \(\$32.50\).
| \(\text{dollars}\) | \(=\) | \(\$5 \text{ for each}\) |
| \(\text{compare cents}\) | \(:\) | \(09 < 19 < 90\) |
In order: \(\$5.09,\ \$5.19,\ \$5.90\).
Use the biggest coin that fits each time.
| \(85 - 50\) | \(=\) | \(35\) |
| \(35 - 20\) | \(=\) | \(15\) |
| \(15 - 10\) | \(=\) | \(5\) |
| \(5 - 5\) | \(=\) | \(0\) |
The coins are \(50\)c, \(20\)c, \(10\)c and \(5\)c, so the fewest is \(4\) coins.
| \(\$2\) | \(=\) | \(200\text{c}\) |
| \(200 \div 10\) | \(=\) | \(20\) |
\(20\) ten-cent coins have the same value as \(\$2\). Another way: one \(\$1\) coin and ten \(10\)c coins also make \(\$2\).
Common pitfalls
Frequently asked questions
How do you write an amount in dollars and cents?
Write the dollars before the point and the cents after it. Four dollars and sixty-five cents is \(\$4.65\). Always write two figures for the cents.
How many cents are in a dollar?
One dollar is \(100\) cents, so \(\$1 = 100\) cents. That means \(\$4\) is \(400\) cents and \(\$6\) is \(600\) cents.
How do you change cents into dollars?
Split the cents into whole hundreds and what is left over. \(340\) cents is \(300\) cents and \(40\) cents, which is \(\$3.40\).
What coins and notes does Australia have?
The coins are \(5\)c, \(10\)c, \(20\)c, \(50\)c, \(\$1\) and \(\$2\). The notes are \(\$5\), \(\$10\), \(\$20\), \(\$50\) and \(\$100\). There is no \(1\)c or \(2\)c coin.
Why do you write 05 after the point for five cents?
The cents part always has two figures. Five cents is \(\$0.05\) and fifty cents is \(\$0.50\). Writing \(\$0.5\) would look like fifty cents.
How do you compare two money amounts?
Compare the dollars first. If the dollars are the same, compare the cents. So \(\$4.09\) is smaller than \(\$4.90\) because \(9\) cents is less than \(90\) cents.
How do you make an amount with the fewest coins?
Start with the biggest coin that is not more than the amount, take it away, and repeat. For \(85\)c use \(50\)c, \(20\)c, \(10\)c and \(5\)c, which is \(4\) coins.
How do you find the total of two prices?
Add the dollars, then add the cents. A \(\$3.25\) book and a \(\$1.50\) pen cost \(\$4 + 75\)c, which is \(\$4.75\).