Paying more than the price
A pencil costs 65 cents. You pay with a dollar, which is 100 cents. That is more than the pencil costs, so the shopkeeper gives some money back. The money that comes back is called change.
The change is the gap between the price and what you paid: the part of the 100 cents that the pencil does not use.
You pay with a $1 bill, which is 100 cents, for a pencil that costs 65 cents.
Count up from the price
To find the change, start at the price and count up to what you paid, one coin at a time. Start at 65. A 10¢ coin takes the count to 75. A 25¢ coin takes it from 75 to 100. Now the count has reached the dollar, so stop.
The coins you handed over on the way are the change: a 10¢ coin and a 25¢ coin. This is the way a shopkeeper counts change into your hand.
65¢ + ? = 100¢: count up from the price, one coin at a time, until you reach the dollar paid
Hand over coins until the count reaches 100¢
The bar is the dollar you paid, and the price fills the first 65 cents of it. Each coin you hand over lays its own length after the price. When the coins reach the end of the bar, they are the change.
The coins that filled the gap
The coins that filled the gap from 65 to 100 are 10¢ and 25¢, and 10 + 25 = 35. So the change is 35 cents.
Check it by adding the price and the change. They must make what you paid: 65 + 35 = 100 cents, which is the dollar.
Counting up from 65: 75, then 100. The two coins are 35¢ of change.
Another price
An eraser costs 35 cents and you pay with two 25¢ coins, which is 50 cents. Count up from 35: a 5¢ coin reaches 40, the next ten, and a 10¢ coin reaches 50. The change is 5 + 10 = 15 cents. Check: 35 + 15 = 50.
Counting up from 35 to 50: 40, then 50. The change is 15¢.
Count all the way to what you paid
The count stops at the amount you paid, not before. For the pencil, a 5¢ coin would take 65 to 70, the next ten, but that is not the end: the count has to go on to 100. Stopping at the first ten would give only 5¢ of change.
The price is not the change. The 65 cents is what the shop keeps for the pencil. The change is what comes back on top of it.
Worked example: Change from a One-Dollar Coin and from a Two-Dollar Note
Question An eraser costs 75 cents. (a) Lina pays with a $1 coin. How much change does she get? (b) Tom buys the same eraser and pays with a $2 note. How much change does he get?
1.Start at the price, 75 cents. Count up to the next ten cents: 75 + 5 = 80.
From 75 cents to the next ten cents is 5 cents. 2.Count up from 80 cents to $1, which is 100 cents: 80 + 20 = 100.
From 80 cents to $1 is 20 cents. 3.(a) Add the jumps: 5 + 20 = 25. Lina gets 25 cents change.
(a) 5 + 20 = 25. Lina gets 25 cents change. 4.For Tom, count up one more jump, from $1 to $2. That jump is $1.
Tom pays $2, so there is one more jump of $1. 5.(b) Tom gets $1 and 25 cents, which is $1.25 change. Check: 75 cents and $1.25 make $2.
(b) Tom gets $1.25 change.
Answer: (a) 25 cents; (b) $1.25
Common mistakes
- Giving the price as the change. 75 cents is what the shop keeps. The change is what is left of the $1 after the eraser is paid for.
- Counting up to $1 and stopping when the money paid was $2. The count has to go all the way to the amount paid.