Money and making change

Coins and notes

United States money is built on the dollar. One dollar is 100 cents, and the cent sign (¢) marks amounts smaller than a dollar. Four coins do most of the work: the penny is 1¢, the nickel is 5¢, the dime is 10¢, and the quarter is 25¢. Notes come in dollars: $1, $5, $10 and $20 are the ones you see most often.

Counting coins is adding in tens and fives. Start with the largest coin and keep a running total. The coins below are two quarters, one dime, one nickel and two pennies: 25 + 25 + 10 + 5 + 1 + 1 = 72 cents.

Equal amounts

Many groups of coins name the same amount, and the smallest group is not always the one you have in your pocket. Five pennies make a nickel. Two nickels make a dime. Two dimes and a nickel make a quarter. Four quarters make a dollar, and ten dimes make a dollar too. A price can be paid in more than one way, which is useful when the coins you want are not in the drawer.

Prices are written with two decimal places because cents are the hundredth part of a dollar. The price 45¢ is the same as $0.45, and three quarters and a nickel make 80¢, which is $0.80. Writing the cents as decimals keeps money and place value in step.

The count-up method for change

Change is the money you get back when you pay more than the price. The easiest way to find it is to count up from the price to the amount you paid. A pencil costs 45¢ and you pay with 50¢. Count from 45 to 50: five more cents, so the change is 5¢. Count in the coins you would really use, which is one nickel or five pennies.

Counting up also works with dollars. If something costs $4.30 and you pay with a $5 note, count from $4.30 to $5.00. The jump is 70 cents, so the change is $0.70. On a number line, the price sits near the end of the line and the change is the gap between the price and the note.

Checking your change

Addition is the check on every money answer. The change plus the price must come back to the money you paid. For the notebook: $4.30 + $0.70 = $5.00, so the change is right. If the sum is too small, the change is too small; if the sum is too large, the change is too large. This check catches a slip in the counting before it reaches the till.

When a question gives prices for more than one item, add the prices first. Then take the total away from the note, or count up from the total to the note. Two snacks at 60¢ each cost $1.20, and paying with $2.00 leaves 80¢, because $1.20 + $0.80 = $2.00.