Add, Subtract, Multiply, and Divide Money and Decimals

Start with adding and subtracting. The answer when you add is the sum. The answer when you subtract is the difference.

You can only join or take away things of the same kind: dollars with dollars, tenths with tenths, hundredths with hundredths. Lining up the decimal points puts every digit in the correct column.

A whole number of dollars shows no cents, so write them in: $3$ dollars is $3.00$ dollars. When you add or subtract whole cents, you get whole cents. So a sum or difference of two money amounts never needs rounding. It only needs its two decimal places.

Here is $12.50 + 3$ set up this way. The $3$ goes under the $2$, because both digits count single dollars. The sum is $15.50$ dollars. Keep the zero at the end, so the $50$ cents are easy to see.

Now multiply. The answer when you multiply is the product.

To multiply money by a whole number, think in cents. $2.35$ dollars is $235$ cents. Three of those make $3 \times 235 = 705$ cents, which is $7.05$ dollars. Notice the $0$ in the tenths place: $705$ cents is $7$ dollars and $5$ cents, not $7$ dollars and $50$ cents.

A whole number of cents always fits in two decimal places. So a money amount times a whole number never needs rounding.

Dividing is different. The answer when you divide is the quotient, and it does not always land on a whole cent.

Share $1.00$ dollar equally among $3$ people. Each gets $1.00 \div 3 = 0.333\ldots$ dollars. The dots mean the digit $3$ keeps repeating. That is a little more than $33$ cents, and nobody can pay part of a cent. So you round to the nearest cent, which here is $0.33$ dollars.

You round only when the quotient has more than two decimal places. To do it, divide as far as the thousandths place, the third digit after the decimal point. If that digit is $5$ or more, the quotient is at least halfway to the next cent, so add $1$ cent. If it is $4$ or less, keep the cents you have. Then drop every digit after the hundredths place.

Money is only one use of decimals. You add, subtract, multiply and divide lengths, weights and other decimal amounts in the same ways. What changes from one operation to the next is how you treat the decimal point.

Here is why. Adding and subtracting join or remove amounts, so the places must match. Multiplying changes the size of the parts: a tenth of a tenth is a hundredth. Dividing by a decimal asks how many of that decimal fit, and that is easier to count once you divide by a whole number.

You have used each of these methods before. The new skill is choosing the right one. First ask which answer you need: a sum, a difference, a product or a quotient. Then follow the matching row of the table.

Here is the idea to keep. Money is a decimal in which each hundredth of a dollar is one cent, so the decimal methods you know all work on money. To add or subtract, line up the decimal points. To multiply, work with whole numbers first, then count the decimal places in both numbers together. To divide by a decimal, first multiply both numbers by $10$ or $100$ so you divide by a whole number. For a money answer, show two decimal places, and round to the nearest cent when a result has more than two.

Next, you will divide a total cost to find a unit price, which is the cost of one item. You will use unit prices to compare two offers, and you will solve decimal problems that take more than one step.