Operations with Decimals

Adding and Subtracting Decimals

Adding and subtracting decimals is easy if you're comfortable with carrying and borrowing. Just line up the decimal points, and (if necessary) add zeros to the end of one number, so they have the same number of decimal places. Then add (or subtract) as you usually would.

In your answer, the decimal point should go exactly below where it is in the numbers being added (or subtracted).

Multiplying and Dividing with Decimals

Multiplying Decimals

To multiply decimals, first just multiply the numbers as if they were whole numbers . (Don't line up the decimal points!)

Then count the total number of places to the right of the decimal point in BOTH numbers you're multiplying. Let's call this number $n$ . In your answer, start from the right and move $n$ places to the left, and put a decimal point.

Dividing with Decimals

Dividing with decimals is a bit more difficult. These days, most teachers don't mind much if you use a calculator. But it's good to know how to do it yourself, too, and you always need to be good at estimating the answer, so you can make sure the calculator's answer is reasonable.

Recall that in the problem $x÷y=z$ , also written

$\begin{array}{c}\\ y\end{array}\begin{array}{c}\hfill z\\ \hfill \overline{)x}\end{array}$

$x$ is called the dividend , $y$ is the divisor , and $z$ is the quotient .

Step 1: Estimate the answer by rounding . You'll use this estimate to check your answer later.

Step 2: If the divisor is not a whole number, then move the decimal place $n$ places to the right to make it a whole number. Then move the decimal place in the dividend the same number of places to the right (adding some extra zeros if necessary.)

Step 3: Divide as usual. If the divisor doesn't go in evenly, add zeros to the right of the dividend and keep dividing until you get a $0$ remainder, or until a repeating pattern shows up.

Step 4: Put the decimal point in the quotient directly above where the decimal point now is in the dividend.

Step 5: Check your answer against your estimate to see if it's reasonable.

See also: Multiplying and Dividing with Decimals