Performing Operations with Decimals

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  • 0:04 Why Do We Use Decimals?
  • 0:47 Adding With Decimals
  • 2:24 Subtracting With Decimals
  • 2:37 Multiplying with Decimals
  • 3:09 Dividing with Decimals
  • 3:50 Lesson Summary
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Lesson Transcript
Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

Decimals are used to represent parts of a whole and are very useful in many types of measurements and calculations. In this lesson, learn how to add, subtract, multiply, and divide decimals.

Why Do We Use Decimals?

Imagine that you threw a party for your friends and bought 5 pizzas, each with 10 slices. After the party, you look in the boxes and see that one box has 2 slices left, one has 3 slices left, one only has 1 slice left, and two boxes have 4 slices left. How many pizzas total do you have left over? You could write each of these numbers as a fraction of a pizza, but fractions are not that easy to add. Instead, you can convert the fractions to decimals, which are much easier to work with.

Just like fractions, we use decimal numbers to represent parts of a whole, and they can be added, subtracted, multiplied, and divided using simple rules. We'll come back to the problem of the leftover pizza in a minute, but first let's look at the rules for performing these mathematical operations with decimals.

Adding with Decimals

When adding or subtracting two numbers with decimals, you want to remember one important rule: always line up the decimals before doing anything else! If you can remember to do that first, then the rest of the problem will be easy.

For example, suppose you want to add the numbers 12.8 and 9.602. Even though 12.8 has one digit after the decimal while 9.602 has 3 digits, we can still add these numbers together. To add them, you need to write them in vertical format with one underneath the other, being careful to line up the decimals.

addition with decimals

Easy, right? To finish this problem, you need to add zeros to the shorter number so that each number has the same number of digits after the decimal. Then simply add each column of numbers.

part 2 of addition with decimals

So, the sum of 12.8 and 9.602 is 22.402.

Going back to the problem of the leftover pizza, we can now also determine exactly how many pizzas you have left over.

First, determine how much pizza was left in each box:

Box 1: 2/10 = 0.2 pizzas
Box 2: 3/10 = 0.3 pizzas
Box 3: 1/10 = 0.1 pizzas
Box 4: 4/10 = 0.4 pizzas
Box 5: 4/10 = 0.4 pizzas

Now add all these decimals together to get the total amount of pizza:

0.2 + 0.3 + 0.1 + 0.4 + 0.4 = 1.4 pizzas left over

Subtracting with Decimals

Subtraction is done exactly the same way, except you would subtract the two columns of numbers instead of adding them. Don't forget: line up the decimals. Let's now subtract 9.602 from 12.8.

subtraction with decimals

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