Study Guide

# Fractions & Decimals - Adding & Subtracting Decimals

Getting to the next level in our favorite video game was cool, but also kind of a letdown. The next level is almost exactly the same as the previous one, but with a few more challenges thrown in. Adding and subtracting decimals is the same. It's mostly just like adding whole numbers, but with one or two more challenges.

First, when we add and subtract decimals, we need to stack the numbers on top of each other just like whole numbers. The new challenge is that we also need to make sure the decimal points in each number line up, one above the other. This makes the place values line up, too.

Graph paper may come in handy here. If you need some, you can print graph paper for free online.

The most important thing is to keep the decimal point in the right place for each number you're adding or subtracting. When the decimals are lined up properly, everything else falls into place.

The other challenge happens when there's no digit in a place value for one of the numbers, but there is for the other. To overcome this challenge, all we need to do is fill in the empty spots with zeros.

In the problem 0.569 + 45.1, the first number has a 6 in the tenths place and a 9 in the thousandths place. But the second number, 45.1, doesn't have a digit in either of these place values. The second number also has a digit in the tens place where the first doesn't.

When we stack them and line up the decimals, they look like this:

 0 . 5 6 9 4 5 . 1

What is that gaping hole above the 4? What about the ones below the 6 and 9? Is it some portal a monster can get through and take our awesome cache of gold? Let's fill up those holes with zeros.

 0 0 . 5 6 9 4 5 . 1 0 0

Now we can add like normal.

00.569
+ 45.100
45.669

### Sample Problem

What is 0.3 + 0.04 + 0.001?

To add decimals, we put zeros in any empty place values as needed so that all of the numbers have the same number of decimal places.

0.300
0.040
+ 0.001
0.341

Subtraction is similar. To subtract one decimal number from another, first give the two decimals the same number of decimal places by adding zeros as needed. Line up the decimal points, and then rock that subtraction exactly like you would with whole numbers.