Addition and Subtraction
When we have two whole numbers:
– If both have the same sign, we add their absolute values and put the common sign:
3 + 4 = 7 – 3 – 4 = – 7
– If both have different signs, we subtract the bigger absolute value minus the lower absolute value and put the sign of the number which has bigger absolute value:
3 – 7 = – 4 11 – 7 = 4
When we have more whole numbers:
Just Add
Natural numbers ( etc.) are the numbers you see most often. They don’t have any fractions or decimals attached to them, and they exist above or to the right of on the number line.
Natural numbers are above zero on the number line.
When you add natural numbers, you just move up (or to the right) on the number line. For example, when you add you can start at :
![The number line. There's a dot on 4.](https://d20khd7ddkh5ls.cloudfront.net/4_on_number_line.png)
Then, count up points. You can think of “” as sending a number to the right.
![The number line. The dot was moved from 4 to 9.](https://d20khd7ddkh5ls.cloudfront.net/4plus5_2.png)
Adding means we stepped places up the number line, so .
Count Backwards
Subtracting a positive number from a positive number works the same way as adding a negative number to a positive number. It might help to conceptualize it a little differently, though. Let’s work with the expression .
First, let’s find all our numbers on the number line.
We’re working with 2 and 6
Since we’re subtracting from , we’re going want to use as our new anchor point and figure out ‘s position from it. So, let’s find ‘s position relative to .
![The same number line. Two spaces are moved to get from 0 to 2.](https://d20khd7ddkh5ls.cloudfront.net/find2and6_3.png)
Now, we’re subtracting . Subtracting a number is pretty much the same as adding the negative version of the same number, so we could rewrite our expression as . To find this, we can just flip ‘s position relative to :
![Two spaces are moved backwards from 0 to get to -2.](https://d20khd7ddkh5ls.cloudfront.net/findneg2and6_2.png)
Now, let’s just transpose to the same relative position to as it is to now.
As you can see from the image, you can also count backward on the number line to find the answer.
Now we can see that . When you subtract a number, you basically change its sign (so positive numbers become negative, and negative numbers become positive) and then add it as you would otherwise.