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Adding a Positive Is the Same as Subtracting a Negative

When you add a positive integer, or subtract a negative, you are moving up (to the right) on the number line.

Let’s take a look at an example. Solve $-5+1$.

First, let’s draw a number line and place a point at $-5$.

Next, add $1$ to $-5$. Count up $1$ unit starting from $-5$.

Answer: $-5+1=-4$

Let’s look at another example: $-2+3$.

First, let’s draw a number line and start at $-2$.

Next, add $3$ to $-2$. Count up $3$ units starting from $-2$.

Answer: $-2+3=1$

Now, try a couple of examples without drawing a number line.

$$-7+19=12$$

$$\begin{align} -3+2+3&= -1+3 \\ &= 2 \\ \end{align}$$

$$\begin{align} -18+23+(-7)+0&= 5+(-7)+0 \\ &= 5-7+0 \\ &=-2+0 \\ &= -2 \\ \end{align}$$

(Video) Adding and Subtracting Integers

by Math Antics

This video by Math Antics goes over all the different ways to add and subtract integers. It covers adding and subtracting whole numbers, adding negatives, and subtracting negatives.

$\large{\text{Summary}}$

This section video covers a case where you are taking a negative number and making it more positive. We can do this because subtracting a negative the number is the same as adding a positive number. $$-8-(-5)$$ We can think of this as $-8+5$. We are moving $5$ spaces to the right on the number line to $-3$.

(It's essentially adding a positive number)

When you add a negative number, it's essentially subtraction. When you subtract a negative number, it works a lot like addition. This is because the two negatives (the subtraction and the negative number) essentially cancel each other out, becoming positive. Let's look on a number line, using the expression $4 - (-3)$. First, find $4$ and $-3$ on the number line.

$-3$ appears three steps to the left of $0$. If we were adding, we would then count those three steps away from $4$, like in the following picture:

However, we're subtracting. So, we flip the direction of the steps we count:

So it looks like $4 - (-3) = 7$, which is the same as $4 + 3$!

Subtracting a negative always makes a number worth more

When you subtract a negative number from a negative number, the resulting number will be more than the original negative. In other words, subtracting a negative number is the same as adding a positive number. Think of it like blocks on either side of a line: negatives pull down, and positives pull up. Subtracting reverses the direction a block pulls:

Notice that in the above graphic, subtracting $-6$ from $-2$ results in a positive number. That's because the $-6$ marches upwards towards the positives and past $0$, so that the final answer will be a positive number itself. Take a look at a similar problem on the number line:

If the negative being subtracted is smaller than the starting number, then the answer will still be a negative: