Subtracting Positive and Negative numbers

Subtracting Using a Number Line.

In the video above we subtracted using Algebra tile, another way to thing about subtracting integers is by using a number line. Remember: if a number does not have a sign it is positive, so 4 – 5 is the same as saying positive 4 minus positive 5.

A positive number minus a positive number:

Ex. 1   Lets look at the problem $4-5$.

To do this problem lets pretend that you are walking along a number line.
First you would start by standing on the $4$
Because this is a subtraction problem you will be facing as if you were to walk toward the negative numbers.

Since the $5$ is positive, you would move forward $5$ spaces.

The Adding Opposites Property of Subtraction:

says that subtracting a number is the same as adding the opposite of that number.

Going back to $4-5$, we could think of it as $4$   $+$ the opposite of $5$ or $4 + {^-5}$, and using the rules for addition we know that $4 + {^-5} = {^-1}$.
In both cases the answer was ${^-1}$ and we can see that $4-5$ is equivalent to $4 + {^-5}$

A negative number minus a positive number:

Ex. 2     ${^-4}-5$.

First you would start by standing on the  ${^-4}$. Because this is a subtraction problem you will be facing as if you were to walk toward the negative numbers, and move forward $5$ spaces.

Using the Adding Opposites Property of Subtraction:
${^-4}-5 = {^-4} + {^-5} = {^-9}$

A positive number minus a negative number:

Ex. 3    $4$   $- {^-5}$.

We will start at  $4$, face toward the negative numbers and go $5$ spaces backwards (the opposite direction as ${^-5}$)

Using the Adding Opposites Property of Subtraction:
$4$  $- {^-5} = 4 + 5 = 9$

A negative number minus a negative number:

Ex. 4    ${^-4}$   $- {^-5}$.

We will start at ${^-4}$, face toward the negative numbers and go $5$ spaces backwards (the opposite direction as ${^-5}$)

Using the Adding Opposites Property of Subtraction:
${^-4}$   $- {^-5} = {^-4} + 5 = 1$