## 3.3 Negative Numbers

This section is not completed yet, but in the meantime here are some practice questions.

Remember:
Adding a negative number is the same as subtracting: \begin{align*} 9 + (-6) &= 9 - 6\\ &= 3 \end{align*}

Subtracting a negative number is the same as adding a positive number: \begin{align*} 5 - (-3) &= 5 + 3\\ &= 8 \end{align*}

When adding a positive number to a negative number, the numbers can be rearranged to make a subtraction: \begin{align*} -3 + 8 &= 8 + (-3)\\ &= 8 - 3\\ &= 5 \end{align*} In other words, if you take $3$ steps to the left, then $8$ steps to the right, you’ll end up $5$ steps to the right of the starting point:

To subtract a larger number from a smaller number, you can subtract the smaller one from the larger, then make it negative: \begin{align*} 2 - 7 &= -(7-2)\\ &= -5 \end{align*} In other words, if you take $2$ steps to the right, then $7$ steps to the left, you’ll end up $5$ steps to the left of the starting point:

That also applies when adding a small positive number to a negative number: \begin{align*} -7 + 2 &= -(7 - 2)\\ &= -5 \end{align*} In other words, if you take $7$ steps to the left, then $2$ steps to the right, you’ll end up $5$ steps to the left of the starting point:

To subtract a number from a negative number, you can do an addition, then make it negative: \begin{align*} -4 - 5 &= - (4 + 5)\\ &= -9 \end{align*} In other words, if you take $4$ steps to the left, then $5$ steps to the left, you’ll end up $9$ steps to the left of the starting point: