Adding and subtracting integers
You already know how to add 3 + 4 and so on. But there are many ways to add integers. One way to add integers is by using a number line.
$$ -4+(-3)=\, ?$$
We always start at zero. Our first number is negative four (-4) so we move 4 units to the left. We then have plus negative three (-3) which is the same as subtracting 3 so we move 3 more units to the left. This gives us the value of negative seven, (-7).
We do the same thing if we have a positive integer, but instead we move to the right.
You can also add integers and variables.
When subtracting something from something we wish to find out the difference between the two numbers. When you subtract a negative number from any number the difference is even bigger. The distance from the seabed at a depth of 150ft and an airplane flying at 3000ft altitude at sea level is
$$3000-(-150) = 3000 + 150 = 3150ft.$$
Thus when we subtract negative numbers, we get:
$$4-(-3) = 4 + 3 = 7$$
Subtracting −3 is the same as adding 3.
If we have a plus sign before the parentheses then we will not change the signs within the parentheses
If we have a minus sign before the parentheses then we the signs within the parentheses will change.
Two negatives make one positive!
Calculate -3 + (-6) on a number line