Hi there! I am back from vacation with a new installment of It All Adds Up! Today, I would like to discuss the topic of absolute value, and the idea that a number and it’s reciprocal are always the same distance away from zero on a number line.

Let’s take a standard number line, like this one:

We notice that are two copies of the numbers 1, 2, and 3, but one copy has a negative sign in front of it. For example, 3 and -3 are the same number, but are on different sides of the number line. There is, of course, a reason for this. -3 and 3 are *opposites, *as they are on opposite sides of the number line. In mathematical terms, -3 is the *reciprocal *of 3, and 3 is the reciprocal of -3. We can tell that, while -3 and 3 are on opposite sides of the equation, they are both an equal distance away from zero.

Another idea that goes along with this is *absolute value. *For absolute value, we have to remember this: *THE ABSOLUTE VALUE OF A NUMBER IS ALWAYS POSITIVE! *

If you were given a problem such as this, how would you solve it? Hint- || is the symbol for absolute value.

**|-7|+4=y**

This would be a very simple problem in the first place, and it makes little difference when the absolute value symbol is added in. For a number that is negative, we simply change it into it’s reciprocal on the number line, which will be positive. For a number that is positive, the number stays positive. After we figure out the absolute value of -7, we end up with this problem:

**7+4=y**

The problem now becomes very easy to solve. Do you understand the concept of absolute value? If so, try these problems. Check your answers on Saturday, August 27.

## -21 + x = |-72|

## |7| + |93| + |6.9| = y

## |-7| – |-93| – |6.9| = y

Thanks for reading! Please be sure to check out my reading response to The Boys in the Boat later today!

Gabe