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.
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:
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!