hi there it's kaylee this lesson is an introduction to absolute value
absolute value is used to measure magnitudes or sizes of quantities like distances ready let's go
sarah and david are standing back to back at a red flag if sarah takes 20 steps to the right
and david takes 20 steps to the left who has traveled the farthest well they have
both taken 20 steps so they've traveled the same distance from the flag right they each took 20
equal size steps just in different directions but the distance they each traveled is the same length
another way to think about this is with our number line if we have a point here at 3 and a point
here at negative 4 the absolute value of these numbers is their distance from our starting point
zero so what's the distance from zero to three well we need to move over one two three places
to get to three so that means the distance from zero to three here is three now how about for
negative four what's the distance from zero to negative four well we need to go over one two
three four places to get to negative four so the distance from zero all the way over to
negative four is equal to four now distance to zero is the same as saying the absolute value
so the absolute value of three is the same as the distance three is from zero which we found to be
three now the same is true for negative four the absolute value of negative four
is the same as the distance negative four is to zero which we found to be
four let's look at a few examples what is the absolute value of x if x is equal to 12 negative 6
or negative 2 well first let's learn a little shorthand or the symbol for absolute value
instead of having to write out the words absolute value of x we can put vertical lines on either
side of the number we're evaluating let's use this shorthand to help with our examples
so here we're finding the absolute value when x is equal to 12. so when x is equal to 12. if i'm
trying to find the absolute value of x when x is equal to 12 i'm finding the absolute value of 12.
now remember absolute value is the distance from 0. so how far from 0 is 12 that's right 12 spaces
so the absolute value of 12 is 12. let's do another one when x is equal to negative 6.
so remember i'm trying to find the absolute value of x and in this case x is equal to negative six
so what's the absolute value of negative six the distance from zero that's right negative six
is six spaces to the left but direction doesn't matter with absolute value it's just six the
absolute value of negative six is six okay our last one here is when x is equal to negative two
so just like everything else i'm trying to find the absolute value of x
when x is equal to negative two i can plug that in there so what's the absolute value of negative two
so how many spaces or what's the distance negative two is from zero
that's right two spaces so the distance is two and that means the absolute value is two
do you notice anything about all of these answers
yeah the one thing we notice right away is they're all positive numbers
now you know the absolute value of a number just means the distance that number is from zero
join me in the next video to do some practice problems and a real life application see you there