hey there it's kaylee let's do some absolute value practice problems together
grab some paper and a pencil and help me solve these problems let's go
so let's do these examples together my first one says what is the absolute value of four minus nine
so remember absolute value is these brackets here
but i have an expression inside of my brackets so what i need to do first is solve my expression
what is four minus nine well 4 is a smaller number than 9 so we know our answer will be a
negative number what is 4 minus 9 well if we have 4 here we have to go 4 spaces over to get to zero
but then i'm going nine spaces over so i need to go five more spaces to get a distance of nine here
and 0 minus these 5 will give me negative 5 so my answer here is negative 5. so i'm going to
plug negative 5 in for my expression so the absolute value of 4 minus 9 is equal to the
absolute value of negative five so now i have a problem that i know how to do what's the absolute
value of negative five that means what's the distance negative five is from zero yeah we know
it it's a distance of five so positive five is my answer nice work okay let's try this one down here
again i have my absolute value bars here but i have an expression on the inside it says negative
19 times two so if i'm multiplying a negative number by a positive number what is my answer
that's right it's going to be negative a negative number times a positive number is always equal to
a negative number so what's 19 times 2 do you know it off the top of your head
yeah it's 38 but since this is a negative number it's going to be negative 38.
so negative 19 times 2 is equal to negative 38. and i can plug that in here to my absolute value
brackets and i'm trying to find the absolute value of negative thirty eight what does that equal
how far from zero is negative thirty-eight yeah that's right it's just 38 spaces so the absolute
value of negative 38 is positive 38. this one says what is negative absolute value of negative five
hmm that's tricky do you remember this negative sign also means something besides just negative
do you remember what it is yeah it's opposite so this
is really asking me what is the opposite of the absolute value of negative five
well first let's let's figure out what's the absolute value of negative five
that's right the distance from zero to negative 5 is 5 right so that's the answer there
but i want the opposite so what is the opposite here of the absolute value of negative 5 well
the opposite of 5 would be negative five so the opposite of the absolute value of negative five
is going to be equal to negative five good job okay this next one here i have absolute value
bracket here expression subtracting from another one okay so i have two things i need to do first
i need to figure out what this is equal to and i need to figure out what this is equal to
and then i can subtract them so negative 6 times 2 what is that negative 6 times 2 a negative times
a positive is going to be a negative so i know that 6 times 2 is 12 minus the absolute value
of negative eight so now i have two absolute value problems what's the absolute value of negative 12
negative 12 is a distance of 12 from zero so that's equal to 12 minus the absolute value
of negative eight how far from zero is negative eight positive eight that's right perfect so now i
just have 12 minus eight do you know what that is yeah it's four and that's my answer there good job
john is a truck driver he's out making deliveries when he realizes he needs to stop for gas
when he pulls up his gps he sees the two closest gas stations pop up on the map
there is one gas station 15 miles behind him we'll cause call that distance negative 15 miles
the other gas station is a distance of 40 miles in front of him so we'll call that positive 40 miles
which gas station is closer to john well this doesn't seem too tricky right if we think about
john's location as our zero point we can just find the distances to each gas station we can do this
by taking the absolute value of both distances so the absolute value of negative 15 miles would be
positive 15 miles and the absolute value of positive 40 miles would give us positive 40 miles
so the gas station that's behind john is actually closer to him it's only
15 miles away but let's say john turns around and travels back to this closer gas station
how far will he have traveled that's right 15 miles he had to turn around and go 15 miles but
now to get back to his starting point the zero point he'll have to drive back another 15 miles
so how many total miles will john add to his trip by going back to the gas station behind him
well he'll drive 15 miles plus another 15 miles what's 15 plus 15 that's right
30 miles so john will have to travel 30 extra miles to go back to this
closer gas station nice job using absolute value to solve a real life problem
nice work thanks for doing those practice problems together now you're ready to do
absolute value on your own if you get stuck you can come back and watch these intro to absolute
value videos again check out the absolute value practice have fun and remember to always be
clever