hey everyone it's kayleigh in this lesson we're going to
do some examples of ordering negative numbers with and without a number line
let's try this one order the numbers from greatest to least negative 5 3 negative 1
to negative 3. so it looks like in this problem we have some positive numbers mixed in
3 and 2. and right off the bat are positive numbers bigger or smaller than negative numbers
yeah positive numbers are greater than negative numbers so right off the bat we know that 3 and 2
are going to be over on this side of our list on the greatest side
and we can order them we know that three is greater than two so we can start our list
three comma two okay so now we have negative five negative one and negative three which of
these negative numbers is the greatest what's our rule again oh yeah the closest to zero the
greater the negative number so if we plot these here we'll have negative 1 here negative 3 here
and then negative 5. so the next number in our list is going to be the number that is closest
to zero which one of these numbers is closest to zero that's right negative one right here so
that's our next greatest now we have two more what's bigger negative three or negative five
well negative three here is only three spaces to zero but negative five has to go five spaces over
so that means negative three is closer to zero and it goes here and that leaves negative five
as our smallest number or our least valued number so we can write this list out a little
bit nicer over here from greatest to least we have 3 2 negative 1 negative 3 and negative 5.
we can also have negative rational numbers remember a rational number is a number that
can be turned into a fraction so let's order these fractions from greatest to least now
which of these negative fractions is the closest to zero remember that would make it the biggest
see how i have these marks here on my number line in between zero and one what
do these represent well if here's zero and here's one this would be my halfway point
and that means this would be one quarter and this would be three quarters okay so now that we have
that let's start off with our first number here we have negative one quarter so if i start here
zero i know that one tick mark over right there is going to be negative one
quarter or a fourth okay our next one is negative three halves so remember negative three halves we
can think of as being negative 2 over 2 plus negative 1 half but what's negative 2 over 2
yeah that's just equal to negative 1 plus negative 1 half which i know i can write as negative one
and a half okay so how would i plot negative one and a half on my number line well if here's zero
i can bop all the way over here to one or negative one and i need to go half so here's negative one
and a quarter and then here's negative one and a half great now how about this last one here
negative five tenths well this fraction is kind of hard for me to think about but i know i can
simplify it if i divide the numerator and the denominator by my greatest common factor which for
5 and 10 is 5. so i'll divide here by 5 whatever i do to the top i have to do to the bottom and this
will give me negative 5 divided by 5 is negative 1 and 10 divided by 5 is 2. so this is an equivalent
fraction here to negative five tenths so where would i plot negative one-half on my number line
well if i start here at zero i know that going to here it gives me negative a quarter so if
i go over one more tick mark right here would be negative half so if i want to
order these from greatest to least i know that my greatest negative number is going to be the
number closest to 0 here so the closest one is negative 1 4th. what's the next closest yep negative
a half and which one's the farthest from 0 or our smallest number negative one and a half perfect
do you know another method for ordering fractions yeah we can find a common denominator
and then compare them so let's start by simplifying all three of these fractions
is negative one-fourth as simplified as it can be yep how about negative three-halves
yep can't get any smaller how about negative five-tenths yeah we can reduce this one by
dividing the top and the bottom both by five and this will give us negative one half so now
that these are all simplified can you think of a common denominator if we have four two and two
well since negative one fourth is already as simplified as it can be we need to turn our
negative three-halves and our negative one-half into fractions with four in the denominator
so let's start with negative three-halves if we have negative three-halves and we want
it to be a fraction with a 4 on the bottom what do i need to multiply my denominator by
yeah 2 and that means i have to do my numerator also by 2 negative three times two is negative
six fourths so this is negative six fourths okay so now i'm going to need to do the same thing
for negative one half if i have negative half times what will give me a fraction with a 4
on the bottom still have to multiply 2 on the bottom so that means 2 on the top that gives me
negative 2 4ths. so here is negative two fourths and i'm also comparing that to negative one fourth
so what's the rule we're normally ordering fractions that all have the same denominator
yeah we say the fraction with the largest numerator the largest number on top is the
biggest fraction but since these are negative numbers the opposite is true since all of these
fractions have matching denominators we know that the fraction with the biggest number on
top is actually the smallest number because it's negative right it'll be the farthest away from 0.
so with that being said which of these numbers has the largest numerator
yep that's right negative 6 4ths right here so that is our smallest so then which one of these has the
smallest number on top yep negative one fourth so that will be our greatest negative fraction
so now we could order these right my greatest one is negative 1 4th and then what comes next
yeah that middle one negative 2 4ths and then which one did i say is my smallest
yep negative 6 4ths. but i can rewrite these now as my equivalent fractions
so this would be negative 1 4th comes first and then what's my green fraction negative 2 4ths is
the same as negative 5 tenths and what's my equivalent fraction for negative six fourths
yeah negative three halves so these are now ordered from greatest to least
we're really getting the gist of it now we just have one more video
on ordering negative numbers where we will solve a real life problem
called ordering negative numbers in real life i'll see you there