hi my name is Kaylee welcome to
equivalent ratios and double number
lines make sure you've watched the
ratios video before jumping into this
one here we have two rulers of different
units the top ruler is in centimeters
and the bottom ruler is in millimeters
we're going to work together to find the
relationship between these two
quantities or the ratio of millimeters
per centimeter let's explore this in a
ck-12 simulation so here we are in the
ck-12 diagram and I have my centimeter
ruler up here and my millimeter ruler
down here and I can also go over to my
tape diagram let's start with our rulers
I'm here at 0 I'm gonna move over to one
centimeter when I do that I get 10
millimeters are highlighted can you
think of a ratio phrase that we can
describe this relationship has like for
every 1 centimeter there's 10
millimeters or there are 10 millimeters
per 1 centimeter let's try it in our
tape diagram so you have 1 centimeter
and 10 millimeters what if I move to 2
centimeters so now I have 2 centimeters
10 20 millimeters if I go back to my
ruler it's gonna show the same thing 2
centimeters per 20 millimeters and if I
go to 3 centimeters I get 30 millimeters
so do you see the relationship between
centimeters and millimeters now from
what we have learned about centimeters
and millimeters we can say for every 1
centimeter there are 10 millimeters we
can write this ratio as 1 to 10 this
tells us that 1 cent
meter is equivalent to ten millimeters
now why do you think I use the word
equivalent instead of equal equal is a
very special word in math and that means
that that two things are exactly the
same way one centimeter is only equal to
one centimeter but the word equivalent
means that two things are the same in a
certain way one centimeter is equivalent
to ten millimeters are the same length
but they are in different units in
different ways of measuring we use the
three horizontal lines to represent the
word equivalent or translates to in math
and we can talk about ratios being
equivalent also to pens per box is
equivalent to eight pens per four boxes
we can write their ratios out as two
pens to one box
two to one is equivalent to eight pens
to four boxes eight to four you can find
an equivalent ratio by multiplying or
dividing both sides of the ratio by the
same number in this case we multiply
both sides of the two-to-one ratio by
four and we get eight to four but let's
take our ideas of equivalent ratios to
the double number line the double number
line is very similar to the double
ruler's we used in the last example but
there's no picture just two horizontal
lines we are comparing how much sugar is
in cans of soda for the double number
line you can can you determine how much
sugar is in eight fluid ounces of soda
imagine we draw an imaginary line down
from the 8-ounce tick mark and we find a
tick mark for 31 grams of sugar so we
can say for every eight fluid ounces of
soda there are 31 grams of
sugar we can write this as a ratio and
as a fraction being careful to choose
the right number for the numerator and
the first number of our ratio so they're
asking us how much sugar is in 16 fluid
ounces and if we know the ratio of 8
fluid ounces for every 31 grams of sugar
how can we find that for 16 fluid ounces
so what they're asking us really is to
find the equivalent ratio here so we
know the ratio of 8 fluid ounces is 231
grams of sugar but they want us to find
the equivalent one of 16 to how many
grams of sugar remember to do this we
need to multiply the top and bottom of
our fraction by the same number to get
this equivalent fraction so that looks
like we're going to need to multiply
this side 2 over 2 so I multiply to my
numerator and my denominator each by 2
because I know 2 times 8 will give me 16
so I know 2 times 31 I can do that math
I'll be 16 31 times 2 will be 62 so if I
know that this is 62 I can put my number
in here and you've just found the
equivalent ratio so 8 to 31 the
equivalent ratio is 16 to 60 2 so that
tells us in a 16 fluid ounces there are
62 grams of sugar great job
awesome work working with double number
lines and equivalent ratios I know it
can be a little trickier adding all that
math in but practice what you've learned
by completing the activities and playing
our games and remember have fun and
always be clever
