What is meant by Equivalent Ratios? Video Lecture - Class 7

hey there everyone welcome back to
mashup math my name is Anthony and thank
you for joining me on this mini lesson
let's go ahead and get started hi
everyone and thank you again for joining
me on this lesson where we are going to
explore the properties of equivalent
ratios so in this lunchtime scenario we
have Kevin and Christina for a both
ordering lunch to bring back to their
co-workers Kevin orders six hamburgers
and two tacos while Christina orders
three hamburgers and one taco and we
want to explore the ratio of hamburgers
to tacos in this situation so with this
ratio in mind let's regroup both Kevin
and Christina's orders
doing this allows us to see that for
both Kevin and Christina for every three
hamburgers ordered there is one taco so
even though Kevin ordered twice the
amount of food that Christina did the
ratios are still equivalent because for
every three hamburgers
there is one taco in this case a three
to one ratio so now let's move forward
and explore the questions what does it
mean when two ratios are equivalent how
can I show that two ratios are
equivalent and where can I get one of
those tacos
kidding kidding so now let's get some
practice in determining whether or not
two ratios are equivalent in this case
we have the ratio of 4 to 5 and the
ratio of 12 to 15 and we want to see if
they are equivalent ratios now a ratio
can be written in fraction form with a
numerator and a denominator so we're
going to go ahead and start by
transforming these two ratios into
fractions
doing this allows us to determine if the
two ratios are equivalent because we
know that two fractions are equivalent
if their cross products are equal so
we're going to go ahead and find those
cross products and see if they're equal
and if they are then we can say that
these are equivalent fractions so let's
start by cross multiplying and we'll
start out with five times 12 which we
know equals 60
and then we'll find our second cross
product by multiplying 4 and 15 and that
product is also equal to 60 so notice
that in this case our cross products
were equal and that means that we can
make the determination that these two
ratios are equivalent and we can justify
that statement because as we just showed
the cross products are equal oh cool so
now let's go ahead and take a look at
one last example in this case we want to
see if the ratio 4 to 7 and the ratio 6
to 12 are equivalent just like in the
last example we can start off by
converting the ratios to fractions with
the numerator and the denominator then
we can go ahead and find the cross
products and see whether or not they are
equal we could start with 4 times 12
whose product is 48 and then compare
that to the second cross product 7 times
6 whose product is 42 notice here that
in this example the cross products of 48
and 42 are not equal therefore we can
conclude that these two ratios are not
equivalent so now that we have explored
both the concept and the procedures
involved with exploring equivalent
ratios you can now extend this
understanding to future problems thanks
again for stopping by everyone and I
will see you soon haha cool alright so
that's it for this lesson thank you
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you all next time bye