Understanding equivalent ratios

- [Voiceover] We're told that Burger Barn

makes dipping sauce by
mixing two spoonfuls of honey

with one half spoonful of mustard.

Sandwich Town makes dipping sauce

by mixing four spoonfuls of honey

with one spoonful of mustard.

Which dipping sauce has a
stronger mustard flavor?

So pause this video and see if you can

work through that on your own.

All right, now let's
think about the ratios

of honey to mustard at
each of these restaurants.

So first let's think about
the scenario with Burger Barn.

So I'll just say BB for
short, for Burger Burn.

So they have two spoonfuls of honey

for every one half spoonful of mustard,

so the ratio of honey to mustard

in terms of spoonfuls is
two spoonfuls of honey

for every one half spoonful of mustard,

so this is the ratio of honey to mustard.

Let me write this.

This is honey, and this
right over here is mustard.

Now, let's look at Sandwich
Town, so I'll call that ST.

So Sandwich Town makes dipping sauce

by having four spoonfuls of honey

for every one spoonful of mustard.

So the ratio of honey to mustard

is four spoonfuls to one spoonful,

so once again, that is
honey and that is mustard.

Now, can we make these equivalent ratios

or can we compare them somehow?

Well, let's see.

We have one half spoonful of mustard here.

We have one spoon of mustard here,

so what if we multiplied both the mustard

and the honey spoonfuls by two?

That still would be an equivalent ratio

because we're multiplying
by the same amount.

So if we multiply by
two in both situations,

you have four spoonfuls of honey

for every one spoonful of mustard.

Well, that's the exact same ratio

that we have at Sandwich Town.

So it actually turns out that they have

the same concentration of mustard.

They have the same ratio
of honey to mustard.

Four spoonfuls of honey for
every spoonful of mustard

in either situation.

Let's do another example.

So here, we are asked or
we are told, we are told,

Patrick's favorite shade of purple paint

is made with four ounces of blue paint,

so underline that in blue,
four ounces of blue paint,

for every three ounces of red paint,

for every three ounces of red paint.

So the ratio of blue paint to red paint

is four ounces of blue,
four ounces of blue,

for every three ounces
of red, so four to three.

Which of the following paint mixtures

will create the same shade of purple?

All right, pause this video

and see if you can figure
it out on your own.

So this is three ounces of blue paint

mixed with four ounces of red paint.

Well, this is a ratio
here of three to four,

and even though it's dealing
with the same numbers,

this is a different ratio.

The order matters.

This is four ounces of blue
for every three ounces of red.

This is saying three ounces of blue

for every four ounces of red,
so we could rule this one out.

Eight ounces of blue paint mixed

with six ounces of red paint.

So here, this ratio is
eight ounces of blue

for every six ounces of red.

Well, are these equivalent ratios?

Well, the difference, or you can go,

if you multiply by two in either case,

you will get to eight to six.

Four times two is eight,
three times two is six.

So this is indeed an equivalent ratio,

so we would select this one.

All right, here they say
six ounces of blue paint

mixed with eight ounces of red paint.

So this is, they've swapped
the blues and the red

relative to this one, so this
is a ratio of six to eight,

so let me write this down.

So this is a ratio, six
ounces of blue paint

for every eight ounces of red paint.

So just like we ruled out that first one,

this is dealing with the same numbers

but in a different order
and the order matters,

so we'll rule that out.

20 ounces of blue paint,
20 ounces of blue paint,

for every 15 ounces of red paint.

So are these equivalent?

Well, let's think about it.

To go from four to 20,
you can multiply by five,

and to go from three to 15,
you could multiply by five,

so we can multiply by the same factor

to go from four to three to 20 to 15,

so this is indeed an equivalent ratio.

12 ounces of blue paint mixed
with 16 ounces of red paint.

All right, so this is a ratio here

of 12 ounces of blue for
every 16 ounces of red.

So let's think about this.

To go from four to 12, you
would multiply by three.

Now, if you multiplied three by three,

you would have a nine here, not a 16,

so this is definitely
not an equivalent ratio.

Another way of thinking about it,

you have, in terms of ounces,

you have more ounces of
blue than you have of red

for any of the equivalent ratios,

but here you have more
ounces of red than blue,

so once again, another way of realizing

that that is not equivalent,

so only B and D are
the equivalent mixtures

that will provide the
same shade of purple.

To have that same shade,

you need the same ratio of blue to red.