Welcome to a lesson on the household system of measurement.
In this lesson we will define household volume units of measure.
And then convert between household units of measure
using proportions.
A household unit of measures is the most commonly used
system of measurement in homes of the United States.
Usually in the kitchen.
Units are given here on the left
with their abbreviations on the right.
We have
a drop
teaspoon
tablespoon
fluid ounce
cup
pint
quart
and gallon.
And here the conversions between units.
One teaspoon equal 60 drops.
One tablespoon equals three teaspoons.
One ounce equals two tablespoons.
One cup equals eight ounces.
One pint equals two cups.
One quart equals two pints.
And one gallon equals four quarts.
In this lesson
to perform the conversions
we'll be using proportions.
Where proportion states that two ratios or rates are equal.
So if a to b and c to d are two equal ratios.
Once we set them equal to each other
this is a proportion.
And what's special about a proportion
is that the cross products are always equal
as long as a unit of a and c are the same
and the unit of b and d are the same.
So again if we have a proportion
then
a times d
must equal
b times c.
The reason this helps is because
if one of these four values is unknown
we can cross multiply
and solve for the unknown.
As an example
let's say your car gets 28 miles per gallon
and you want to determine how far you can drive on three and a half gallons of gas.
Well 28 miles per gallon is a rate which we see here in fraction form.
We can set this equal to
x
to three point five gallons.
Where x is the number of miles you can drive
on three point five gallons.
And now we can cross multiply and solve for x.
So ignoring the units for a moment.
One times x would be x.
So x must equal
28 times three point five.
So again we have x equal 28
times three point five.
which is 98.
We can say the units would be miles.
Let's look at some more conversions.
Here we want to convert
two teaspoons to drops.
So we set up two ratios comparing teaspoons to drops.
Using this information
with the unknown
and one of our conversions.
So we'll have two teaspoons.
Two and unknown number of drops
must equal
looking at our conversions
one teaspoon
to 60 drops.
Notice how we have teaspoons on the top
and drops on the bottom.
Now we can cross multiply and solve for x.
X times one which is x.
Must equal
two time 60
which is 120.
Which means
two teaspoons
is equal to 120 drops.
Next we have half a tablespoon
equals
a certain number of teaspoons.
So now we have two ratios comparing
tablespoons and teaspoons.
One half
tablespoon
to
an unknown number of teaspoons. Let's say x teaspoons.
Must equal.
Looking at our conversions.
Notice one tablespoon equals three teaspoons.
And notice a tablespoons are on top so we'll have one tablespoon.
to three teaspoons.
And again now we cross multiply to solve for x.
Here we have x times one which is x.
Must equal
one half times three that would be three halves.
So we have three halves of a teaspoon.
Let's convert this to a mixed number or a decimal.
So we have three
divided by two there's one, two, and three.
One times two is two we subtract.
We have a remainder of one.
Which means three halves is equal to one and one half.
Which should be one point five.
Now we want to convert drops to teaspoons.
So now we have two ratios comparing drops to teaspoons.
45
drops
to an unknown number of teaspoons.
Must equal.
We already know that one teaspoon equal 60 drops.
Notice how we have drops on top.
So we must have 60 drops on top.
And one teaspoon
in the denominator.
Now we cross multiply.
Notice here we have x time 60 that would be 60 x.
equals
45 times one that just 45.
Here we have to solve for x by dividing both sides by 60.
So we have x equals
forty-five sixtieth
which does simplify
these two
do have a common factor of 15.
45 divided by 15 is three.
And 60 divided by 15 is four.
So 45 drops is equal to three fourth
of a teaspoon.
Next we want to convert tablespoons to ounces.
So we'll have two ratios
comparing tablespoons to ounces.
So we have five tablespoons to an unknown number of ounces.
Must equal.
Notice here that one ounce equals two tablespoons.
But tablespoons must be in the numerator or on top.
So we'll have two tablespoons
to
one ounce.
And now again we cross multiply.
So we have x times two that's 2x
equals
five times one that's five.
Divide both sides by two.
We have x equals five halves.
Let's convert that to a mixed number or a decimal.
Five divided by two or two two's in five two times two is four subtract
remainder of one this would be two and one half.
Or two point five.
Let's go and write two and one half.
Now were gonna convert eight ounces to tablespoons.
So we'll have two ratios comparing ounces to tablespoons.
First ratio is eight ounces to an unknown number of tablespoons.
Must equal.
We just saw that one ounce equals two tablespoons.
Ounces is on top so we'll have one ounce
to
two tablespoons.
Cross multiply.
Here we have x times one that x.
Equals
eight times two that sixteen.
So eight ounces equals 16 tablespoons.
Next we want to convert 12 teaspoons to tablespoons. So we'll have two ratios comparing teaspoons
to tablespoons.
And again the conversion is one tablespoon equals three teaspoons.
So we'll have three teaspoons.
Over one tablespoon.
Notice how the unit are the same on the top and on the bottom.
And now we cross multiply.
So x times three would be 3x
equals
12 times one is 12
divide both sides by three
and we have x equals four.
So 12 teaspoons equals four
tablespoons.
We are running short on time.
But I do want to take a look at one more example where
where there's not a direct conversion
provided here in the table.
So let's go ahead and take a look at this last example here.
Where we want to convert 28 pints to gallons.
Again there's no conversion in the table
that converts pints
directly to gallons.
But we can convert
pints to quarts
and then quarts to gallons.
So we have an option using two proportion
or using unit fractions.
To keep it consistence.
Let's go ahead and use proportions.
So instead of setting up a ratio from pints to gallons.
Were gonna set up a ratio comparing
pints to quarts first.
So we'll have 28 pints.
To an unknown number of quarts.
Must equal.
Again the conversion is one quart equals two pints.
So we'll have two pints
to one quart.
Cross multiply.
We have x times two that's 2x
equals
28 times one that's 28.
Divide both sides by two.
Notice how x is equal to 14.
Which means 28 pints
is equal to 14 quarts.
And now we convert the quarts
to gallons.
So again we'll have
14 quarts
to x number of gallons.
Must equal.
One gallon equals four quarts.
The quarts must go on top so four quarts
to one gallon
and we cross multiply again.
So x times four that be four x.
And 14 times one that's 14.
Divide both sides by four.
And we have x equals fourteen fourth
these two have a common factors of two.
So we can say x equals seven halves.
But to convert this to a mixed number or decimal.
We have to perform this division.
Seven divided by two.
There are three two's in seven three times two is six and we subtract remainder is one.
So seven halves is equal to three and one half.
Or three point five.
Let's leave it as three and one half.
The other option here would be to use unit fractions
which I do show in a different lesson.
I hope you found this helpful.