Welcome to the first example
of a one-step dosage calculation.
To determine the dosage, we'll be using a proportion
which we see here below,
which is formed by setting two ratios
or rates equal to each other.
So once we form the proportion,
the cross products will be equal,
meaning a times d, will always equal b times c.
So if we have one unknown value,
we can solve for the unknown by cross-multiplying
and solving this equation.
Looking at our example,
it says "Suppose a drug is available in 150 mg tablets.
The dosage ordered is 375 mg. How many tablets are needed?"
So we know the drug is available in 150 mg tablets,
which we can write as a rate.
We can write this as 150 mg,
per one tablet.
And now for the second rate,
we're going to use the fact that we need 375 mg.
So that rate would be 375 mg per
an unknown number of tablets, which we'll call x tablets.
And before we cross-multiply,
it's important to recognize that we have the same units,
and the numerators are on top,
unless they're both milligrams.
And the same units on the bottom or in the denominators.
They are both tablets.
If these weren't the same,
we'd have to perform an additional conversion.
When we cross-multiply,
it doesn't matter which cross product we do first.
I prefer to find the cross product containing the variable.
So 150 times x must equal one times 375.
Again, 150 times x is 150x must equal
one times 375, that's 375.
Notice how when cross-multiplying,
we do leave the units off to simplify our equation.
And now to solve for x we'll divide both sides by 150.
So we have x equals 375 divided by 150.
We do want to simplify this though.
These two do share a common factor of 75.
There are five 75's in 375.
And there are two 75's in 150.
So we have x equals five halves.
Let's also write this as a mixed number and a decimal.
To do this we'll perform this division,
remember a fraction bar means division.
So five divided by two,
there are two two's in five,
two times two is four.
We subtract.
So that means that five halves is equal to two and one half.
The fraction is formed by the remainder over the divisor.
We should recognize this as 2.5,
but by hand we can put a decimal point after the five here,
move it up into the quotient,
and after we add a zero here, notice how this is still five.
So we can bring the zero down,
and there are five twos in 10.
Five times two is 10.
We subtract.
Now we have zero, verifying the quotient is 2.5
Of course if we're allowed to use a calculator,
we can find this value much quicker.
375 divided by 150,
is 2.5.
So to answer the question,
if the dosage is 375 mg,
we need 2.5 or two and a half tablets.
I hope you found this helpful.