#### Ex 2: Medication Dosage Calculation Using a Proportion – One Step

Welcome to a one-step dosage calculation. The order is for fifteen mEq and ten mEg
per five cc’s is available. How many cc’s are needed? To determine the dosage, we’ll be setting up a proportion where we
set two rates equal to each other, and as long as the units of A and C and the units of B and D are the same, then A times D will always equal B times C. So if we have one unknown, we can solve for the unknown using this equation here. And just for some background information, mEq means milliequivalent, this is one thousandth of a gram equivalent. To set up our first rate, let’s use this information here. Ten mEq per five cc’s. So ten mEq per five cc’s equals now for the second rate, we know we need fifteen mEq, so we’ll put fifteen mEq to and unknown number of cc’s, we’ll call it X cc’s. And again, notice how the units in the numerators, or the top are the
same, and the units in the denominator on the bottom are the same. So now we can cross multiply and solve for X. When cross multiplying, we will leave off the units to form the equation. So ten times X must equal five times fifteen. Again ten times X would be ten X, and five times fifteen is seventy-five. Notice both fractions, we’ll divide both sides by ten. So we have X equals seventy-five tenths. This is an improper fraction it’s also not simplified. So we’ll simplify this, then express it as a mixed number and a
decimal. These two do share a common factor of five, there are fifteen fives in seventy-five and two fives in ten. So fifteen-halves is a number of cc’s we need, based upon the order. To convert this to
a mixed number, or decimal, we’ll perform this division, remember a
fraction bar means division. So fifteen divided by two, there are seven twos in fifteen. Seven times two is fourteen, subtract, the remainder of one. Which means fifteen-halves is equal to seven and one-half, with the remainder over the divisor for the
fraction. We should recognize this as seven point five. By hand we need to put a decimal point here after the fifteen, move it up to the quotient. Now we can add a zero here, notice how this is still fifteen, we bring the zero down, notice there are five, twos in ten. Five times two is ten, subtract, the remainder will be zero, verifying our quotient is seven point five. And therefore, to fill this order, we need seven point five cc’s. Of course we could find this answer much quicker if we use a calculator. Notice from here, seventy-five divided by ten would give us the seven point five. I hope you found this helpful.