ratio and proportions

Ratios and Proportions

Ratios

• Ratios represent one value to another.

• Ex. for every 2 girls there could be three boys

• The ratio can be written these ways:

Medication Concentration

The concentration of liquid medication is often expressed as a ratio. The anesthetic Propofol comes in a concentration of 10 mg per mL and would appear as 10mg/mL (10mg per 1 mL).

To understand medication dosage we need to know how PROPORTIONS work.

Proportions compare two ratios. They work just like equivalent fractions!

What is a proportion?

A proportion demonstrates the relationship between two ratios. In a true proportion, the two ratios are equal. Using the 100 mg tablets, we can say if 1 tablet contains 100 mg then 2 tablets contain 200 mg.

To find a missing value in a proportion cross multiply then divide.

 $\frac{75\ mg}{5\ mL}\ =\frac{187.5\ mg}{x\ mL}\ \ \ \$  

Cross multiply first

 $5\ \times\ 187.5\ =\ 937.5\ \ \ \ \ \ \ \ \ \ 75\ \times\ 1x\ =\ 75x$  

Our answer looks like this:

 $937.5=75x$  

Divide

 $\frac{937.5}{75}=\frac{75x}{75}$  

Our answer should be in mL

 $\frac{937.5}{75}=12.5\ mL$  

Multiple Choice

  $\frac{17\ mg}{3\ tabs}\ =\ \frac{42.5\ mg}{x\ tabs}$ Find out how many tablets should be administered.

• 127.5 tablets

• 17 tablets

• 5.2 tablets

• 7.5 tablets

Remember to start by cross multiplying

 $42.5\ \times3\ =127.5\ \ \ \ 17\times x=17x$  

Then we divide to solve for x

 $\frac{127.5}{17}=\frac{17x}{17}$  

For this question our answer should be in tablets.

 $\frac{127.5}{17}=7.5\ tablets$  

Challenge Question!!

Cefaclor is available in 187 mg per 5 mL

A physician orders 374 mg of Cefaclor for a child with an ear infection. How many mL of Cefaclor should the child receive?

Set up the problem!!

 $\frac{187\ mg}{5mL}=\frac{374\ mg}{x\ mL}$  

Start by cross multiplying

5mL x 374mg = 187mg x

Cross multiplying leaves us with:

 $1,870=187x$  

Next we divide by the number that holds the veriable (x).

 $\frac{1870}{187}=\frac{187x}{187}$  

Your answer is 10 mL of Cefaclor.