Ratio and Proportion

A ratio is the same as a fraction and can be expressed as a fraction (1/2) or in the algebraic form (1:2). This relationship is stated as one is to two.

A proportion is an equation of equal fractions or ratios.

• 1/2 = 4/8

To calculate doses, begin each proportion with the two known values, for example, 15 grains = 1 gram (known equivalent) or 10 milligrams = 2 milliliters (dosage available) on one side of the equation. Next, make certain that the units of measure on the opposite side of the equation are the same as the units of the known values and are placed on the same level of the equation.

• Problem A:
• (15 gr/1 g) = (10 gr/x g)
• Problem B:
• (10 mg/2 ml) = (5 mg/x ml)

Once the proportion is set up correctly, cross-multiply the opposing values of the proportion.

• Problem A:
  
• Problem B:
  

Next, divide each side of the equation by the number with the x to determine the answer. Then, add the unit of measure corresponding to x in the original equation.

• Problem A:
• (15x/15) = (10/15)
  x = 2/3 or 0.6 g
• Problem B:
• (10x/10) = (10/10)
  x = 1 ml

Calculation of IV Drip Rate

To calculate the drip rate for an intravenous infusion, 3 values are needed:

1. The amount of solution and corresponding time for infusion. May be ordered as:
   • 1000 ml over 8 hr
     or
   • 125 ml/hr
2. The equivalent in time to convert hours to minutes.
   • 1 hr = 60 min
3. The drop factor or number of drops that equal 1 ml of fluid. (This information can found on the IV tubing box.)
   • 10 gtt = 1 ml

Set up the problem by placing each of the 3 values in a proportion.

• (125 ml/1 hr) × (1 hr/60 min) × (10 gtt/1 ml)

Numbers and units of measure can be canceled out from the upper and lower levels of the equation.

• The numbers cancel, leaving:
  
• The units cancel, leaving:
  

Next, multiply each level across and divide the numerator by the denominator for the answer.

Calculation of Creatinine Clearance (CCr) in Adults from Serum Creatinine

• Men: CCr = (weight (kg) × (140 – age))/72 × serum creatinine (mg/dl)
• Women: CCr = 0.85 × calculation for men

Calculation of Body Surface Area (BSA) in Adults and Children

• Dubois method:
• SA (cm²) = wt (kg)^0.425 × 71.84
  
• Simplified method:
  

Body Mass Index

• BMI = wt (kg) ÷ ht (m²)