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Ratios and Proportions

Nursing Knowledge

# Ratios and Proportions

Ratios and proportions are foundational mathematical concepts used in the dosage calculation tasks that nurses perform regularly. Using ratios and proportions allows nurses to scale dosages up or down, based on various patient factors like weight or renal function. Mastering these calculations is vital for administering the right amount of medication, be it in tablet or liquid form, or even for IV infusions, and avoiding medication errors.
Last updated: December 4, 2023

## What is a ratio?

A ratio is a number that describes the relationship between 2 numbers.

## What is a proportion?

A proportion means that 2 ratios or fractions are equal.

## Why are ratios and proportions important in dosage calculation?

Ratios and proportions help nurses accurately scale dosages up or down based on patient-specific factors like weight. If a medication is prescribed at a certain amount per kg of body weight, the nurse needs to figure out how much medication to give a patient according to their weight.

Medications in solutions are also described using ratios.
For example: epinephrine 1:10,000 means that there is 1 part medication (epinephrine) in 10,000 parts of solution.

## Example calculations

### Identifying proportions: Does 3:4 equal 6:8?

To determine if a ratio is equal, multiply the means by the extremes: In proportions, the product of the means always equals the product of the extremes. Cross-multiplication of the ratios as fractions will determine if they are equal and a proportion.

3/4 = 6/8

Multiplying means by extremes/cross-multiplying the ratios as fractions:

3*8 = 4*6; 24 =24 → 3/4 = 6/8 is true, so the ratio is a proportion.

### Medication example

Let’s say a medication is prescribed at 5 mg/kg and you have a patient who weighs 70 kg. Using ratios, set up the equation first:

• 5 mg / 1 kg = x mg / 70 kg
• Solve for x to find the correct dosage: x = 5 mg/kg × 70 kg = 350 mg
• So, you would administer 350 mg of the medication for this 70 kg patient.

Following the rule of multiplying means and extremes:

• 5 mg / 1 kg = x mg / 70 kg
• 5*70 = 1*x
• 350 = x

Multiple the units, and you reach 350 mg for this patient.

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