Ratios and Proportions

Ratios and proportions are fundamental to nursing math, especially for medication dosages and IV calculations. The TEAS heavily tests these concepts.

Ratios

A ratio compares two quantities. It can be written three ways:

Types of Ratios

Unit Rates

A unit rate has a denominator of 1.

Example: If a nurse walks 12 miles in 3 hours, what is the rate per hour?

• 12 miles ÷ 3 hours = 4 miles per hour

Proportions

A proportion is an equation stating that two ratios are equal.

Example: 1/2 = 2/4

Cross-multiplication: If a/b = c/d, then ad = bc

Solving Proportions

Method: Cross-Multiply and Solve

Example: Solve for x: 3/4 = x/12

1. Cross-multiply: 3 × 12 = 4 × x
2. Simplify: 36 = 4x
3. Divide: x = 9

Setting Up Proportions

Key: Keep units consistent on each side.

Example: If 500 mg is in 10 mL, how many mL contain 250 mg?

Setup:

• 500 mg / 10 mL = 250 mg / x mL

Solve:

• 500x = 250 × 10
• 500x = 2500
• x = 5 mL

Dosage Calculations Using Proportions

Formula: Desired/Have = x/Quantity

Example: Order: 750 mg. Available: 250 mg tablets. How many tablets?

• 750/250 = x/1
• x = 3 tablets

Example: Order: 0.5 g. Available: 250 mg/5 mL. How many mL?

1. Convert: 0.5 g = 500 mg
2. Set up: 250 mg / 5 mL = 500 mg / x mL
3. Cross-multiply: 250x = 2500
4. Solve: x = 10 mL

Scale and Similar Figures

Proportions are used with maps and scale drawings.

Example: A map scale is 1 inch = 50 miles. If two cities are 3.5 inches apart on the map, what is the actual distance?

• 1/50 = 3.5/x
• x = 175 miles

Direct and Inverse Proportions

Direct Proportion: y = kx (k is constant) Inverse Proportion: xy = k (k is constant)

Common Proportion Problems in Healthcare

Problem-Solving Tips

1. Identify what you know and what you need to find
2. Set up the proportion with units labeled
3. Keep units consistent on each side
4. Cross-multiply and solve for the unknown
5. Check your answer - does it make sense?