Ratio and Fraction Conversion: TEAS Practice Question with Answer & Explanation

Understanding Ratios and Fractions

In the TEAS 7 Math section, you will frequently be asked to convert between ratios, fractions, and percentages. A ratio compares two quantities. In this case, the ratio is 24:36 (24 nurses to 36 patients).

To convert any ratio to a fraction, the first number in the ratio becomes the numerator (top) and the second number becomes the denominator (bottom).

1. Write as a fraction: 24/36
2. Simplify the fraction: To simplify, find the Greatest Common Factor (GCF) of both numbers.

Step-by-Step Simplification

To simplify 24/36, we look for a number that divides evenly into both:

• Both are divisible by 2: 12/18
• Both are divisible by 2 again: 6/9
• Both are divisible by 3: 2/3

Alternatively, if you recognized that 12 is the GCF:

• 24 ÷ 12 = 2
• 36 ÷ 12 = 3
• Result: 2/3

Analysis of the Options

• Choice A: 5/6 – This is an incorrect simplification. While 30/36 would simplify to 5/6, our numerator is 24.
• Choice B: 6/5 – This is an improper fraction that reverses the relationship and uses incorrect values.
• Choice C: 2/3 (Correct) – This is the most reduced fractional form of the ratio 24:36. For every 2 nurses, there are 3 patients.
• Choice D: 3/2 – This is the reciprocal of the correct answer. This would represent a patient-to-nurse ratio (36:24), rather than the nurse-to-patient ratio requested.

TEAS Concept: Ratio to Fraction Conversion

The TEAS exam tests your ability to interpret "parts of a whole" vs. "parts to parts." In this question, the ratio is a direct comparison of two groups. Always ensure you keep the numbers in the same order they were presented: First Number : Second Number = Numerator / Denominator.

Memory Tip

Think of the colon (:) in a ratio as a "tilted" fraction bar. The number on the left stays on top, and the number on the right slides underneath. 24 : 36 → 24 / 36.