Fractions and Decimals: TEAS Practice Question with Answer & Explanation

Understanding Fraction Ordering for the TEAS

To successfully compare and order fractions on the TEAS, you need a reliable method to determine their relative values. While finding a least common denominator (LCD) is one way, it can be time-consuming when denominators are prime or unrelated (like 7, 3, 9, and 5). The most efficient method for the TEAS is often converting fractions to decimals.

Step-by-Step Conversion

To convert a fraction to a decimal, divide the numerator (top) by the denominator (bottom).

1. 5/9: Divide 5 by 9.
   • $5 \div 9 = 0.555...$ (repeating)
2. 4/7: Divide 4 by 7.
   • $4 \div 7 \approx 0.571$
3. 3/5: Divide 3 by 5.
   • $3 \div 5 = 0.60$
4. 2/3: Divide 2 by 3.
   • $2 \div 3 = 0.666...$ (repeating)

Comparing the Values

Now that all numbers are in decimal form, align them by the decimal point to compare the tenths and hundredths places:

• 0.555 (Smallest)
• 0.571
• 0.600
• 0.666 (Largest)

Matching these back to the original fractions, we get: 5/9 < 4/7 < 3/5 < 2/3.

Why the Other Options are Incorrect

• Option B (4/7, 5/9, 2/3, 3/5): This is incorrect because 4/7 (0.571) is larger than 5/9 (0.555).
• Option C (2/3, 3/5, 4/7, 5/9): This is the reverse order (greatest to least). The question specifically asks for least to greatest.
• Option D (5/9, 3/5, 4/7, 2/3): This switches 4/7 and 3/5. Although 3/5 (0.60) looks "smaller" because the numbers are lower, its value is higher than 4/7 (0.57).

TEAS Math Tip: The "Cross-Multiplication" Hack

If you only need to compare two fractions quickly (like 4/7 and 5/9), multiply across:

• $4 \times 9 = 36$
• $7 \times 5 = 35$ Since 36 is greater than 35, 4/7 is greater than 5/9. This is faster than division for smaller sets!