**GRE Arithmetic Mastery: Fractions, Decimals, Percentages – Conversion & Calculation**

GRE Arithmetic Mastery: Fractions, Decimals, Percentages – Conversion & Calculation

By an Elite GRE Instructor (320+ Scorer Guarantee)

What This Is

The GRE tests fractions, decimals, and percentages in three core ways: 1. Conversion (e.g., What is 3/8 as a decimal?), 2. Calculation (e.g., What is 20% of 150?), 3. Comparison (e.g., Which is larger: 0.375 or 3/8?).

These questions appear in Quantitative Comparison, Problem Solving, and Data Interpretation—often as time-sinks if you don’t have a system. Mastering them saves 30+ seconds per question, letting you tackle harder problems (e.g., word problems, algebra) with confidence.

Real GRE-Style Example:
Which of the following is equal to 62.5%? A) 5/8 B) 6/8 C) 7/8 D) 5/6 E) 6/5

(Answer: A. 62.5% = 0.625 = 5/8.)

Key Concepts & Techniques

1. Fraction → Decimal Conversion

• How: Divide numerator by denominator (e.g., 3/4 = 3 ÷ 4 = 0.75).
• When to use: When comparing fractions to decimals/percentages (e.g., Is 0.6 > 3/5?).

2. Decimal → Fraction Conversion

• How: Count decimal places, write as fraction over 10/100/1000, simplify (e.g., 0.125 = 125/1000 = 1/8).
• When to use: When the answer choices are fractions (e.g., 0.375 = ?).

3. Percentage → Decimal Conversion

• How: Move decimal two places left (e.g., 45% = 0.45).
• When to use: For calculations (e.g., 20% of 80 = 0.20 × 80).

4. Decimal → Percentage Conversion

• How: Move decimal two places right (e.g., 0.03 = 3%).
• When to use: When the question asks for a percentage (e.g., What % is 0.25?).

5. Percentage → Fraction Conversion

• How: Write as fraction over 100, simplify (e.g., 75% = 75/100 = 3/4).
• When to use: When answer choices are fractions (e.g., 60% = ?).

6. Fraction → Percentage Conversion

• How: Convert to decimal first, then to % (e.g., 2/5 = 0.4 = 40%).
• When to use: When comparing fractions to percentages (e.g., Is 3/8 > 30%?).

7. Benchmark Fractions/Decimals/Percentages

• Memorize these:
• 1/2 = 0.5 = 50%
• 1/3 ≈ 0.333 = 33.3%
• 1/4 = 0.25 = 25%
• 1/5 = 0.2 = 20%
• 1/8 = 0.125 = 12.5%
• 3/8 = 0.375 = 37.5%
• 5/8 = 0.625 = 62.5%
• 7/8 = 0.875 = 87.5%
• When to use: For quick elimination in multiple-choice questions.

8. Cross-Multiplication for Fraction Comparison

• How: Compare a/b vs. c/d by checking if a × d > b × c.
• When to use: When comparing two fractions (e.g., Is 5/9 > 4/7?).

9. Percentage Increase/Decrease

• How:
• Increase: New = Original × (1 + %/100)
• Decrease: New = Original × (1 – %/100)
• When to use: For word problems (e.g., A price increases by 20%, then decreases by 20%. What’s the net change?).

10. Reverse Percentage (Finding Original Value)

• How: If 20% of X = 50, then X = 50 ÷ 0.20 = 250.
• When to use: When given a percentage of an unknown (e.g., After a 25% increase, the price is $120. What was the original price?).

Step-by-Step Strategy (For Any Conversion/Calculation Question)

Step 1: Identify the Target Format

• Ask: What form does the answer need to be in? (Fraction, decimal, or percentage?)
• Example: If the question asks "What is 3/5 as a percentage?", your target is percentage.

Step 2: Convert to a Common Format (Decimal is Safest)

• Why? Decimals are easiest for calculations and comparisons.
• How:
• Fractions → Divide numerator by denominator.
• Percentages → Move decimal two places left.
• Decimals → Already in the best form.

Step 3: Perform the Calculation (If Needed)

• For percentages of a number: Multiply decimal by the number (e.g., 30% of 200 = 0.30 × 200).
• For comparisons: Convert all to decimals and compare directly.

Step 4: Convert Back to the Required Format

• If the answer needs a fraction: Simplify the decimal (e.g., 0.6 = 6/10 = 3/5).
• If the answer needs a percentage: Move decimal two places right (e.g., 0.45 = 45%).

Step 5: Check Against Answer Choices

• Eliminate impossible options (e.g., if the answer is 0.625, eliminate 0.6 and 0.7).
• Use benchmarks (e.g., 0.625 = 5/8, so eliminate 6/8).

Step 6: Verify with Cross-Checking

• For fractions: Cross-multiply to confirm (e.g., 5/8 vs. 0.625 → 5 × 1 = 5, 8 × 0.625 = 5 → equal).
• For percentages: Reconvert to decimal to confirm (e.g., 62.5% = 0.625).

Fully Worked GRE-Style Example

Question:
Which of the following is equal to 0.375? A) 3/7 B) 3/8 C) 5/12 D) 7/16 E) 9/24

Step 1: Identify Target Format
- The question asks for a fraction equal to 0.375.

Step 2: Convert to Common Format (Decimal)
- 0.375 is already a decimal.

Step 3: Perform Calculation (Not Needed Here)
- We’re comparing, not calculating.

Step 4: Convert 0.375 to Fraction
- 0.375 = 375/1000 = (divide numerator/denominator by 125) = 3/8.

Step 5: Check Answer Choices
- A) 3/7 ≈ 0.428 → Not equal.
- B) 3/8 = 0.375 → Match!
- C) 5/12 ≈ 0.416 → Not equal.
- D) 7/16 ≈ 0.4375 → Not equal.
- E) 9/24 = 3/8 → Also a match!

Step 6: Verify with Cross-Checking
- 3/8 = 0.375 (confirmed).
- 9/24 simplifies to 3/8 → Both B and E are correct.

Wait—What?
- The GRE rarely has two correct answers. This is a trap—E is a simplified version of B, but the question asks for equal to 0.375, not the simplest form.
- Correct answer: B (since E is just a less simplified version of B).

Key Takeaway: Always check if answer choices are equivalent but not identical.

Common Mistakes

Mistake 1: Forgetting to Simplify Fractions

• Why it happens: Students stop at 375/1000 and don’t simplify to 3/8.
• Correct approach: Always simplify fractions to match answer choices.

Mistake 2: Misplacing the Decimal in Percentage Conversions

• Why it happens: Moving the decimal the wrong way (e.g., 0.05 = 50% instead of 5%).
• Correct approach: Left for % → decimal, right for decimal → %.

Mistake 3: Assuming All Fractions Convert to Terminating Decimals

• Why it happens: Students forget that 1/3 = 0.333... (repeating).
• Correct approach: Memorize repeating decimals (1/3, 1/6, 1/7, 1/9).

Mistake 4: Incorrectly Calculating Percentage Increase/Decrease

• Why it happens: Using addition instead of multiplication (e.g., 20% increase = ×1.20, not +20).
• Correct approach: New = Original × (1 ± %/100).

Mistake 5: Comparing Fractions Without Cross-Multiplication

• Why it happens: Guessing (e.g., thinking 5/9 > 4/7 because 5 > 4).
• Correct approach: Cross-multiply to compare (5×7 = 35 vs. 9×4 = 36 → 5/9 < 4/7).

GRE Traps & Timing

Trap 1: Equivalent but Non-Identical Answer Choices

• Example: 3/8 vs. 6/16 vs. 9/24 (all equal to 0.375).
• How to avoid: Simplify all fractions to lowest terms before comparing.

Trap 2: Repeating Decimals in Answer Choices

• Example: 1/3 ≈ 0.333, but answer choices might include 0.33 or 0.3333.
• How to avoid: Recognize repeating decimals and round only at the end.

Trap 3: Percentage vs. Decimal Confusion

• Example: 0.5% = 0.005, not 0.5.
• How to avoid: Always move the decimal two places for percentages.

Timing Budget

• Easy questions (direct conversion): 30–45 seconds.
• Medium questions (calculation + conversion): 60–75 seconds.
• Hard questions (word problems, reverse percentages): 90 seconds max.

Quick Practice

Question 1:
What is 45% of 160? A) 54 B) 72 C) 80 D) 90 E) 108

Answer: B (0.45 × 160 = 72).

Question 2:
Which is larger: 7/12 or 0.58? A) 7/12 B) 0.58 C) They are equal

Answer: A (7/12 ≈ 0.583 > 0.58).

Last-Minute Cram Sheet

1. Fraction → Decimal: Divide numerator by denominator.
2. Decimal → Fraction: Count decimal places, write over 10/100/1000, simplify.
3. Percentage → Decimal: Move decimal two places left.
4. Decimal → Percentage: Move decimal two places right.
5. Percentage → Fraction: Write over 100, simplify.
6. Fraction → Percentage: Convert to decimal first, then to %.
7. Benchmark conversions:
8. 1/8 = 0.125 = 12.5%
9. 3/8 = 0.375 = 37.5%
10. 5/8 = 0.625 = 62.5%
11. 7/8 = 0.875 = 87.5%
12. Percentage increase/decrease: New = Original × (1 ± %/100).
13. Reverse percentage: Original = New ÷ (1 ± %/100).
14. ⚠️ Trap: Always simplify fractions—equivalent answers may be traps!

Final Tip: On test day, convert everything to decimals first—it’s the fastest way to compare and calculate. Memorize the benchmarks to save time. Practice 5–10 questions daily until conversions feel automatic.