GRE Fractions Questions Practice Questions with Answers

Fractions represent numerical values that are not whole numbers, expressed as one integer divided by another. Success on the Quantitative Reasoning section of the GRE requires a firm grasp of how to manipulate these values, whether you are comparing quantities, solving complex word problems, or simplifying algebraic expressions. Since the GRE often combines fractions with ratios, percentages, and decimals, understanding their underlying mechanics is a prerequisite for a high score. You can build a solid foundation for these topics by exploring our comprehensive GRE Prep hub, which covers all math domains in detail.

Concept Explanation

A fraction is a mathematical expression consisting of a numerator and a denominator that represents a part of a whole or a ratio between two quantities. In the form $\frac{a}{b}$, the top number (numerator) indicates how many parts we have, while the bottom number (denominator) indicates the total number of equal parts that make up a whole. To excel at GRE fractions questions, you must be proficient in four primary operations: addition, subtraction, multiplication, and division. Addition and subtraction require a common denominator, which is often found using the Least Common Multiple (LCM). Multiplication is performed by multiplying numerators together and denominators together, while division involves multiplying by the reciprocal of the divisor. Additionally, the GRE frequently tests "fractional parts of a whole" in word problems, where you must translate phrases like "two-thirds of the remaining balance" into precise algebraic equations. For more advanced practice, tools like the AI Question Generator can help you create custom problems that mix fractions with other complex topics.

Solved Examples

1. Example 1: Addition and Simplification
   Simplify the expression: $\frac{3}{8} + \frac{5}{12}$.
   1. Find the Least Common Denominator (LCD) for 8 and 12. The multiples of 8 are 8, 16, 24, and the multiples of 12 are 12, 24. The LCD is 24.
   2. Convert each fraction: $\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}$ and $\frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24}$.
   3. Add the numerators: $\frac{9 + 10}{24} = \frac{19}{24}$.
   4. The fraction is already in simplest form. Final Answer: $\frac{19}{24}$.
2. Example 2: Division of Fractions
   Calculate $\frac{7}{10} \div \frac{14}{5}$.
   1. Change the division sign to multiplication and flip the second fraction (the reciprocal): $\frac{7}{10} \times \frac{5}{14}$.
   2. Multiply the numerators and denominators: $\frac{7 \times 5}{10 \times 14} = \frac{35}{140}$.
   3. Simplify by dividing both by their greatest common divisor (35): $\frac{35 \div 35}{140 \div 35} = \frac{1}{4}$. Final Answer: $\frac{1}{4}$.
3. Example 3: Word Problem Application
   A student spends $\frac{1}{4}$ of her study time on math and $\frac{2}{5}$ of the remaining time on verbal. What fraction of her total study time is spent on verbal?
   1. Let the total study time be 1.
   2. Time spent on math is $\frac{1}{4}$. The remaining time is $1 - \frac{1}{4} = \frac{3}{4}$.
   3. Time spent on verbal is $\frac{2}{5}$ of the remaining time: $\frac{2}{5} \times \frac{3}{4}$.
   4. Multiply: $\frac{6}{20}$.
   5. Simplify: $\frac{3}{10}$. Final Answer: $\frac{3}{10}$.

Practice Questions

1. Which of the following is greater: $\frac{5}{9}$ or $\frac{11}{20}$?

2. Solve for $x$: $\frac{2}{3}x - \frac{1}{4} = \frac{5}{6}$.

3. A jar contains red, blue, and green marbles. If $\frac{1}{3}$ are red and $\frac{2}{7}$ are blue, what fraction of the marbles are green?

4. Simplify the complex fraction: $\frac{\frac{3}{5}}{\frac{9}{10}}$.

5. If a recipe requires $2\frac{3}{4}$ cups of flour and you want to make $\frac{1}{3}$ of the recipe, how many cups of flour do you need?

6. Compare Quantity A and Quantity B:
Quantity A: $\frac{1}{2} + \frac{1}{3} + \frac{1}{4}$
Quantity B: $1$

7. A tank is $\frac{3}{8}$ full. After adding 10 gallons, it is $\frac{5}{8}$ full. What is the total capacity of the tank in gallons?

8. What is the value of $(\frac{2}{3})^3 \times \frac{9}{4}$?

Answers & Explanations

1. Answer: $\frac{5}{9}$
   To compare $\frac{5}{9}$ and $\frac{11}{20}$, use cross-multiplication. $5 \times 20 = 100$ and $9 \times 11 = 99$. Since 100 is greater than 99, $\frac{5}{9}$ is the larger fraction.
2. Answer: $x = \frac{13}{8}$ or $1.625$
   Add $\frac{1}{4}$ to both sides: $\frac{2}{3}x = \frac{5}{6} + \frac{1}{4}$. The LCD of 6 and 4 is 12. So, $\frac{2}{3}x = \frac{10}{12} + \frac{3}{12} = \frac{13}{12}$. Multiply both sides by the reciprocal $\frac{3}{2}$: $x = \frac{13}{12} \times \frac{3}{2} = \frac{39}{24} = \frac{13}{8}$.
3. Answer: $\frac{8}{21}$
   Add the red and blue fractions: $\frac{1}{3} + \frac{2}{7}$. The LCD is 21. $\frac{7}{21} + \frac{6}{21} = \frac{13}{21}$. Subtract from the whole: $1 - \frac{13}{21} = \frac{8}{21}$.
4. Answer: $\frac{2}{3}$
   Treat this as division: $\frac{3}{5} \div \frac{9}{10}$. Multiply by the reciprocal: $\frac{3}{5} \times \frac{10}{9} = \frac{30}{45}$. Simplify by dividing by 15: $\frac{2}{3}$.
5. Answer: $\frac{11}{12}$
   Convert the mixed number to an improper fraction: $2\frac{3}{4} = \frac{11}{4}$. Multiply by $\frac{1}{3}$: $\frac{11}{4} \times \frac{1}{3} = \frac{11}{12}$.
6. Answer: Quantity A is greater
   Find a common denominator for Quantity A (12): $\frac{6}{12} + \frac{4}{12} + \frac{3}{12} = \frac{13}{12}$. Since $\frac{13}{12} > 1$, Quantity A is greater.
7. Answer: 40 gallons
   Let $C$ be the capacity. The equation is $\frac{3}{8}C + 10 = \frac{5}{8}C$. Subtract $\frac{3}{8}C$ from both sides: $10 = \frac{2}{8}C$, which simplifies to $10 = \frac{1}{4}C$. Multiply by 4: $C = 40$.
8. Answer: $\frac{2}{3}$
   First, cube the fraction: $(\frac{2}{3})^3 = \frac{8}{27}$. Then multiply: $\frac{8}{27} \times \frac{9}{4}$. Cross-cancel: 8 and 4 simplify to 2 and 1; 9 and 27 simplify to 1 and 3. The result is $\frac{2 \times 1}{3 \times 1} = \frac{2}{3}$.

1. If a pizza is cut into 12 slices and you eat 3, what fraction of the pizza remains?

• A1/4
• B1/2
• C3/4
• D2/3

Frequently Asked Questions

How do I compare two fractions quickly on the GRE?

The fastest way to compare two fractions is the cross-multiplication method, where you multiply the numerator of the first by the denominator of the second and vice versa. The side with the larger product corresponds to the larger fraction.

What is the difference between a proper and improper fraction?

A proper fraction has a numerator smaller than its denominator (e.g., 3/4), whereas an improper fraction has a numerator equal to or larger than its denominator (e.g., 5/4). On the GRE, you may need to convert improper fractions to mixed numbers or decimals depending on the question format.

Can I use a calculator for fractions on the GRE?

The GRE on-screen calculator does not have a fraction button, so you must either convert fractions to decimals or perform the arithmetic manually. Understanding how to simplify fractions by hand is often faster than using the calculator for every step.

When should I convert fractions to decimals?

Conversion to decimals is useful when comparing multiple values or when the question involves currency, but keeping numbers as fractions is generally better for maintaining precision. You can practice these conversions using the Retrieval Challenge to sharpen your mental math speed.

What is a "complex fraction" on the GRE?

A complex fraction is a fraction where the numerator, the denominator, or both contain another fraction. These are simplified by treating the main fraction bar as a division symbol and multiplying the top fraction by the reciprocal of the bottom one.