Easy GRE Fractions Questions Practice Questions

A fraction represents a part of a whole, consisting of a numerator over a denominator that indicates how many equal parts make up a unit. Understanding these numerical relationships is a fundamental requirement for the GRE Prep process, as they appear frequently in both Quant Comparison and Problem Solving formats. While the exam covers advanced topics, high performance relies on your ability to quickly manipulate basic values without calculation errors.

Concept Explanation

Easy GRE fractions questions test your proficiency with basic operations such as addition, subtraction, multiplication, and division, alongside the ability to simplify and compare values. A fraction is defined as the ratio $\frac{a}{b}$, where $a$ is the numerator (the number of parts we have) and $b$ is the denominator (the total number of equal parts). According to Khan Academy's arithmetic standards, mastering these involves several key rules:

• Simplification: Dividing both the numerator and denominator by their greatest common factor to reduce the fraction to its lowest terms.
• Common Denominators: To add or subtract fractions, you must find a Least Common Multiple (LCM) for the denominators.
• Multiplication: Multiply the numerators together and the denominators together: $\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$.
• Division: Multiply the first fraction by the reciprocal (the flipped version) of the second: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$.

Fractions are also closely linked to decimals and percentages. For instance, $\frac{1}{4}$ is equivalent to $0.25$ or $25\%$. On the GRE, you may encounter mixed numbers, which combine a whole number and a fraction, such as $2\frac{1}{3}$. These should usually be converted to improper fractions (where the numerator is larger than the denominator) before performing operations: $2\frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{7}{3}$.

Solved Examples

1. Addition: Calculate the sum of $\frac{2}{5}$ and $\frac{1}{3}$.

1. Find a common denominator. The LCM of 5 and 3 is 15.
2. Convert the fractions: $\frac{2}{5} = \frac{6}{15}$ and $\frac{1}{3} = \frac{5}{15}$.
3. Add the numerators: $6 + 5 = 11$.
4. The result is $\frac{11}{15}$.

2. Multiplication and Simplification: Solve $\frac{4}{9} \times \frac{3}{8}$.

1. Multiply the numerators: $4 \times 3 = 12$.
2. Multiply the denominators: $9 \times 8 = 72$.
3. Simplify the fraction $\frac{12}{72}$. Both are divisible by 12.
4. Divide by 12: $\frac{12 \div 12}{72 \div 12} = \frac{1}{6}$.

3. Division: Divide $\frac{5}{6}$ by $\frac{2}{3}$.

1. Identify the reciprocal of the divisor: The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$.
2. Rewrite as multiplication: $\frac{5}{6} \times \frac{3}{2}$.
3. Multiply: $\frac{15}{12}$.
4. Simplify by dividing both by 3: $\frac{5}{4}$, or $1\frac{1}{4}$.

Practice Questions

1. Which of the following is equivalent to $\frac{3}{8} + \frac{1}{4}$? 2. Solve for $x$: $x = \frac{7}{10} - \frac{2}{5}$. 3. A recipe calls for $\frac{2}{3}$ cup of sugar. If you are making 4 batches, how many cups of sugar are needed? 4. Simplify the expression: $\frac{15}{25} \div \frac{3}{5}$. 5. Compare Quantity A and Quantity B: Quantity A: $\frac{1}{2} \times \frac{4}{5}$ Quantity B: $\frac{2}{5}$ 6. If a pizza is cut into 12 equal slices and John eats 3 slices, what fraction of the pizza remains? 7. Convert the mixed number $4\frac{5}{6}$ into an improper fraction. 8. Calculate $\frac{3}{4}$ of 60. 9. Which fraction is larger: $\frac{5}{9}$ or $\frac{6}{11}$? 10. Solve: $(\frac{1}{2} + \frac{1}{4}) \times \frac{2}{3}$.

Answers & Explanations

1. Answer: $\frac{5}{8}$. To add $\frac{3}{8}$ and $\frac{1}{4}$, convert $\frac{1}{4}$ to $\frac{2}{8}$. Then, $3 + 2 = 5$, resulting in $\frac{5}{8}$.
2. Answer: $\frac{3}{10}$. Convert $\frac{2}{5}$ to $\frac{4}{10}$. Subtracting $\frac{4}{10}$ from $\frac{7}{10}$ gives $\frac{3}{10}$.
3. Answer: $2\frac{2}{3}$. Multiply $\frac{2}{3} \times 4 = \frac{8}{3}$. Converting to a mixed number gives $2\frac{2}{3}$.
4. Answer: 1. First, simplify $\frac{15}{25}$ to $\frac{3}{5}$. Then, $\frac{3}{5} \div \frac{3}{5} = \frac{3}{5} \times \frac{5}{3} = 1$.
5. Answer: The two quantities are equal. Quantity A is $\frac{1 \times 4}{2 \times 5} = \frac{4}{10}$, which simplifies to $\frac{2}{5}$. Quantity B is also $\frac{2}{5}$.
6. Answer: $\frac{3}{4}$. If 3 slices are eaten, $12 - 3 = 9$ slices remain. The fraction is $\frac{9}{12}$, which simplifies to $\frac{3}{4}$.
7. Answer: $\frac{29}{6}$. Multiply the whole number 4 by the denominator 6 ($4 \times 6 = 24$) and add the numerator 5 ($24 + 5 = 29$). The result is $\frac{29}{6}$.
8. Answer: 45. Multiply $\frac{3}{4} \times 60 = 3 \times 15 = 45$.
9. Answer: $\frac{5}{9}$. Cross-multiply to compare: $5 \times 11 = 55$ and $6 \times 9 = 54$. Since 55 is greater than 54, $\frac{5}{9}$ is the larger fraction.
10. Answer: $\frac{1}{2}$. Inside the parentheses, $\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$. Then, $\frac{3}{4} \times \frac{2}{3} = \frac{6}{12} = \frac{1}{2}$.

Frequently Asked Questions

How do I compare two fractions quickly on the GRE?

Use the cross-multiplication method by multiplying the numerator of the first fraction by the denominator of the second and vice-versa. The side with the larger product represents the larger fraction.

Can I use a calculator for fractions on the GRE?

Yes, the GRE Practice Questions with Answers section often involves the on-screen calculator, but it only provides decimals, so you must know how to convert between formats.

What is the difference between a proper and improper fraction?

A proper fraction has a numerator smaller than the denominator (e.g., $\frac{2}{3}$), while an improper fraction has a numerator equal to or larger than the denominator (e.g., $\frac{5}{4}$).

How do I simplify a large fraction?

Find the greatest common divisor (GCD) for both the top and bottom numbers and divide both by that number until they share no more common factors. You can also use the AI Question Generator to practice simplifying various values.

Why do we flip the second fraction when dividing?

Dividing by a number is mathematically identical to multiplying by its reciprocal, which is why the "keep, change, flip" rule is a standard procedure for fraction division.