GMAT Fractions: Essential Tips, Practice Problems & Strategies

Key Takeaways

• Key Fractions to Memorize: Familiarize yourself with commonly used fractions and their decimal equivalents to save time during the exam.
• Simplifying Fractions: Learn techniques to simplify fractions efficiently for faster problem-solving.
• Converting Fractions to Decimals: Understanding how to convert between fractions and decimals is critical for solving various GMAT questions.
• Comparing Fractions: Discover methods to compare fractions quickly without needing complex calculations.

Fractions play a significant role in the GMAT Quantitative section, appearing in everything from problem-solving to data sufficiency questions. Understanding how to manipulate and simplify fractions quickly is essential for boosting your score. Whether it's converting fractions to decimals, comparing fractions, or solving complex word problems, mastering these concepts will give you a competitive edge on test day. This guide covers the key fraction-related skills you need to excel in the GMAT.

Understanding GMAT Fractions

Fractions are an essential part of the GMAT quantitative section. Whether you're solving word problems, comparing ratios, or simplifying complex equations, a strong grasp of fractions can make a significant difference in your performance. On the GMAT, you will often see questions requiring quick calculations involving fractions, so it's crucial to understand how they work and the common fractions you need to memorize.

GMAT Fractions to Memorize

Memorizing key fractions and their decimal equivalents can significantly improve your speed on the GMAT. While it’s possible to calculate these values during the test, knowing them by heart will allow you to focus on solving the problem instead of doing basic conversions. Here’s a deeper look at why memorization is essential and the key fractions to know.

Why Memorizing Fractions Helps

Many GMAT questions, especially in the Quantitative section, involve operations with fractions. Whether you’re dealing with ratio questions, percentage problems, or even algebraic expressions, having these fractions already in mind will make solving questions much faster.

For example:

• Ratio problems: If a problem involves ratios, fractions like 1/3, 1/4, and 3/5 frequently appear. Knowing their decimal equivalents can help in calculating the final answer.
• Percentage problems: Percentages can often be expressed as fractions. For example, 25% is equal to 1/4, and 66.67% is 2/3. Instead of converting these during the test, knowing them beforehand will give you an edge.

Knowing these conversions also reduces the risk of calculation errors, which are common when you’re under time pressure. Memorizing even a few key fractions can lead to quicker problem-solving, which is vital when you only have a limited time to answer each question.

Key Fractions to Memorize

Here is an extended list of fractions and their decimal equivalents that you should memorize for the GMAT. These are among the most commonly encountered in GMAT questions:

Please refer GMAT Quantitative: Fractions and Percents for detailed analysis of GMAT Fractions

Common Fraction for GMAT

In the GMAT Quantitative section, fractions are frequently used across different problem types like ratios, algebra, and word problems. Understanding how to manipulate common fractions is essential for answering these questions efficiently.

Overview of Frequently Used Fractions

Some fractions appear more regularly in GMAT problems than others. These fractions, often paired with percentages or ratios, are used in both problem-solving and data sufficiency questions. Below is a list of common fractions that every GMAT test-taker should be comfortable with:

Fractions in Word Problems

Word problems often involve fractions in the context of dividing quantities or calculating parts of a total. For instance:

“A company’s annual budget is $1,200,000. If 1/3 of the budget is allocated to marketing, how much is spent on marketing?”

To solve this problem, you multiply $1,200,000 by 1/3. Knowing that 1/3 is 0.3333 makes this calculation much faster. The answer is $400,000.

Similarly, percentage problems frequently involve fractions. For example, if a question asks what 25% of 320 is, recognizing that 25% is equivalent to 1/4 will help you solve the problem in seconds (1/4 of 320 = 80).

Fractions in Ratio and Proportion Problems

In ratio problems, you often need to convert ratios into fractions. For example, a question may ask for the total number of parts in a ratio of 3:2. This is equivalent to 3/5 and 2/5 of the total. Understanding how to work with these fractions allows for quicker and more accurate problem-solving.

Here’s an example:

“A recipe calls for 3 parts water to 2 parts flour. If you have 500 grams of flour, how much water should you use?”

To solve this, you recognize that flour makes up 2/5 of the total mixture, so 500 grams represents 2/5 of the total weight. Solving for the total weight and subtracting the weight of the flour gives you the amount of water needed.

By mastering the manipulation of these common fractions, you can solve these types of GMAT questions more efficiently and confidently.

Converting Fractions to Decimals

Being able to quickly convert fractions to decimals is a key skill for the GMAT. Not only does it help in solving fractions-based problems, but it’s also useful when dealing with percentage questions. Mastering fraction-to-decimal conversions can make many questions much faster to solve, especially when dealing with GMAT’s multiple-choice format.

Quick Conversion Tricks

There are some shortcuts and tricks you can use to easily convert common fractions to decimals. Here's a breakdown of some common conversions:

Use of Conversion in GMAT Problem-Solving

Fraction-to-decimal conversions are often useful in questions where you need to compare two values. For example, if you’re comparing 3/8 to 0.4, converting both into decimals will make it easier. In this case, 3/8 converts to 0.375, which is smaller than 0.4.

Here’s an example:

“Which is greater, 5/6 or 0.85?”

By converting 5/6 to a decimal (which equals 0.8333), it’s clear that 0.85 is larger. These kinds of comparisons are frequent in GMAT problems, particularly in data sufficiency questions.

Practice Conversions

Below are a few practice problems to help you get comfortable with fraction-to-decimal conversions. Try solving these without using a calculator to speed up your mental math skills:

• Convert 7/8 to a decimal
• Convert 3/5 to a decimal
• Compare 2/3 and 0.66 – which is larger?
• Is 0.25 greater or smaller than 1/4?

By practicing these conversions regularly, you’ll be able to answer GMAT questions involving fractions and decimals more confidently and quickly.

Please refer GMAT Practice Questions with Fractions and Decimals for detailed analysis of GMAT Fractions

Simplifying Fractions for GMAT

Another key skill tested on the GMAT is the ability to simplify fractions. This often involves reducing fractions to their simplest form, making it easier to work with them in calculations. Simplifying fractions is especially useful in GMAT problem-solving and data-sufficiency questions, where clear and efficient calculations are necessary.

The Importance of Simplifying Fractions

On the GMAT, questions often involve complex calculations with fractions. Simplifying fractions early in the process makes these problems more manageable. For example, rather than multiplying large numbers, simplify the fractions first to reduce the numbers you're working with.

For instance:

“Solve for x: (6/8) * (4/6) = x”

Rather than multiplying 6 by 4 and 8 by 6, first simplify 6/8 to 3/4, and 4/6 to 2/3. Now, the problem becomes:

“(3/4) * (2/3) = x”

The answer is 1/2, much easier to calculate when the fractions are simplified first.

Techniques to Simplify Fractions

The main technique for simplifying fractions is to divide both the numerator and the denominator by their greatest common divisor (GCD). Here’s how you can simplify fractions:

• Identify the greatest common divisor of the numerator and denominator.
• Divide both the numerator and denominator by the GCD.
• The resulting fraction is the simplified version.

For example, to simplify 18/24:

• The GCD of 18 and 24 is 6.
• Divide both by 6: (18 ÷ 6) / (24 ÷ 6) = 3/4.

Examples of Simplification in GMAT Problems

Here are a few examples where simplifying fractions makes solving GMAT problems easier:

• Simplify 9/12 before multiplying it with another fraction (3/4).
• In a data sufficiency question, you may need to simplify ratios (e.g., 12:8 simplifies to 3:2).
• Simplify 15/35 in a word problem to 3/7 for easier calculations.

Mastering this technique will make fraction problems more manageable and help improve your speed on the GMAT.

GMAT Fractions in Data Sufficiency Questions

The GMAT’s data sufficiency section is unique because it tests your ability to determine whether you have enough information to solve a problem, rather than actually solving it. Fractions often appear in data sufficiency questions, and being able to work with them efficiently is crucial for answering these questions correctly.

How Fractions are Tested in Data Sufficiency

In data sufficiency questions, fractions may appear in the form of ratios, parts of a whole, or percentages. The challenge is to determine whether the given statements provide enough information to solve the problem.

For example, a typical data sufficiency question involving fractions might look like this:

“If 3/4 of a tank is filled with water, and Statement (1) says that the tank’s total capacity is 100 liters, can you determine how much water is in the tank?”

Here, knowing how to work with the fraction 3/4 will help you quickly determine that 3/4 of 100 liters is 75 liters, meaning the problem can be solved with the information provided in Statement (1).

Approach to Solving Fraction-Related Data Sufficiency Questions

To solve fraction-related data sufficiency questions, follow these steps:

• Step 1: Analyze the problem – Determine whether the fraction given is essential to the problem.
• Step 2: Check each statement independently – Assess whether each statement provides enough information to solve for the unknown using the fraction provided.
• Step 3: Combine the statements (if necessary) – If neither statement alone is sufficient, check if both statements together provide the information needed.

It’s important to remember that in data sufficiency questions, you do not need to calculate the exact answer; you only need to decide whether the statements give you enough information to solve the problem.

Example Problems with Solutions

Here’s an example data sufficiency question involving fractions:

“If 2/3 of a team are engineers, and Statement (1) says that the total number of team members is 15, while Statement (2) says that 10 team members are engineers, can you determine the number of non-engineers on the team?”

Solution: By analyzing both statements, you can use Statement (1) to calculate that 2/3 of 15 members are engineers (i.e., 10 engineers), so 5 team members are not engineers. Therefore, each statement alone provides sufficient information to solve the problem.

Common Mistakes Students Make with GMAT Fractions

Fractions can be tricky to work with, and many students make common mistakes when dealing with them on the GMAT. Understanding these mistakes can help you avoid them and improve your score.

Misinterpreting Fraction Problems

A common mistake is misinterpreting fraction problems, particularly in word problems. Students often confuse the part with the whole or fail to properly understand what the fraction is representing. For example:

“If 1/4 of a shipment is damaged, how much is undamaged?”

Many students mistakenly calculate 1/4 of the shipment instead of subtracting 1/4 from the whole, which leaves 3/4 of the shipment undamaged.

Not Simplifying Fractions

Another common mistake is failing to simplify fractions when it is appropriate. Simplified fractions make calculations easier, and neglecting to simplify can lead to errors in solving GMAT problems.

For example, when solving (6/8) * (4/6), it’s better to simplify 6/8 to 3/4 and 4/6 to 2/3 before multiplying, which makes the problem easier to manage and reduces the chance of mistakes.

Strategies to Avoid These Mistakes

Here are some strategies to help avoid these common mistakes:

• Always read the problem carefully to understand what the fraction represents.
• Simplify fractions whenever possible before performing any calculations.
• Double-check your interpretation of the problem to ensure you are calculating the correct value.
• Practice fraction-based GMAT problems to become more comfortable with how they are tested on the exam.

Additional Practice Questions

Here are a few additional practice questions to help reinforce your understanding of fractions on the GMAT:

• If 3/5 of a group of 20 people are men, how many women are in the group?
• If a recipe calls for 1/3 cup of sugar and you want to double the recipe, how much sugar do you need?
• If 7/10 of a class passed an exam, how many students failed if the class has 40 students?

Practice Questions for GMAT Fractions

Practicing GMAT fraction questions is one of the most effective ways to improve your understanding of how fractions are tested. These questions often require quick calculations, conversions, and simplifications. Below, you’ll find a variety of practice questions designed to test your ability to work with fractions under different problem types.

Fraction-Based Problem-Solving Questions

These questions involve applying your knowledge of fractions to solve real GMAT-style problems. Try to work through them without using a calculator, as this will improve your mental math skills for the exam.

1. Question 1: If 2/3 of a box is filled with marbles and the total number of marbles is 60, how many marbles are in the box?
2. Question 2: A team’s winning percentage is 75%. What fraction of their games have they won?
3. Question 3: If 1/5 of the employees at a company are managers, and the company has 200 employees, how many managers are there?
4. Question 4: A recipe requires 3/4 cup of flour. If you want to make 1/2 of the recipe, how much flour should you use?
5. Question 5: If a tank is 2/3 full and holds 90 liters of water when full, how many liters are in the tank?

Solutions to Practice Problems

Here are the solutions to the practice problems. Compare your answers to these solutions to see where you may have made mistakes or to reinforce your understanding of the concepts.

1. Solution 1: To find 2/3 of 60, multiply 60 by 2/3. 60 * (2/3) = 40 marbles.
2. Solution 2: A winning percentage of 75% is the same as 3/4. The fraction of games won is 3/4.
3. Solution 3: 1/5 of 200 is 40. So, there are 40 managers.
4. Solution 4: Half of 3/4 is 3/8, so you will need 3/8 cup of flour.
5. Solution 5: 2/3 of 90 liters is 60 liters. The tank contains 60 liters of water.

These types of problems help you practice real GMAT scenarios involving fractions. The more comfortable you become with solving these problems, the faster and more accurate your calculations will be on the actual exam.

GMAT Fractions in Word Problems

Fractions are commonly found in GMAT word problems. These problems require you to translate real-life scenarios into mathematical terms using fractions. Whether you’re working with percentages, ratios, or quantities, being able to manipulate fractions is essential for solving word problems effectively.

How Fractions Are Used in Word Problems

In GMAT word problems, fractions are often used to represent parts of a whole, percentages, or proportions. For instance, a problem might ask how much of a total budget is allocated to a specific department or what fraction of a total group is involved in a task.

Here’s an example:

“A class of 80 students went on a field trip. If 1/4 of the students missed the bus, how many students missed the bus?”

In this problem, you need to find 1/4 of 80. Multiply 80 by 1/4 to get 20 students who missed the bus.

Step-by-Step Approach to Solving Word Problems Involving Fractions

Follow these steps to solve word problems that involve fractions:

• Step 1: Read the problem carefully – Understand what part of the whole the fraction is representing.
• Step 2: Identify the total – Find the total quantity or value that the fraction is being applied to.
• Step 3: Multiply the total by the fraction – This will give you the part of the total that the fraction represents.
• Step 4: Double-check your work – Ensure that your interpretation of the fraction is correct and that your calculations are accurate.

Let’s go through another example:

“A company has 120 employees. If 3/5 of the employees work in the sales department, how many employees work in sales?”

To solve this, multiply 120 by 3/5. The calculation is:

120 * (3/5) = 72 employees work in sales.

Common Types of Word Problems Using Fractions

Here are the most common types of word problems on the GMAT that use fractions:

• Percentage Problems: These problems often involve converting percentages to fractions. For example, 25% of a group can be expressed as 1/4 of the group.
• Ratio Problems: Ratios like 2:3 are expressed as fractions (2/5 and 3/5) to find proportions of a total.
• Proportion Problems: These involve direct application of fractions to find parts of a whole, such as calculating 2/3 of a budget or 1/4 of a shipment.

Being able to identify these types of problems and apply fractions correctly is essential for success on the GMAT.

GMAT Fractions in Ratio and Proportion Problems

Ratio and proportion problems are commonly tested on the GMAT, and many of these involve fractions. In these types of problems, you are often asked to find the relationship between two or more quantities, which can usually be expressed as fractions. Understanding how to convert ratios into fractions and apply them correctly is essential for solving these questions.

How Ratios and Proportions Are Tested Using Fractions

In GMAT ratio and proportion problems, fractions help to express the relative sizes of two or more quantities. For example, a ratio of 3:2 means that for every 5 units, 3 belong to one group, and 2 belong to the other. This ratio can be expressed as fractions: 3/5 for the first group and 2/5 for the second group.

Let’s look at an example:

“A company has a ratio of 3 salespeople for every 2 marketing personnel. If there are 45 total employees, how many are salespeople?”

To solve this, you first add the ratio parts (3 + 2 = 5). This means salespeople represent 3/5 of the total employees. So, multiply 45 by 3/5 to find the number of salespeople:

45 * (3/5) = 27 salespeople

Practice Ratio and Proportion Problems

Below are more practice problems for ratio and proportion involving fractions:

1. Question 1: In a class, the ratio of boys to girls is 3:2. If there are 30 students in the class, how many are boys?
2. Question 2: A recipe requires a ratio of 2 parts sugar to 3 parts flour. If you have 10 cups of flour, how much sugar should you use?
3. Question 3: A company’s staff ratio is 5 developers to 3 designers. If there are 64 total staff members, how many developers are there?
4. Question 4: A juice blend has a ratio of 4 parts apple juice to 1 part orange juice. If there are 25 liters of the blend, how many liters of apple juice are in the blend?
5. Question 5: In a school, the ratio of teachers to students is 1:20. If there are 300 students, how many teachers are there?

Solutions to Ratio and Proportion Problems

1. Solution 1: The ratio of boys to total students is 3/5. Multiply 30 by 3/5 to get 18 boys.
2. Solution 2: The ratio of sugar to flour is 2/3. Multiply 10 by 2/3 to get 6.67 cups of sugar.
3. Solution 3: The ratio of developers to total staff is 5/8. Multiply 64 by 5/8 to get 40 developers.
4. Solution 4: The ratio of apple juice to total blend is 4/5. Multiply 25 by 4/5 to get 20 liters of apple juice.
5. Solution 5: The ratio of teachers to students is 1/20. Multiply 300 by 1/20 to get 15 teachers.

Comparing Fractions on the GMAT

Comparing fractions is another essential skill for the GMAT. In some questions, you may need to determine which of two fractions is larger or smaller. This is especially common in data sufficiency and problem-solving questions. Knowing how to quickly compare fractions can save valuable time during the test.

Methods for Comparing Fractions

There are a few methods you can use to compare fractions:

• Cross-Multiplication: Multiply the numerator of the first fraction by the denominator of the second, and the numerator of the second by the denominator of the first. The larger product will indicate the larger fraction.
• Converting to Decimals: Convert both fractions to decimal form and compare their values. This method works best when dealing with fractions that are commonly used.
• Benchmark Fractions: Compare each fraction to a known benchmark, like 1/2 or 1. For example, fractions larger than 1/2 are always greater than those less than 1/2.

Let’s look at an example:

“Which is larger, 5/8 or 7/12?”

Using cross-multiplication:

5 * 12 = 60
8 * 7 = 56

Since 60 is greater than 56, 5/8 is larger than 7/12.

Practice Questions for Comparing Fractions

Here are several questions to help you practice comparing fractions:

1. Question 1: Which is larger, 3/4 or 5/6?
2. Question 2: Compare 7/10 and 2/3. Which fraction is greater?
3. Question 3: Is 5/12 greater than or less than 1/3?
4. Question 4: Which is smaller, 9/16 or 1/2?
5. Question 5: Compare 4/5 and 9/10. Which is greater?

Solutions to Comparing Fractions Questions

1. Solution 1: Using cross-multiplication: 3 * 6 = 18, 4 * 5 = 20. Since 20 is larger, 5/6 is greater than 3/4.
2. Solution 2: Convert to decimals: 7/10 = 0.7, 2/3 = 0.666... So, 7/10 is larger.
3. Solution 3: Using cross-multiplication: 5 * 3 = 15, 12 * 1 = 12. Since 15 is larger, 5/12 is greater than 1/3.
4. Solution 4: Convert to decimals: 9/16 = 0.5625, 1/2 = 0.5. So, 1/2 is smaller than 9/16.
5. Solution 5: Convert to decimals: 4/5 = 0.8, 9/10 = 0.9. So, 9/10 is greater than 4/5.

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Conclusion 

Understanding and mastering GMAT fractions is essential for improving your performance in the quantitative section. By learning how to convert, compare, and simplify fractions, you’ll be able to solve problems faster and with greater accuracy. Regular practice with real GMAT-style questions, focusing on fractions in ratios, proportions, and word problems, will help you gain confidence in handling these concepts. Keep practicing, and with time, fractions will become one of the most manageable parts of the GMAT.