Fractions can be difficult for students because they involve a different approach to numbers, particularly when adding and subtracting fractions with like denominators.

This guide will help simplify the process of adding and subtracting fractions with like denominators. We will list simple steps and give examples and tips to help you practice.

Whether you’re studying for the ACT® WorkKeys Applied Math Test or want to enhance your understanding of fractions, this guide is for you.

Let us begin our journey into this topic.

Understanding Fractions and Common Denominators

Before starting operations, let’s review fractions. A fraction consists of two parts: the numerator and the denominator. The numerator shows how many parts there are, and the denominator indicates how many equal parts make a whole.

When adding or subtracting fractions, a common denominator simplifies things. A common denominator means that both fractions have the same number at the bottom.

Here’s why this is important:

• It simplifies addition and subtraction.
• It makes the problems easier to handle.
• It reduces calculation errors.

Step-by-Step: Adding Fractions with a Common Denominator

To add fractions with the same denominator, simply add the numerators while keeping the denominator the same.

For example, with the fractions 3/8 and 4/8, you add the numerators: 3 + 4 = 7. The denominator stays 8, resulting in 7/8.

Be sure to simplify the fraction if necessary, as this makes it easier to understand.

Step-by-Step: Subtracting Fractions with a Common Denominator

Subtraction works similarly. First, find a common denominator. Then, subtract the second numerator from the first while keeping the common denominator.

For example, with 5/9 and 2/9, subtract the numerators: 5 - 2 = 3. The denominator remains 9, giving you the fraction 3/9.

Finally, check if it can be simplified. Simplified fractions are easier to read and preferred in tests.

Simplifying Fractions: The Finishing Touch

Simplifying fractions means making them as simple as possible. To do this, find the greatest common divisor (GCD) of the numerator and the denominator.

To simplify, divide both the numerator and denominator by their GCD. This makes the fraction easier to understand and is often needed for correct answers.

Simplified fractions are neat and improve understanding of math.

Practice Makes Perfect: Examples and Tips

Regular practice is essential for mastering fractions. Try different types of problems to build confidence.

Here’s a quick example: Add 3/8 and 2/8. Simply add the numerators: 3 + 2 = 5. The result is 5/8.

Here are some tips to keep in mind:

• Double-check your calculations.
• Simplify fractions where possible.
• Practice under timed conditions for test prep.

Examples and Solutions

Understanding how to add and subtract fractions can be very helpful in real-life situations. Below are three examples that illustrate these concepts, along with step-by-step solutions.

Example 1: Adding Fractions

Problem: Add 5/12 and 7/12.

Solution:

1. Since both fractions have the same denominator (12), we can add the numerators directly.
2. Add the numerators: 5 + 7 = 12.
3. Write the result over the common denominator: 12/12.
4. Simplify: 12/12 = 1.

So, 5/12 + 7/12 = 1.

Example 2: Subtracting Fractions

Problem: Subtract 9/10 from 4/10.

Solution:

1. Both fractions have the same denominator (10), so we subtract the numerators.
2. Subtract the numerators: 4 – 9 = -5.
3. Write the result over the common denominator: -5/10.
4. Simplify: -5/10 = -1/2.

Thus, 4/10 – 9/10 = -1/2.

Example 3: Adding Mixed Numbers

Problem: Add 2 1/4 and 3 3/4.

Solution:

1. Convert the mixed numbers to improper fractions. 2 1/4 = (2 × 4 + 1)/4 = 9/4 and 3 3/4 = (3 × 4 + 3)/4 = 15/4
2. Now, add the two improper fractions: 9/4 + 15/4.
3. Add the numerators: 9 + 15 = 24.
4. Write the result over the common denominator: 24/4.
5. Simplify: 24/4 = 6.

Therefore, 2 1/4 + 3 3/4 = 6.

Using these examples, you can practice adding and subtracting fractions with a common denominator, reinforcing your understanding of how these operations work in various situations. Be sure to keep practicing to gain confidence in your skills!

Common Mistakes to Avoid when Adding and Subtracting Fractions with Like Denominators

Mixing up adding and subtracting numerators and denominators in fractions can be easy. Remember that you only change the numerators when you add or subtract fractions. The denominators stay the same. This is important for getting the correct answer.

Another common mistake is not simplifying fractions. Simplifying is an important step that makes your answers clear and accurate. Reducing fractions to their simplest form helps make your solution easier to understand and removes extra complexity.

Preparing for the ACT® WorkKeys Applied Math Test

To prepare well for the ACT® WorkKeys Applied Math Test, focus on understanding fractions. You should learn the basic concepts of fractions and how to use them in different situations. Knowing these basics will help you solve more complicated math problems on the test.

It is also helpful to take practice tests that look like the real exam. This will help you get used to the types of questions and manage your time better during the actual test. Regular practice, whether by timing yourself or solving various fraction problems, can greatly improve your skills and boost your confidence for the exam.

Additional Resources and Study Tips

Think about using different online platforms or apps made for extra practice. These tools usually have many exercises and fun features to help you learn better. Joining study groups can also be helpful. In these groups, you can get support from classmates who have similar academic goals. You can work together, share ideas, and talk about difficult topics, which can improve your understanding of the material.

Conclusion: Adding and Subtracting Fractions with Like Denominators

A basic skill in math is adding and subtracting fractions with the same bottom number, called the denominator. At first, this might seem hard, but regular practice will make it easier and feel more natural.

Keep practicing often and use different resources, like textbooks, online tutorials, or worksheets. Every problem you solve helps you understand better and boosts your confidence with fractions. This confidence will set you up for tougher math challenges later on.

Sharpen Your Skills for ACT® WorkKeys Applied Math

Are you preparing for the ACT® WorkKeys Applied Math test? We’ve got you covered! Dive into our review articles designed to help you tackle real-world math problems with confidence. You’ll find everything you need to succeed from quick tips to detailed strategies. Start exploring now!

• Dividing Positive and Numbers with Fractions
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Need help preparing for the ACT® WorkKeys Applied Math Test?

Albert has hundreds of ACT® WorkKeys practice questions and full-length practice tests to try out.