Adding and Subtracting Fractions: A Step-by-Step Guide

Fractions can often be a challenging concept to understand and work with, especially when it comes to adding and subtracting them. However, with the right approach and step-by-step guidance, you can become proficient in performing these operations. In this article, we will provide a clear and concise guide to adding and subtracting fractions.

To start, let’s recall that a fraction represents a part of a whole or a ratio of two numbers. A fraction consists of a numerator, which represents the number of parts we have, and a denominator, which represents the total number of equal parts the whole is divided into. For example, in the fraction 3/4, 3 is the numerator, and 4 is the denominator.

When adding or subtracting fractions, the first requirement is that the denominators must be the same. If they are not initially the same, we must find a common denominator by finding the least common multiple (LCM) of the original denominators. Once we have identified the common denominator, we can proceed to perform the addition or subtraction.

Let’s go over the step-by-step process of adding fractions:

1. Identify whether the fractions have the same denominator. If they do, proceed to step 4. If not, move to step 2.

2. Find the least common multiple (LCM) of the denominators. The LCM is the smallest number that is divisible by both denominators. For example, if we have to add 1/3 and 1/5, the LCM of 3 and 5 is 15.

3. Modify the fractions to have the common denominator. To do this, we need to multiply both the numerator and the denominator of each fraction by the appropriate factor. For instance, in the example above, 1/3 can be modified to 5/15 by multiplying both the numerator and denominator by 5, and 1/5 can be modified to 3/15 by multiplying both the numerator and denominator by 3.

4. Add the modified fractions. We simply add the numerators of the fractions together while keeping the common denominator. Using the example above, 5/15 + 3/15 equals 8/15.

5. If necessary, simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). In the case of 8/15, the GCD is 1, so the fraction is already in its simplest form.

Now, let’s move on to the step-by-step process of subtracting fractions:

1. Follow the same steps 1 and 2 as outlined above.

2. Modify the fractions to have the common denominator using the same approach as in step 3 of adding fractions.

3. Subtract the modified fractions. Subtract the numerators of the fractions while keeping the common denominator. For example, if we have 7/8 – 3/8, the result would be 4/8, which can be further simplified to 1/2.

4. Simplify the fraction, if necessary, by dividing both the numerator and denominator by their GCD. In our example, the GCD of 4/8 is 4, so the simplified fraction is 1/2.

By following these step-by-step instructions, adding and subtracting fractions should become more accessible and less intimidating. It is essential to remember that practice is key in mastering these operations. With time and effort, adding and subtracting fractions will become second nature, allowing you to confidently tackle more complex mathematical problems.