# How to Add Fractions with Different Denominators

Adding fractions with different denominators may seem like a daunting task, but with a little practice, it becomes much easier. In this guide, we’ll walk you through the process of adding fractions with different denominators step by step. This way, you’ll be able to confidently solve these types of problems in the future. Let’s get started!

## Step 1: Find the Least Common Denominator (LCD)

The first step in adding fractions with different denominators is to find the least common denominator (LCD). The LCD is the smallest number that is a multiple of both denominators. To find the LCD:

1. List the multiples of each denominator.
2. Identify the smallest number that appears in both lists.

Example:

Suppose you want to add 1/4 and 2/3. Start by listing the multiples of 4 and 3:

Multiples of 4: 4, 8, 12, 16, 20, … Multiples of 3: 3, 6, 9, 12, 15, …

The smallest common multiple is 12, so the LCD is 12.

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## Step 2: Convert the Fractions to Equivalent Fractions with the LCD

Now that you’ve found the LCD, you need to convert the original fractions to equivalent fractions with the LCD as their denominator. To do this:

1. Divide the LCD by the original denominator.
2. Multiply the numerator and denominator of the original fraction by the result from step 1.

Example:

Continuing with our example of 1/4 + 2/3:

1. Convert 1/4 to an equivalent fraction with a denominator of 12:LCD (12) ÷ original denominator (4) = 3 1/4 × 3/3 = 3/12
2. Convert 2/3 to an equivalent fraction with a denominator of 12:LCD (12) ÷ original denominator (3) = 4 2/3 × 4/4 = 8/12

Now you have the equivalent fractions 3/12 and 8/12.

## Step 3: Add the Equivalent Fractions

Now that both fractions have the same denominator, you can add them together by simply adding their numerators:

Example:

3/12 + 8/12 = (3 + 8)/12 = 11/12

So, 1/4 + 2/3 = 11/12.

## Step 4: Simplify the Resulting Fraction (if necessary)

In some cases, the resulting fraction can be simplified further. To do this:

1. Find the greatest common divisor (GCD) of the numerator and the denominator.
2. Divide the numerator and the denominator by the GCD.

Example:

In our example, the resulting fraction was 11/12, which is already in its simplest form. However, let’s consider a different example: 2/6 + 3/8.

Following the steps outlined above, we find the LCD to be 24, and the equivalent fractions to be 8/24 and 9/24. Adding these together gives us 17/24. Now let’s check for simplification:

GCD(17, 24) = 1 (17 and 24 have no common factors other than 1)

Since the GCD is 1, the fraction is already in its simplest form, and we can conclude that 2/6 + 3/8 = 17/24.

## Summary of the Steps to Add Fractions with Different Denominators

Here’s a quick recap of the steps to follow when adding fractions with different denominators:

1. Find the least common denominator (LCD) of the two fractions.
2. Convert the original fractions to equivalent fractions with the LCD as their denominator.
3. Add the numerators of the equivalent fractions while keeping the denominator the same.
4. Simplify the resulting fraction, if necessary.