How to Add Mixed Fractions with Different Denominators

Adding mixed fractions with different denominators can seem like a daunting task, but with the right approach, it’s actually quite simple. In this guide, we’ll walk you through a step-by-step process to add mixed fractions with different denominators, making it easy for you to understand and apply this skill in various mathematical scenarios.

How to Add Mixed Fractions with Different Denominators

Step 1: Identify the Mixed Fractions

First, let’s identify the mixed fractions that need to be added. A mixed fraction is a combination of a whole number and a proper fraction. For example, 2 1/3 is a mixed fraction, where 2 is the whole number and 1/3 is the proper fraction.

Suppose we want to add the following mixed fractions:

3 1/2 + 2 2/3

Step 2: Find the Least Common Denominator (LCD)

The next step is to find the least common denominator (LCD) for the fractions. The LCD is the smallest number that is a multiple of both denominators. In our example, the denominators are 2 and 3. The smallest multiple of both numbers is 6, so the LCD is 6.

Step 3: Convert Fractions to Equivalent Fractions with the LCD

Now that we have our LCD, we can convert each fraction to an equivalent fraction with the LCD as the new denominator. To do this, we need to multiply both the numerator and the denominator by the same number to get the equivalent fraction.

For the first fraction (1/2):

1/2 * (3/3) = 3/6

For the second fraction (2/3):

2/3 * (2/2) = 4/6

Our new mixed fractions are:

3 3/6 + 2 4/6

Step 4: Add the Fractions

Now that we have equivalent fractions with the same denominator, we can add them together. To do this, we simply add the numerators while keeping the denominators the same.

3/6 + 4/6 = (3+4)/6 = 7/6

Step 5: Add the Whole Numbers

Next, we need to add the whole numbers:

3 + 2 = 5

Step 6: Combine the Whole Numbers and Fractions

Now that we have the sum of the whole numbers and the sum of the fractions, we can combine them:

5 + 7/6

However, the fraction part (7/6) is an improper fraction, meaning the numerator is greater than the denominator. We need to convert it into a mixed fraction.

Step 7: Convert the Improper Fraction to a Mixed Fraction

To convert an improper fraction to a mixed fraction, we divide the numerator by the denominator and write down the quotient and the remainder as the whole number and the proper fraction, respectively.

7 ÷ 6 = 1 R 1

This means that 7/6 is equal to 1 1/6.

Step 8: Add the New Mixed Fraction to the Whole Number

Finally, we add the new mixed fraction (1 1/6) to the whole number we obtained in step 5:

5 + 1 1/6 = 6 1/6

And that’s our final answer! So, 3 1/2 + 2 2/3 = 6 1/6.

By following these easy-to-understand steps, you can confidently add mixed fractions with different denominators and tackle a wide range of mathematical problems.


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