# Tri-Fractional Operations: How to Add and Subtract Three Fractions with Different Denominators

When faced with the task of adding or subtracting three fractions with different denominators, it might seem like a complex puzzle. However, with a systematic approach, this puzzle can be solved with ease.

In this guide, we’ll walk you through the steps to add or subtract three fractions, even when they have different denominators.

## Step-by-step Guide to Add and Subtract Three Fractions with Different Denominators:

**1. Basics of Fractions: **

Recall that a fraction consists of a numerator (top number) and a denominator (bottom number). The denominator indicates the total number of equal parts, while the numerator tells us how many of those parts we’re considering.

**2. Identifying Different Denominators: **

If the fractions you’re working with don’t have the same denominator, they have different denominators. For instance, in the fractions \(\frac{1}{2}\), \(\frac{3}{4}\), and \(\frac{5}{6}\), the denominators 2, 4, and 6 are all different.

**3. Finding the Least Common Denominator (LCD):**

The LCD is the smallest number into which all the denominators can divide. This ensures that the fractions are of comparable sizes.

**4. Adjusting Each Fraction to the LCD:**

Multiply the numerator and denominator of each fraction by the necessary factor to achieve the LCD.

**5. Performing the Operation:**

With the same denominator in place, either add or subtract the numerators of the fractions to get the final result.

### Example 1 (Addition):

Add \(\frac{1}{3}\), \(\frac{1}{4}\), and \(\frac{1}{5}\).

**Solution:**

The LCD for 3, 4, and 5 is 60. Adjusting the fractions:

– \(\frac{1}{3}\) becomes \(\frac{20}{60}\).

– \(\frac{1}{4}\) becomes \(\frac{15}{60}\).

– \(\frac{1}{5}\) becomes \(\frac{12}{60}\).

Adding them up, the result is \(\frac{47}{60}\).

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### Example 2 (Subtraction):

Subtract \(\frac{1}{6}\) and \(\frac{1}{8}\) from \(\frac{1}{4}\).

**Solution:**

The LCD for 6, 8, and 4 is 24. Adjusting the fractions:

– \(\frac{1}{6}\) becomes \(\frac{4}{24}\).

– \(\frac{1}{8}\) becomes \(\frac{3}{24}\).

– \(\frac{1}{4}\) becomes \(\frac{6}{24}\).

Subtracting, the result is \(\frac{6 – 4 – 3}{24} = \(\frac{-1}{24}\).

### Practice Questions:

1. Add \(\frac{1}{7}\), \(\frac{2}{9}\), and \(\frac{3}{11}\).

2. Subtract \(\frac{2}{8}\) and \(\frac{3}{12}\) from \(\frac{1}{6}\).

3. Add \(\frac{1}{10}\), \(\frac{2}{15}\), and \(\frac{3}{20}\).

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**Answers: **

1. \(\frac{293}{693}\)

2. \(\frac{1}{24}\)

3. \(\frac{11}{30}\)

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