# 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.

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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1. $$\frac{293}{693}$$

2. $$\frac{1}{24}$$

3. $$\frac{11}{30}$$

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