A Comprehensive Guide to Learning How to Add Three or More Fractions with Unlike Denominators

However, with a systematic approach and a bit of patience, it’s entirely manageable. In this post, we’ll guide you through the steps to smoothly add three or more fractions, even if they have unlike denominators.

Step-by-step Guide:

1. Recap on Fractions: 

Every fraction has a numerator (the top number) and a denominator (the bottom number). The denominator tells us into how many equal parts a whole is divided, while the numerator indicates how many of those parts we’re considering.

2. Identifying Unlike Denominators: 

If the fractions you’re adding don’t have the same denominator, they have unlike 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. For our example, the LCD for 2, 4, and 6 is 12.

4. Adjusting Each Fraction to the LCD: 

Multiply the numerator and denominator of each fraction by the necessary factor to achieve the LCD. For our example:

– \(\frac{1}{2}\) becomes \(\frac{6}{12}\) (multiplied by 6).

– \(\frac{3}{4}\) becomes \(\frac{9}{12}\) (multiplied by 3).

– \(\frac{5}{6}\) becomes \(\frac{10}{12}\) (multiplied by 2).

5. Adding All the Fractions: 

With the same denominator in place, simply add up all the numerators. Using our example, \(6 + 9 + 10 = 25\). So, \(\frac{1}{2} + \frac{3}{4}+\frac{5}{6}=\frac{25}{12}\), which can be expressed as \(2 \frac{1}{12}\).

Examples:

Example 1: 

Add \(\frac{1}{3}\), \(\frac{2}{6}\), and \(\frac{3}{9}\). 

Solution: 

The LCD is 9. Adjusting the fractions:

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– \(\frac{1}{3}\) becomes \(\frac{3}{9}\).

– \(\frac{2}{6}\) becomes \(\frac{3}{9}\).

– \(\frac{3}{9}\) remains the same. 

So, \(\frac{1}{3} + \frac{2}{6} + \frac{3}{9} = \frac{9}{9}\), which is equal to 1.

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Example 2: 

Add \(\frac{1}{4}\), \(\frac{2}{5}\), and \(\frac{3}{10}\). 

Solution: 

The LCD is 20. Adjusting the fractions:

– \(\frac{1}{4}\) becomes \(\frac{5}{20}\).

– \(\frac{2}{5}\) becomes \(\frac{8}{20}\).

– \(\frac{3}{10}\) becomes \(\frac{6}{20}\). 

So, \(\frac{1}{4} + \frac{2}{5} + \frac{3}{10} = \frac{19}{20}\).

Practice Questions: 

1. Add \(\frac{1}{7}\), \(\frac{2}{14}\), and \(\frac{3}{21}\).

2. Add \(\frac{2}{8}\), \(\frac{3}{12}\), and \(\frac{4}{24}\).

3. Add \(\frac{1}{5}\), \(\frac{2}{10}\), and \(\frac{3}{15}\).

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Answers: 

1. \(\frac{6}{7}\)

2. \(\frac{7}{8}\)

3. 1

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