A Comprehensive Guide to Learning How to Add Three or More Fractions with Unlike Denominators
While adding two fractions might be familiar territory for many, adding three or more fractions with different denominators can seem like a daunting task.
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 seamlessly 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:
– \(\frac{1}{3}\) 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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