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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