How to Demystify Differences: A Guide to Subtracting Fractions with Unlike Denominators

Step-by-step Guide:

1. Basics of Fractions: 

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

2. Spotting Unlike Denominators: 

If two fractions don’t share the same denominator, they have unlike denominators. For instance, in the fractions \(\frac{3}{4}\) and \(\frac{5}{6}\), the denominators 4 and 6 are different.

3. Finding the Least Common Denominator (LCD): 

The LCD is the smallest number that both denominators can divide into. This ensures that we’re working with fractions that describe parts of the same size. For our example, the LCD for 4 and 6 is 12.

4. Adjusting the Fractions to the LCD: 

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

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

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

5. Subtracting the Fractions: 

With the same denominator in place, subtract the numerator of the second fraction from the first. Using our example, \(9 – 10 = -1\). So, \(\frac{3}{4} – \(\frac{5}{6}\) = \frac{-1}{12}\).

Example 1: 

Subtract \(\frac{2}{5}\) from \(\frac{3}{10}\). 

Solution: 

The LCD is 10. Adjusting the fractions:

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– \(\frac{2}{5}\) becomes \(\frac{4}{10}\).

– \(\frac{3}{10}\) remains the same. 

So, \(\frac{3}{10} – \frac{2}{5} = \frac{-1}{10}\).

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Example 2: 

Subtract \(\frac{1}{6}\) from \(\frac{1}{3}\). 

Solution: 

The LCD is 6. Adjusting the fractions:

– \(\frac{1}{6}\) remains the same.

– \(\frac{1}{3}\) becomes \(\frac{2}{6}\). 

So, \(\frac{1}{3} – \frac{1}{6} = \frac{1}{6}\).

Practice Questions: 

1. Subtract \(\frac{3}{8}\) from \(\frac{1}{4}\).

2. Subtract \(\frac{2}{7}\) from \(\frac{3}{14}\).

3. Subtract \(\frac{5}{9}\) from \(\frac{2}{3}\).

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Answers: 

1. \(\frac{-1}{8}\)

2. \(\frac{1}{14}\)

3. \(\frac{-1}{9}\)

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