Questions: Compute the difference and simplify your answer. 1/5 - 6/9

Solution Steps

To solve the problem of computing the difference between the fractions \(\frac{1}{5}\) and \(\frac{6}{9}\), we need to follow these steps:

1. Find a common denominator for the fractions.
2. Convert each fraction to an equivalent fraction with the common denominator.
3. Subtract the numerators of the equivalent fractions.
4. Simplify the resulting fraction if possible.

We start with the fractions \( \frac{1}{5} \) and \( \frac{6}{9} \).

The least common denominator (LCD) of \( 5 \) and \( 3 \) (the denominator of \( \frac{6}{9} \) simplified) is \( 15 \).

We convert each fraction to have the common denominator of \( 15 \): \[ \frac{1}{5} = \frac{3}{15} \quad \text{and} \quad \frac{6}{9} = \frac{10}{15} \]

Now we subtract the two equivalent fractions: \[ \frac{3}{15} - \frac{10}{15} = \frac{3 - 10}{15} = \frac{-7}{15} \]

The result \( \frac{-7}{15} \) is already in its simplest form.

Final Answer