Question

perform the operation and, if possible, simplify.
\\(\frac{7}{12} - \frac{9}{20}\\)
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Explanation:

Step1: Find the least common denominator (LCD) of 12 and 20.

The prime factorization of 12 is \(2^2\times3\) and of 20 is \(2^2\times5\). So, the LCD is \(2^2\times3\times5 = 60\).

Step2: Rewrite the fractions with the LCD.

For \(\frac{7}{12}\), multiply numerator and denominator by 5: \(\frac{7\times5}{12\times5}=\frac{35}{60}\).
For \(\frac{9}{20}\), multiply numerator and denominator by 3: \(\frac{9\times3}{20\times3}=\frac{27}{60}\).

Step3: Subtract the fractions.

\(\frac{35}{60}-\frac{27}{60}=\frac{35 - 27}{60}=\frac{8}{60}\).

Step4: Simplify the result.

Divide numerator and denominator by their greatest common divisor, which is 4. \(\frac{8\div4}{60\div4}=\frac{2}{15}\).

Answer:

\(\frac{2}{15}\)