Question

find a common denominator you can use to subtract the fractions shown. then, find the difference.
\\(\frac{7}{4} - \frac{1}{10}\\)

Explanation:

Step1: Find LCM of denominators

Denominators are 4 and 10. Prime factors: \(4 = 2^2\), \(10 = 2\times5\). LCM is \(2^2\times5 = 20\).

Step2: Rewrite fractions with LCD

\(\frac{7}{4}=\frac{7\times5}{4\times5}=\frac{35}{20}\), \(\frac{1}{10}=\frac{1\times2}{10\times2}=\frac{2}{20}\)

Step3: Subtract the fractions

\(\frac{35}{20}-\frac{2}{20}=\frac{35 - 2}{20}=\frac{33}{20}\)

Answer:

Common denominator is 20, and the difference is \(\frac{33}{20}\) (or \(1\frac{13}{20}\)).