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Evaluating the expression of \(\frac{\frac{3}{8}}{1\frac{7}{8}}-\frac{1}{6}\)

 

\(\frac{\frac{3}{8}}{1\frac{7}{8}}-\frac{1}{6}\)	First, convert the fraction in the denominator into an improper fraction.
\(\frac{\frac{3}{8}}{1\frac{7}{8}}-\frac{1}{6}=\frac{\frac{3}{8}}{\frac{8*1+7}{8}}-\frac{1}{6}=\frac{\frac{3}{8}}{\frac{15}{8}}-\frac{1}{6}\)	Multiply by the reciprocal of the denominator to eliminate it.
\(\frac{\frac{8}{15}}{\frac{8}{15}}*\frac{\frac{3}{8}}{\frac{15}{8}}-\frac{1}{6}\)	Doing this isn't actually changing the value of the fraction because we are just multiplying by 1.
\(\frac{8}{15}*\frac{3}{8}-\frac{1}{6}\)	Before beginning the multiplication, we can drastically simplify the numbers in both fractions by identifying the GCF of opposite numerators and denominators. In this example, 8 and 8 have a GCF of 8. 3 and 15 have a GCF if 3.
\(\frac{1}{5}-\frac{1}{6}\)	Convert 1/5 and 1/6 into fractions with a common denominator.
\(\frac{6}{30}-\frac{5}{30}\)	Now subtract the numerators while maintaining the denominator.
\(\frac{1}{30}\)