Answer:
The answer is the option a
\(\frac{1}{2}\)
Step-by-step explanation:
we have
\(\frac{6}{10}> (\ ) > \frac{1}{3}\)
we know that
In order to compare fractions of different denominator, we are going to multiply each of the fractions by a unit fraction, to obtain a common denominator
Multiply \(\frac{6}{10}\) by \(\frac{6}{6}\)
\((6/6)*\frac{6}{10}=\frac{36}{60}\)
Multiply \(\frac{1}{3}\) by \(\frac{20}{20}\)
\((20/20)*\frac{1}{3}=\frac{20}{60}\)
Verify each case
case a) we have \(\frac{1}{2}\)
Multiply \(\frac{1}{2}\) by \(\frac{30}{30}\)
\((30/30)*\frac{1}{2}=\frac{30}{60}\)
substitute in the expression
\(\frac{36}{60}> \frac{30}{60} > \frac{20}{60}\) ------> is true
The fraction \(\frac{1}{2}\) is a solution
case b) we have \(\frac{1}{4}\)
Multiply \(\frac{1}{4}\) by \(\frac{15}{15}\)
\((15/15)*\frac{1}{4}=\frac{15}{60}\)
substitute in the expression
\(\frac{36}{60}> \frac{15}{60} > \frac{20}{60}\) ------> is not true
The fraction \(\frac{1}{4}\) is not a solution
case c) we have \(\frac{2}{3}\)
Multiply \(\frac{2}{3}\) by \(\frac{20}{20}\)
\((20/20)*\frac{2}{3}=\frac{40}{60}\)
substitute in the expression
\(\frac{36}{60}> \frac{40}{60} > \frac{20}{60}\) ------> is not true
The fraction \(\frac{2}{3}\) is not a solution
case d) we have \(\frac{3}{4}\)
Multiply \(\frac{3}{4}\) by \(\frac{15}{15}\)
\((15/15)*\frac{3}{4}=\frac{45}{60}\)
substitute in the expression
\(\frac{36}{60}> \frac{45}{60} > \frac{20}{60}\) ------> is not true
The fraction \(\frac{3}{4}\) is not a solution
