Question

evaluate,
\\(\frac{1}{2} \div \frac{6}{7} - \frac{1}{3}\\)
write your answer in simplest form,

Explanation:

Step1: Divide the fractions

To divide \(\frac{1}{2}\) by \(\frac{6}{7}\), we multiply \(\frac{1}{2}\) by the reciprocal of \(\frac{6}{7}\), which is \(\frac{7}{6}\). So, \(\frac{1}{2} \div \frac{6}{7} = \frac{1}{2} \times \frac{7}{6} = \frac{7}{12}\).

Step2: Subtract \(\frac{1}{3}\)

Now, we need to subtract \(\frac{1}{3}\) from \(\frac{7}{12}\). First, find a common denominator for \(\frac{7}{12}\) and \(\frac{1}{3}\). The common denominator of 12 and 3 is 12. Convert \(\frac{1}{3}\) to twelfths: \(\frac{1}{3} = \frac{4}{12}\). Then subtract: \(\frac{7}{12} - \frac{4}{12} = \frac{3}{12}\).

Step3: Simplify the result

Simplify \(\frac{3}{12}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 3. So, \(\frac{3 \div 3}{12 \div 3} = \frac{1}{4}\).

Answer:

\(\frac{1}{4}\)