Find the reciprocal of the fraction \(\frac{2}{3}\) and then subtract it from \(\frac{5}{6}\).
Answer
Finally, subtract \(\frac{9}{6}\) from \(\frac{5}{6}\) to get \(-\frac{4}{6}\), which simplifies to \(-\frac{2}{3}\).
Step 1 ：First, find the reciprocal of \(\frac{2}{3}\). The reciprocal of a fraction is obtained by interchanging the numerator and the denominator. So, the reciprocal of \(\frac{2}{3}\) is \(\frac{3}{2}\).
Step 2 ：Next, subtract the reciprocal of \(\frac{2}{3}\) from \(\frac{5}{6}\). In order to subtract fractions, they must have the same denominator. We can achieve this by multiplying both the numerator and the denominator of \(\frac{3}{2}\) by 3 to get \(\frac{9}{6}\).
Step 3 ：Finally, subtract \(\frac{9}{6}\) from \(\frac{5}{6}\) to get \(-\frac{4}{6}\), which simplifies to \(-\frac{2}{3}\).
