Question

solve \\(\frac{4}{5}a = \frac{2}{3}\\).
\\(a = \underline{quadquad}\\)

Explanation:

Step1: Identify the equation

We have the equation \(\frac{4}{5}a=\frac{2}{3}\). Our goal is to solve for \(a\).

Step2: Isolate the variable \(a\)

To isolate \(a\), we need to multiply both sides of the equation by the reciprocal of \(\frac{4}{5}\), which is \(\frac{5}{4}\). So we perform the operation:
\(a=\frac{2}{3}\times\frac{5}{4}\)

Step3: Simplify the right - hand side

When we multiply the fractions \(\frac{2}{3}\) and \(\frac{5}{4}\), we multiply the numerators together (\(2\times5 = 10\)) and the denominators together (\(3\times4=12\)). Then we simplify the fraction \(\frac{10}{12}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So \(\frac{10\div2}{12\div2}=\frac{5}{6}\).

Answer:

\(a = \frac{5}{6}\)