Question

Evaluate the expression for the given value of the variable. (Review 1.1) $$\frac{4}{3} \cdot x \text { when } x=\frac{1}{6}$$

Short answer

The expression evaluates to \(\frac{2}{9}\) when \(x = \frac{1}{6}\)

Step-by-step solution

Substitute the given value

Start by substituting \(x = \frac{1}{6}\) into the expression \(\frac{4}{3} \cdot x\). This gives us \(\frac{4}{3} \cdot \frac{1}{6}\)

Multiply the fractions

Next, multiply the fractions together. Multiply the numerators (the top part of the fractions) together and the denominators (the bottom part) together. We get \((\frac{4}{1} \cdot \frac{1}{1}) / (\frac{3}{1} \cdot \frac{6}{1}) = \frac{4}{18}\)

Simplify the Fraction

Finally, simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (GCD), which in this case is 2. This gives us \(\frac{4}{18}= \frac{2}{9}\)