Question

evaluate the expression below. (\frac{2}{3} div 2)

Explanation:

Step1: Recall division of fractions rule

To divide a fraction by a whole number, we can rewrite the whole number as a fraction (with denominator 1) and then multiply by the reciprocal. So, \(2\) can be written as \(\frac{2}{1}\), and the reciprocal of \(\frac{2}{1}\) is \(\frac{1}{2}\). So the expression \(\frac{2}{3}\div2\) becomes \(\frac{2}{3}\times\frac{1}{2}\).

Step2: Multiply the fractions

When multiplying fractions, we multiply the numerators together and the denominators together. So, \(\frac{2\times1}{3\times2}=\frac{2}{6}\).

Step3: Simplify the fraction

We can simplify \(\frac{2}{6}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, \(\frac{2\div2}{6\div2}=\frac{1}{3}\).

Answer:

\(\frac{1}{3}\)