Question

will the product be less than \\(\frac{2}{3}\\), equal to \\(\frac{2}{3}\\), or greater than \\(\frac{2}{3}\\)? \\(\frac{2}{3} \times \frac{4}{5}\\) options: less than \\(\frac{2}{3}\\), equal to \\(\frac{2}{3}\\), greater than \\(\frac{2}{3}\\)

Explanation:

Step1: Recall fraction multiplication rule

When multiplying a fraction by another fraction, we multiply the numerators and the denominators. Also, if we multiply a number by a fraction less than 1, the product is less than the original number. Here, we have $\frac{2}{3} \times \frac{4}{5}$. The fraction $\frac{4}{5}$ is less than 1 (since $4 < 5$).

Step2: Analyze the product

Let's calculate the product: $\frac{2}{3} \times \frac{4}{5} = \frac{2\times4}{3\times5} = \frac{8}{15}$. Now, let's convert $\frac{2}{3}$ to fifteenths: $\frac{2}{3} = \frac{2\times5}{3\times5} = \frac{10}{15}$. Since $\frac{8}{15} < \frac{10}{15}$, the product $\frac{2}{3} \times \frac{4}{5}$ is less than $\frac{2}{3}$.

Answer:

Less than $\boldsymbol{\frac{2}{3}}$