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}\\)

Explanation:

Step1: Recall fraction multiplication rule

To multiply fractions, we multiply the numerators and the denominators. So for $\frac{2}{3} \times \frac{4}{5}$, we calculate the numerator as $2\times4 = 8$ and the denominator as $3\times5 = 15$. So the product is $\frac{8}{15}$.

Step2: Compare $\frac{8}{15}$ and $\frac{2}{3}$

First, we need to make the denominators the same. The denominator of $\frac{2}{3}$ can be changed to 15 by multiplying both the numerator and denominator by 5. So $\frac{2}{3}=\frac{2\times5}{3\times5}=\frac{10}{15}$.

Now we compare $\frac{8}{15}$ and $\frac{10}{15}$. Since $8 < 10$, we have $\frac{8}{15}<\frac{10}{15}$, which means $\frac{2}{3}\times\frac{4}{5}<\frac{2}{3}$. Also, we can use the rule: when multiplying a positive fraction by a fraction less than 1 (since $\frac{4}{5}<1$), the product is less than the original fraction.

Answer:

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