Question

product be less than \\(\frac{1}{4}\\), equal to \\(\frac{1}{4}\\), or greater than \\(\frac{1}{4}\\)? \\(\frac{1}{4} \times \frac{8}{7}\\) less than \\(\frac{1}{4}\\) equal to \\(\frac{1}{4}\\) greater than \\(\frac{1}{4}\\)

Explanation:

Step1: Analyze the multiplier

The multiplier here is $\frac{8}{7}$, which is greater than 1 (since $8 > 7$).

Step2: Recall the rule of multiplying by a number greater than 1

When a positive number is multiplied by a number greater than 1, the product is greater than the original number. Here, the original number is $\frac{1}{4}$, and we are multiplying it by $\frac{8}{7}$ (which is greater than 1). So, $\frac{1}{4} \times \frac{8}{7}$ will be greater than $\frac{1}{4}$.

Step3: Calculate the product (optional verification)

$\frac{1}{4} \times \frac{8}{7} = \frac{1\times8}{4\times7} = \frac{8}{28} = \frac{2}{7}$. Now, compare $\frac{2}{7}$ and $\frac{1}{4}$. Find a common denominator, which is 28. $\frac{2}{7} = \frac{8}{28}$ and $\frac{1}{4} = \frac{7}{28}$. Since $\frac{8}{28} > \frac{7}{28}$, $\frac{2}{7} > \frac{1}{4}$.

Answer:

Greater than $\frac{1}{4}$