Question

use a benchmark to compare \\(\frac{7}{10}\\) and \\(\frac{9}{8}\\). \\(\frac{7}{10}\\) ? \\(\frac{9}{8}\\)

Explanation:

Step1: Analyze $\frac{7}{10}$

A common benchmark is 1. $\frac{7}{10}$ is less than 1 because the numerator (7) is less than the denominator (10), so $\frac{7}{10}<1$.

Step2: Analyze $\frac{9}{8}$

$\frac{9}{8}$ can be written as $1+\frac{1}{8}$, which is greater than 1 because we are adding a positive fraction to 1, so $\frac{9}{8}>1$.

Step3: Compare the two fractions

Since $\frac{7}{10}<1$ and $\frac{9}{8}>1$, we can conclude that $\frac{7}{10}<\frac{9}{8}$.

Answer:

$\frac{7}{10} < \frac{9}{8}$