Question

graph \\(\frac{2}{5}\\) and \\(\frac{2}{10}\\) on the number line.

\\(\leftarrow\\) \\(\frac{}{0}\\) \\(\frac{}{\frac{1}{10}}\\) \\(\frac{}{\frac{2}{10}}\\) \\(\frac{}{\frac{3}{10}}\\) \\(\frac{}{\frac{4}{10}}\\) \\(\frac{}{\frac{5}{10}}\\) \\(\frac{}{\frac{6}{10}}\\) \\(\frac{}{\frac{7}{10}}\\) \\(\frac{}{\frac{8}{10}}\\) \\(\frac{}{\frac{9}{10}}\\) \\(\frac{}{1}\\) \\(\
ightarrow\\)

write an inequality comparing \\(\frac{2}{5}\\) and \\(\frac{2}{10}\\).

Explanation:

Step1: Convert to common denominator

$\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}$

Step2: Compare the fractions

On the number line, $\frac{4}{10}$ is to the right of $\frac{2}{10}$, so $\frac{4}{10} > \frac{2}{10}$

Step3: Substitute original fraction

Replace $\frac{4}{10}$ with $\frac{2}{5}$

Answer:

$\frac{2}{5} > \frac{2}{10}$

(For the number line graph: Mark a point at $\frac{2}{10}$ (the third tick mark after 0) and a point at $\frac{4}{10}$ (the fifth tick mark after 0) to represent $\frac{2}{5}$)