Question

which fractions are less than \\(\frac{1}{2}\\)? choose all the correct answers. \\(\frac{6}{8}\\) \\(\frac{2}{5}\\) \\(\frac{5}{6}\\) \\(\frac{1}{6}\\) \\(\frac{3}{8}\\) \\(\frac{4}{5}\\)

Explanation:

Step1: Compare $\frac{6}{8}$ with $\frac{1}{2}$

Convert $\frac{1}{2}$ to eighths: $\frac{1}{2}=\frac{4}{8}$. Since $\frac{6}{8}>\frac{4}{8}$, $\frac{6}{8}$ is not less than $\frac{1}{2}$.

Step2: Compare $\frac{2}{5}$ with $\frac{1}{2}$

Find a common denominator, 10. $\frac{2}{5}=\frac{4}{10}$, $\frac{1}{2}=\frac{5}{10}$. Since $\frac{4}{10}<\frac{5}{10}$, $\frac{2}{5}$ is less than $\frac{1}{2}$.

Step3: Compare $\frac{5}{6}$ with $\frac{1}{2}$

Convert $\frac{1}{2}$ to sixths: $\frac{1}{2}=\frac{3}{6}$. Since $\frac{5}{6}>\frac{3}{6}$, $\frac{5}{6}$ is not less than $\frac{1}{2}$.

Step4: Compare $\frac{1}{6}$ with $\frac{1}{2}$

Convert $\frac{1}{2}$ to sixths: $\frac{1}{2}=\frac{3}{6}$. Since $\frac{1}{6}<\frac{3}{6}$, $\frac{1}{6}$ is less than $\frac{1}{2}$.

Step5: Compare $\frac{3}{8}$ with $\frac{1}{2}$

Convert $\frac{1}{2}$ to eighths: $\frac{1}{2}=\frac{4}{8}$. Since $\frac{3}{8}<\frac{4}{8}$, $\frac{3}{8}$ is less than $\frac{1}{2}$.

Step6: Compare $\frac{4}{5}$ with $\frac{1}{2}$

Find a common denominator, 10. $\frac{4}{5}=\frac{8}{10}$, $\frac{1}{2}=\frac{5}{10}$. Since $\frac{8}{10}>\frac{5}{10}$, $\frac{4}{5}$ is not less than $\frac{1}{2}$.

Answer:

$\frac{2}{5}$, $\frac{1}{6}$, $\frac{3}{8}$