Question

which fractions are greater than \\(\frac{1}{2}\\)? choose all the correct answers. \\(\frac{3}{4}\\) \\(\frac{2}{7}\\) \\(\frac{1}{3}\\) \\(\frac{2}{3}\\) \\(\frac{6}{7}\\) \\(\frac{1}{4}\\)

Explanation:

Step1: Compare $\frac{3}{4}$ and $\frac{1}{2}$

Find a common denominator, which is 4. $\frac{1}{2}=\frac{2}{4}$. Since $3 > 2$, $\frac{3}{4}>\frac{1}{2}$.

Step2: Compare $\frac{2}{7}$ and $\frac{1}{2}$

Common denominator is 14. $\frac{2}{7}=\frac{4}{14}$, $\frac{1}{2}=\frac{7}{14}$. Since $4 < 7$, $\frac{2}{7}<\frac{1}{2}$.

Step3: Compare $\frac{1}{3}$ and $\frac{1}{2}$

Common denominator is 6. $\frac{1}{3}=\frac{2}{6}$, $\frac{1}{2}=\frac{3}{6}$. Since $2 < 3$, $\frac{1}{3}<\frac{1}{2}$.

Step4: Compare $\frac{2}{3}$ and $\frac{1}{2}$

Common denominator is 6. $\frac{2}{3}=\frac{4}{6}$, $\frac{1}{2}=\frac{3}{6}$. Since $4 > 3$, $\frac{2}{3}>\frac{1}{2}$.

Step5: Compare $\frac{6}{7}$ and $\frac{1}{2}$

Common denominator is 14. $\frac{6}{7}=\frac{12}{14}$, $\frac{1}{2}=\frac{7}{14}$. Since $12 > 7$, $\frac{6}{7}>\frac{1}{2}$.

Step6: Compare $\frac{1}{4}$ and $\frac{1}{2}$

Common denominator is 4. $\frac{1}{2}=\frac{2}{4}$. Since $1 < 2$, $\frac{1}{4}<\frac{1}{2}$.

Answer:

$\frac{3}{4}$, $\frac{2}{3}$, $\frac{6}{7}$