Question

level 157
here are models of two fractions.
which pair of statements is true about the fractions?
select an answer
a $\frac{4}{7}$ is greater than $\frac{1}{2}$.
$\frac{3}{7}$ is also greater than $\frac{1}{2}$.
b $\frac{4}{7}$ is less than $\frac{1}{2}$.
$\frac{3}{7}$ is also less than $\frac{1}{2}$.
c $\frac{4}{7}$ is less than $\frac{1}{2}$.
$\frac{3}{7}$ is greater than $\frac{1}{2}$.
d $\frac{4}{7}$ is greater than $\frac{1}{2}$.
$\frac{3}{7}$ is less than $\frac{1}{2}$.

Explanation:

Step1: Analyze the first fraction

To compare $\frac{4}{7}$ and $\frac{1}{2}$, find a common denominator. The common denominator of 7 and 2 is 14. Convert the fractions: $\frac{4}{7}=\frac{8}{14}$ and $\frac{1}{2}=\frac{7}{14}$. Since $\frac{8}{14}>\frac{7}{14}$, $\frac{4}{7}>\frac{1}{2}$.

Step2: Analyze the second fraction

Compare $\frac{3}{7}$ and $\frac{1}{2}$. Using the same common denominator 14: $\frac{3}{7}=\frac{6}{14}$ and $\frac{1}{2}=\frac{7}{14}$. Since $\frac{6}{14}<\frac{7}{14}$, $\frac{3}{7}<\frac{1}{2}$.

Step3: Match with options

From the analysis, $\frac{4}{7}$ is greater than $\frac{1}{2}$ and $\frac{3}{7}$ is less than $\frac{1}{2}$, which matches option D.

Answer:

D. $\frac{4}{7}$ is greater than $\frac{1}{2}$. $\frac{3}{7}$ is less than $\frac{1}{2}$.