Question

question 5 (mandatory) (2 points) saved
determine which fraction in the pair is greater.
(\frac{9}{4}) ____ (\frac{7}{3})

the greater fraction is (\frac{7}{3}) (option with radio button)
the greater fraction is (\frac{9}{4}) (option with circle)

Explanation:

Step1: Find a common denominator

To compare $\frac{9}{4}$ and $\frac{7}{3}$, we find the least common denominator (LCD) of 4 and 3, which is 12.

Step2: Convert fractions to equivalent forms

For $\frac{9}{4}$, multiply numerator and denominator by 3: $\frac{9\times3}{4\times3}=\frac{27}{12}$.
For $\frac{7}{3}$, multiply numerator and denominator by 4: $\frac{7\times4}{3\times4}=\frac{28}{12}$.

Step3: Compare the numerators

Now we compare $\frac{27}{12}$ and $\frac{28}{12}$. Since 28 > 27, $\frac{28}{12}>\frac{27}{12}$, so $\frac{7}{3}>\frac{9}{4}$. Wait, but let's check the decimal values too. $\frac{9}{4} = 2.25$ and $\frac{7}{3}\approx2.333...$. So $\frac{7}{3}$ is greater. Wait, but the initial selected option was $\frac{7}{3}$, but let's re - check the calculation. Wait, $\frac{9}{4}=2.25$, $\frac{7}{3}\approx2.333$, so $\frac{7}{3}$ is greater. But wait, maybe I made a mistake? Wait, no. Wait, 9 divided by 4 is 2.25, 7 divided by 3 is approximately 2.333, so 2.333>2.25, so $\frac{7}{3}$ is greater. But wait, the second option says the greater is $\frac{9}{4}$, which is wrong. Wait, no, wait, let's recalculate the common denominator. $\frac{9}{4}=\frac{27}{12}$, $\frac{7}{3}=\frac{28}{12}$. 28 is greater than 27, so $\frac{7}{3}$ is greater. So the correct answer is the first option.

Answer:

The greater fraction is $\boldsymbol{\frac{7}{3}}$ (the option with "The greater fraction is $\frac{7}{3}$")