Question

The difference of the greatest and the smallest of the fractions $\frac{1}{2}$, $\frac{8}{11}$, $\frac{7}{8}$, $\frac{7}{9}$, $\frac{5}{6}$ is:

• A. $\frac{6}{7}$
• B. $\frac{3}{8}$
• C. $\frac{7}{9}$
• D. $\frac{1}{3}$

Answer 1

The Correct Option is B

To determine the difference between the greatest and smallest of the given fractions, we need to compare each of them. The fractions are $\frac{1}{2}$, $\frac{8}{11}$, $\frac{7}{8}$, $\frac{7}{9}$, and $\frac{5}{6}$. To make comparison easy, convert each fraction to a common denominator or compare them in decimal form.

Converting each fraction to decimal: 

• $\frac{1}{2} = 0.5$
• $\frac{8}{11} \approx 0.727$
• $\frac{7}{8} = 0.875$
• $\frac{7}{9} \approx 0.778$
• $\frac{5}{6} \approx 0.833$

By comparing these decimal values, we can identify the smallest and greatest fractions:

• Smallest: $\frac{1}{2} = 0.5$
• Greatest: $\frac{7}{8} = 0.875$

Next, calculate the difference between the greatest and smallest fractions:

Difference = $\frac{7}{8} - \frac{1}{2}$

To subtract, use a common denominator (8):

$\frac{1}{2} = \frac{4}{8}$

So, $\frac{7}{8} - \frac{4}{8} = \frac{3}{8}$

Therefore, the difference between the greatest and smallest fractions is $\frac{3}{8}$.

Answer 2

Finding the Difference Between Fractions

\(\frac{1}{2}, \frac{8}{11}, \frac{7}{8}, \frac{7}{9}, \frac{5}{6}\).

Let's approximate these fractions as decimals to compare them:

• \(\frac{1}{2} = 0.5\)
• \(\frac{8}{11} \approx 0.727\)
• \(\frac{7}{8} = 0.875\)
• \(\frac{7}{9} \approx 0.778\)
• \(\frac{5}{6} \approx 0.833\)

From these approximations, we can see that the greatest fraction is \(\frac{7}{8}\) and the smallest fraction is \(\frac{1}{2}\).

Now, let's find the difference: \(\frac{7}{8} - \frac{1}{2}\). 

To subtract, we need a common denominator, which is 8.

\(\frac{7}{8} - \frac{1}{2} = \frac{7}{8} - \frac{4}{8} = \frac{7-4}{8} = \frac{3}{8}\)

Therefore, the difference between the greatest and smallest fractions is \(\frac{3}{8}\).