What is the difference between the largest and the smallest fractions among \(\frac{5}{9}, \frac{7}{11}, \frac{8}{15}\) and \(\frac{11}{17}\)?

Given:

Fractions: \(\frac{5}{9}, \frac{7}{11}, \frac{8}{15}, \frac{11}{17}\)

Formula Used:

To compare fractions, we can either convert them to decimals or find a common denominator.

Difference = Largest fraction - Smallest fraction

Calculation:

Convert each fraction to a decimal:

\(\frac{5}{9}\) = 0.555...

\(\frac{7}{11}\) = 0.6363...

\(\frac{8}{15}\) = 0.5333...

\(\frac{11}{17}\) = 0.6470...

Comparing the decimal values:

Smallest fraction = 0.5333... which corresponds to \(\frac{8}{15}\)

Largest fraction = 0.6470... which corresponds to \(\frac{11}{17}\)

Difference = Largest fraction - Smallest fraction

Difference = \(\frac{11}{17} - \frac{8}{15}\)

Find a common denominator (LCM of 17 and 15):

LCM(17, 15) = 17 × 15 = 255

Convert the fractions to have a common denominator:

\(\frac{11}{17} = \frac{11 \times 15}{17 \times 15} = \frac{165}{255}\)

\(\frac{8}{15} = \frac{8 \times 17}{15 \times 17} = \frac{136}{255}\)

Difference = \(\frac{165}{255} - \frac{136}{255} = \frac{165 - 136}{255} = \frac{29}{255}\)

The difference between the largest and the smallest fractions is \(\frac{29}{255}\).