Question

The difference between the smallest and the largest fractions among $\frac{3}{8}$, $\frac{5}{9}$, $\frac{26}{27}$, $\frac{15}{32}$ is:

• A. $\frac{127}{216}$
• B. $\frac{127}{219}$
• C. $\frac{127}{214}$
• D. $\frac{127}{213}$

Answer 1

Answer:

$\frac{127}{216}$

The difference between the smallest and the largest fraction is $\frac{127}{216}$.

1: Identify the smallest and largest fractions

We can easily convert each fraction to its approximate decimal value to find the smallest and largest:

• $\frac{3}{8} = 0.375$ (Smallest)

• $\frac{5}{9} \approx 0.555$

• $\frac{15}{32} \approx 0.468$

• $\frac{26}{27} \approx 0.963$ (Largest)

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2: Calculate the difference

Subtract the smallest fraction from the largest fraction:
$\text{Difference} = \frac{26}{27} - \frac{3}{8}$

Find the common denominator for 27 and 8 by multiplying them:
$27 \times 8 = 216$

Now cross-multiply to find the new numerators:
$\text{Difference} = \frac{(26 \times 8) - (3 \times 27)}{216}$
$\text{Difference} = \frac{208 - 81}{216} = \frac{127}{216}$