Question

monte enjoys running. he usually takes one of three trails. trail a is $5\frac{9}{10}$ miles long. trail b is $5\frac{1}{7}$ miles. trail c is $5\frac{5}{9}$ miles. which list has the trails in order from shortest to longest?\
\bigcirc c, b, a\
\bigcirc b, c, a\
\bigcirc a, b, c\
\bigcirc b, a, c

Explanation:

Step1: Compare the fractional parts

The whole number part of each mixed number is 5, so we compare the fractional parts: $\frac{1}{7}$, $\frac{5}{9}$, and $\frac{9}{10}$. To compare these fractions, we can find a common denominator or convert them to decimals.

• $\frac{1}{7} \approx 0.143$
• $\frac{5}{9} \approx 0.556$
• $\frac{9}{10} = 0.9$

Step2: Order the fractional parts

From smallest to largest, the fractional parts are $\frac{1}{7}$ (Trail B), $\frac{5}{9}$ (Trail C), $\frac{9}{10}$ (Trail A).

Step3: Order the trails

Since the whole number parts are the same, the order of the trails from shortest to longest is based on the order of their fractional parts: Trail B, Trail C, Trail A.

Answer:

B. \( 5\frac{1}{7} \) miles, C. \( 5\frac{5}{9} \) miles, A. \( 5\frac{9}{10} \) miles (i.e., B, C, A)