Question

a new road that connects uniontown to springville is 4 1/3 miles long. what is the change in distance when using the new road instead of the dirt roads? write your answer as a mixed number. the change in distance is (square) miles.

Explanation:

Step1: Calculate the distance of the old - route

The old - route consists of two dirt - roads. The lengths of the two dirt - roads are $5\frac{3}{6}$ miles and $3\frac{1}{8}$ miles. First, convert the mixed numbers to improper fractions. $5\frac{3}{6}=\frac{5\times6 + 3}{6}=\frac{33}{6}=\frac{11}{2}$ miles and $3\frac{1}{8}=\frac{3\times8+1}{8}=\frac{25}{8}$ miles. Then find a common denominator, which is 8. $\frac{11}{2}=\frac{11\times4}{2\times4}=\frac{44}{8}$ miles. The sum of the lengths of the two dirt - roads is $\frac{44}{8}+\frac{25}{8}=\frac{44 + 25}{8}=\frac{69}{8}=8\frac{5}{8}$ miles.

Step2: Calculate the change in distance

The length of the new road is $4\frac{1}{3}$ miles. Convert it to an improper fraction: $4\frac{1}{3}=\frac{4\times3 + 1}{3}=\frac{13}{3}$ miles. Now find a common denominator for $\frac{13}{3}$ and $\frac{69}{8}$, which is 24. $\frac{13}{3}=\frac{13\times8}{3\times8}=\frac{104}{24}$ and $\frac{69}{8}=\frac{69\times3}{8\times3}=\frac{207}{24}$. The change in distance is $\frac{207}{24}-\frac{104}{24}=\frac{207 - 104}{24}=\frac{103}{24}=4\frac{7}{24}$ miles.

Answer:

$4\frac{7}{24}$