Question

if you walk \\(\frac{2}{3}\\) mile and then jog \\(\frac{4}{7}\\) mile, what is the total distance covered? how much farther did you walk than jog?

the total distance covered is \\(1\frac{5}{21}\\) miles.
(simplify your answer. type an integer, simplified fraction, or mixed number.)
you walked \\(\square\\) miles farther than you jogged.
(simplify your answer. type an integer, simplified fraction, or mixed number.)

Explanation:

Step1: Find a common denominator

To subtract the fractions \(\frac{2}{3}\) and \(\frac{4}{7}\), we first find the least common denominator (LCD) of 3 and 7. The LCD of 3 and 7 is \(3\times7 = 21\).

Step2: Rewrite the fractions with the LCD

Rewrite \(\frac{2}{3}\) and \(\frac{4}{7}\) with denominator 21:
\(\frac{2}{3}=\frac{2\times7}{3\times7}=\frac{14}{21}\)
\(\frac{4}{7}=\frac{4\times3}{7\times3}=\frac{12}{21}\)

Step3: Subtract the fractions

Subtract the two fractions: \(\frac{14}{21}-\frac{12}{21}=\frac{14 - 12}{21}=\frac{2}{21}\)

Answer:

\(\frac{2}{21}\)