Question

manuel jogs $3\frac{3}{4}$ miles from his house. he then jogs $1\frac{1}{3}$ miles farther. how many miles has manuel jogged in all?
write your answer as a mixed number in simplest form.
\boxed{} miles

Explanation:

Step1: Convert to improper fractions

$3\frac{3}{8} = \frac{3\times8 + 3}{8} = \frac{27}{8}$
$1\frac{1}{3} = \frac{1\times3 + 1}{3} = \frac{4}{3}$

Step2: Find common denominator

The least common denominator of 8 and 3 is 24.
$\frac{27}{8} = \frac{27\times3}{8\times3} = \frac{81}{24}$
$\frac{4}{3} = \frac{4\times8}{3\times8} = \frac{32}{24}$

Step3: Add the fractions

$\frac{81}{24} + \frac{32}{24} = \frac{81+32}{24} = \frac{113}{24}$

Step4: Convert to mixed number

$113 \div 24 = 4$ with a remainder of 17, so $\frac{113}{24} = 4\frac{17}{24}$

Answer:

$4\frac{17}{24}$ miles