Question

multiply mixed numbers
health and fitness
trail running is an exercise that involves running on trails instead of paved roads to reduce the impact on ankles and knees. samantha runs on the lakeside trail. she runs $2\frac{1}{2}$ times around the loop and then walks the remainder of the way. how far does samantha run? write an equation to model the distance samantha runs.

Explanation:

Step1: Convert mixed numbers to fractions

Convert $2\frac{1}{4}$ to $\frac{9}{4}$ and $2\frac{1}{2}$ to $\frac{5}{2}$.

Step2: Multiply the fractions

Multiply the two fractions to find the total running distance.
$\frac{9}{4} \times \frac{5}{2} = \frac{45}{8}$

Step3: Convert back to mixed number

Rewrite the improper fraction as a mixed number.
$\frac{45}{8} = 5\frac{5}{8}$

Step4: Define the model equation

Let $d$ = total running distance, $l$ = loop length, $n$ = number of loops. The equation is $d = l \times n$.

Answer:

Model equation: $d = 2\frac{1}{4} \times 2\frac{1}{2}$
Total distance Samantha runs: $5\frac{5}{8}$ miles