Question

5 on saturday, destiny spends \\(\frac{1}{6}\\) of the day playing in a soccer tournament. she spends \\(\frac{1}{8}\\) of the day volunteering with her parents at the community garden. the rest of the day she spends at home. a day has 24 hours. what fraction of saturday does destiny spend at home? show your work.

Explanation:

Step1: Find total fraction spent outside

To find the total fraction of the day Destiny spends on soccer and volunteering, we add \(\frac{1}{6}\) and \(\frac{1}{8}\). First, find a common denominator, which is 24. Convert the fractions: \(\frac{1}{6}=\frac{1\times4}{6\times4}=\frac{4}{24}\) and \(\frac{1}{8}=\frac{1\times3}{8\times3}=\frac{3}{24}\). Then add them: \(\frac{4}{24}+\frac{3}{24}=\frac{7}{24}\).

Step2: Find fraction spent at home

The whole day is represented by 1 (or \(\frac{24}{24}\)). Subtract the fraction spent outside from 1: \(1 - \frac{7}{24}=\frac{24}{24}-\frac{7}{24}=\frac{17}{24}\).

Answer:

\(\frac{17}{24}\)