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 a common denominator for the fractions

The denominators are 6 and 8. The least common denominator of 6 and 8 is 24.

Step2: Convert the fractions to have the common denominator

For \(\frac{1}{6}\), multiply numerator and denominator by 4: \(\frac{1\times4}{6\times4}=\frac{4}{24}\)
For \(\frac{1}{8}\), multiply numerator and denominator by 3: \(\frac{1\times3}{8\times3}=\frac{3}{24}\)

Step3: Add the two fractions together

\(\frac{4}{24}+\frac{3}{24}=\frac{4 + 3}{24}=\frac{7}{24}\)

Step4: Subtract the sum from 1 (since the total of a day is 1 whole)

\(1-\frac{7}{24}=\frac{24}{24}-\frac{7}{24}=\frac{24 - 7}{24}=\frac{17}{24}\)

Answer:

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