Questions: Solve this problem. Reduce to lowest terms. Josh spent 6 1/2 hours at school, 3 2/3 hours at work, 2 3/4 hours doing homework, and 1 1/3 hours watching television. How much time did Josh spend doing these activities? 12 7/12 hours 14 1/3 hours 14 1/4 hours 14 hours

Solution Steps

To find the total time Josh spent on these activities, we need to add the mixed numbers representing the hours spent on each activity. We will convert each mixed number to an improper fraction, perform the addition, and then convert the result back to a mixed number in its lowest terms.

First, we convert each mixed number to an improper fraction:

• \( 6 \frac{1}{2} = \frac{13}{2} \)
• \( 3 \frac{2}{3} = \frac{11}{3} \)
• \( 2 \frac{3}{4} = \frac{11}{4} \)
• \( 1 \frac{1}{3} = \frac{4}{3} \)

Next, we add the improper fractions: \[ \frac{13}{2} + \frac{11}{3} + \frac{11}{4} + \frac{4}{3} \]

To add these fractions, we find a common denominator. The least common multiple of 2, 3, and 4 is 12. Converting each fraction: \[ \frac{13}{2} = \frac{78}{12}, \quad \frac{11}{3} = \frac{44}{12}, \quad \frac{11}{4} = \frac{33}{12}, \quad \frac{4}{3} = \frac{16}{12} \]

Adding these fractions: \[ \frac{78}{12} + \frac{44}{12} + \frac{33}{12} + \frac{16}{12} = \frac{171}{12} \]

We simplify \(\frac{171}{12}\): \[ \frac{171}{12} = 14 \frac{3}{12} = 14 \frac{1}{4} \]

Final Answer