Question

1. rogelio watches a movie that is $1\frac{3}{4}$ hours long. he stops for dinner after watching $\frac{3}{5}$ of the movie. how many hours of the movie has he watched?

Explanation:

Step1: Convert the mixed number to an improper fraction

The length of the movie is \(1\frac{3}{4}\) hours. To convert a mixed number to an improper fraction, we use the formula \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So, \(1\frac{3}{4}=\frac{1\times4 + 3}{4}=\frac{7}{4}\) hours.

Step2: Multiply the length of the movie by the fraction watched

We need to find \(\frac{3}{5}\) of \(\frac{7}{4}\) hours. To find a fraction of a number, we multiply the number by the fraction. So, we calculate \(\frac{7}{4}\times\frac{3}{5}\). When multiplying fractions, we multiply the numerators together and the denominators together: \(\frac{7\times3}{4\times5}=\frac{21}{20}\).

Step3: Convert the improper fraction to a mixed number (optional, but can be more intuitive)

\(\frac{21}{20}=1\frac{1}{20}\) hours. But we can also leave it as an improper fraction or a decimal. As a decimal, \(\frac{21}{20} = 1.05\) hours. However, the improper fraction \(\frac{21}{20}\) or the mixed number \(1\frac{1}{20}\) is also correct. But let's check the multiplication again. Wait, \(\frac{7}{4}\times\frac{3}{5}=\frac{21}{20}=1.05\) or \(1\frac{1}{20}\). Wait, but maybe we can do it step by step. Wait, \(1\frac{3}{4}\) is \(1.75\) hours. Then, \(\frac{3}{5}\) of \(1.75\) is \(1.75\times\frac{3}{5}\). \(1.75\) is \(\frac{7}{4}\), so \(\frac{7}{4}\times\frac{3}{5}=\frac{21}{20}=1.05\) hours. So that's correct.

Answer:

\(\frac{21}{20}\) hours (or \(1\frac{1}{20}\) hours or \(1.05\) hours)