Certainly! Let's solve this step-by-step.
1. Identify the time the penguin nursery is open at each period:
- At noon: [tex]\(\frac{2}{3}\)[/tex] hour.
- In the afternoon: [tex]\(\frac{5}{12}\)[/tex] hour.
2. Convert the fractions to have a common denominator:
To add the fractions, they need a common denominator. The denominators are 3 and 12. The least common multiple (LCM) of 3 and 12 is 12.
3. Convert [tex]\(\frac{2}{3}\)[/tex] to a fraction with denominator 12:
[tex]\[
\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}
\][/tex]
4. Now we can add the two fractions:
- Noon: [tex]\(\frac{8}{12}\)[/tex]
- Afternoon: [tex]\(\frac{5}{12}\)[/tex]
Add the fractions:
[tex]\[
\frac{8}{12} + \frac{5}{12} = \frac{8 + 5}{12} = \frac{13}{12}
\][/tex]
5. Convert the improper fraction to a mixed number:
[tex]\(\frac{13}{12}\)[/tex] can be expressed as [tex]\(1 \frac{1}{12}\)[/tex].
This means the penguin nursery is open for a total of [tex]\(1 \frac{1}{12}\)[/tex] hours every day, which is the same as approximately [tex]\(1.0833333333333333\)[/tex] hours when expressed as a decimal.
Thus, the penguin nursery is open for about [tex]\(1.0833\)[/tex] hours each day.
