Answer :
Certainly! Let's go through the problem step by step to find out how many hours Lavar spent on these two activities.
1. Understanding the Problem:
- Lavar spent [tex]\(4 \frac{3}{4}\)[/tex] hours in class.
- Lavar spent [tex]\(3 \frac{1}{2}\)[/tex] hours studying.
2. Convert Mixed Numbers to Improper Fractions:
- First, we need to convert these mixed numbers into improper fractions to add them easily.
3. Convert [tex]\(4 \frac{3}{4}\)[/tex] to an Improper Fraction:
- [tex]\(4 \frac{3}{4} = 4 + \frac{3}{4}\)[/tex]
- [tex]\(4 = \frac{16}{4}\)[/tex]
- So, [tex]\(4 \frac{3}{4} = \frac{16}{4} + \frac{3}{4} = \frac{16 + 3}{4} = \frac{19}{4}\)[/tex]
4. Convert [tex]\(3 \frac{1}{2}\)[/tex] to an Improper Fraction:
- [tex]\(3 \frac{1}{2} = 3 + \frac{1}{2}\)[/tex]
- [tex]\(3 = \frac{6}{2}\)[/tex]
- So, [tex]\(3 \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{6 + 1}{2} = \frac{7}{2}\)[/tex]
5. Find a Common Denominator and Add the Fractions:
- The common denominator for [tex]\(\frac{19}{4}\)[/tex] and [tex]\(\frac{7}{2}\)[/tex] is 4.
- Convert [tex]\(\frac{7}{2}\)[/tex] to a fraction with a denominator of 4: [tex]\(\frac{7}{2} = \frac{7 \times 2}{2 \times 2} = \frac{14}{4}\)[/tex]
6. Add the Fractions:
- [tex]\(\frac{19}{4} + \frac{14}{4} = \frac{19 + 14}{4} = \frac{33}{4}\)[/tex]
7. Convert the Improper Fraction to a Mixed Number:
- [tex]\(\frac{33}{4}\)[/tex]
- Divide 33 by 4: [tex]\(33 ÷ 4 = 8\)[/tex] with a remainder of 1, so we get [tex]\(8 \frac{1}{4}\)[/tex]
8. Conclusion:
- Lavar spent a total of [tex]\(8 \frac{1}{4}\)[/tex] hours on these two activities.
Therefore, the correct answer is:
D. [tex]\(8 \frac{1}{4}\)[/tex] hours
1. Understanding the Problem:
- Lavar spent [tex]\(4 \frac{3}{4}\)[/tex] hours in class.
- Lavar spent [tex]\(3 \frac{1}{2}\)[/tex] hours studying.
2. Convert Mixed Numbers to Improper Fractions:
- First, we need to convert these mixed numbers into improper fractions to add them easily.
3. Convert [tex]\(4 \frac{3}{4}\)[/tex] to an Improper Fraction:
- [tex]\(4 \frac{3}{4} = 4 + \frac{3}{4}\)[/tex]
- [tex]\(4 = \frac{16}{4}\)[/tex]
- So, [tex]\(4 \frac{3}{4} = \frac{16}{4} + \frac{3}{4} = \frac{16 + 3}{4} = \frac{19}{4}\)[/tex]
4. Convert [tex]\(3 \frac{1}{2}\)[/tex] to an Improper Fraction:
- [tex]\(3 \frac{1}{2} = 3 + \frac{1}{2}\)[/tex]
- [tex]\(3 = \frac{6}{2}\)[/tex]
- So, [tex]\(3 \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{6 + 1}{2} = \frac{7}{2}\)[/tex]
5. Find a Common Denominator and Add the Fractions:
- The common denominator for [tex]\(\frac{19}{4}\)[/tex] and [tex]\(\frac{7}{2}\)[/tex] is 4.
- Convert [tex]\(\frac{7}{2}\)[/tex] to a fraction with a denominator of 4: [tex]\(\frac{7}{2} = \frac{7 \times 2}{2 \times 2} = \frac{14}{4}\)[/tex]
6. Add the Fractions:
- [tex]\(\frac{19}{4} + \frac{14}{4} = \frac{19 + 14}{4} = \frac{33}{4}\)[/tex]
7. Convert the Improper Fraction to a Mixed Number:
- [tex]\(\frac{33}{4}\)[/tex]
- Divide 33 by 4: [tex]\(33 ÷ 4 = 8\)[/tex] with a remainder of 1, so we get [tex]\(8 \frac{1}{4}\)[/tex]
8. Conclusion:
- Lavar spent a total of [tex]\(8 \frac{1}{4}\)[/tex] hours on these two activities.
Therefore, the correct answer is:
D. [tex]\(8 \frac{1}{4}\)[/tex] hours
