Question
John plans to practice piano at least two 1/2 hours this weekend if he processes one 1/6 hours on Saturday and one one over four hours on Sunday will he meet his goal A Yes he will practice a total of two 5/12 hours and two 5/12 > two 1/2 B No he will practice I total of two 5/12 hours in two 5/12 < two 1/2 C Yes he will practice a total of two seven over 12 hours into 7/12 > 2 1/2 D No he will practice a total of two seven over 12 hours and two 7/12 < 2 1/2
Answers
GPT-4o mini
To determine whether John meets his goal of practicing at least two and a half hours (2 1/2 hours) over the weekend, we first need to calculate the total amount of time he practices on Saturday and Sunday.
1. **Saturday's Practice:**
- He practices 1 1/6 hours.
- To convert this to a fraction:
\[
1 \frac{1}{6} = \frac{6}{6} + \frac{1}{6} = \frac{7}{6} \text{ hours}
\]
2. **Sunday's Practice:**
- He practices 1 1/4 hours.
- To convert this to a fraction:
\[
1 \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4} \text{ hours}
\]
3. **Total Practice Time:**
- Now we add Saturday's and Sunday's practice time together:
\[
\text{Total Practice} = \frac{7}{6} + \frac{5}{4}
\]
- To add these two fractions, we need a common denominator. The least common multiple of 6 and 4 is 12.
- Convert each fraction:
\[
\frac{7}{6} = \frac{14}{12} \quad \text{(by multiplying numerator and denominator by 2)}
\]
\[
\frac{5}{4} = \frac{15}{12} \quad \text{(by multiplying numerator and denominator by 3)}
\]
- Now add the fractions:
\[
\frac{14}{12} + \frac{15}{12} = \frac{29}{12}
\]
4. **Convert \( \frac{29}{12} \) to a mixed number:**
- Divide 29 by 12:
This equals 2 remainder 5, giving us:
\[
\frac{29}{12} = 2 \frac{5}{12} \text{ hours}
\]
5. **Now compare the total to 2 1/2 hours:**
- Convert 2 1/2 hours to a fraction:
\[
2 \frac{1}{2} = \frac{5}{2} = \frac{30}{12} \text{ hours}
\]
From our calculations:
- Total Practice: \( 2 \frac{5}{12} \) hours or \( \frac{29}{12} \)
- Goal: \( 2 \frac{1}{2} \) hours or \( \frac{30}{12} \)
Since \( \frac{29}{12} < \frac{30}{12} \), John does not meet his goal.
So the correct answer is:
**B. No he will practice a total of 2 5/12 hours and 2 5/12 < 2 1/2.**
1. **Saturday's Practice:**
- He practices 1 1/6 hours.
- To convert this to a fraction:
\[
1 \frac{1}{6} = \frac{6}{6} + \frac{1}{6} = \frac{7}{6} \text{ hours}
\]
2. **Sunday's Practice:**
- He practices 1 1/4 hours.
- To convert this to a fraction:
\[
1 \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4} \text{ hours}
\]
3. **Total Practice Time:**
- Now we add Saturday's and Sunday's practice time together:
\[
\text{Total Practice} = \frac{7}{6} + \frac{5}{4}
\]
- To add these two fractions, we need a common denominator. The least common multiple of 6 and 4 is 12.
- Convert each fraction:
\[
\frac{7}{6} = \frac{14}{12} \quad \text{(by multiplying numerator and denominator by 2)}
\]
\[
\frac{5}{4} = \frac{15}{12} \quad \text{(by multiplying numerator and denominator by 3)}
\]
- Now add the fractions:
\[
\frac{14}{12} + \frac{15}{12} = \frac{29}{12}
\]
4. **Convert \( \frac{29}{12} \) to a mixed number:**
- Divide 29 by 12:
This equals 2 remainder 5, giving us:
\[
\frac{29}{12} = 2 \frac{5}{12} \text{ hours}
\]
5. **Now compare the total to 2 1/2 hours:**
- Convert 2 1/2 hours to a fraction:
\[
2 \frac{1}{2} = \frac{5}{2} = \frac{30}{12} \text{ hours}
\]
From our calculations:
- Total Practice: \( 2 \frac{5}{12} \) hours or \( \frac{29}{12} \)
- Goal: \( 2 \frac{1}{2} \) hours or \( \frac{30}{12} \)
Since \( \frac{29}{12} < \frac{30}{12} \), John does not meet his goal.
So the correct answer is:
**B. No he will practice a total of 2 5/12 hours and 2 5/12 < 2 1/2.**