Question
As John plans to practice piano at least two and a half hours this weekend
If he practice 11/6 Hours on Saturday and 1 1/4 hours on Sunday Will he meet his goal
If he practice 11/6 Hours on Saturday and 1 1/4 hours on Sunday Will he meet his goal
Answers
GPT-4o mini
To find out if John meets his goal of practicing at least two and a half hours, we first need to calculate the total time he practiced over the weekend.
1. **Convert the time practiced into a common format (hours):**
- Saturday: \( \frac{11}{6} \) hours
- Sunday: \( 1 \frac{1}{4} \) hours = \( 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4} \) hours
2. **Add the hours together:**
- Total practice time = \( \frac{11}{6} + \frac{5}{4} \)
To add these fractions, we need a common denominator. The least common multiple of 6 and 4 is 12.
- Convert \( \frac{11}{6} \) to a denominator of 12:
\[
\frac{11}{6} = \frac{11 \times 2}{6 \times 2} = \frac{22}{12}
\]
- Convert \( \frac{5}{4} \) to a denominator of 12:
\[
\frac{5}{4} = \frac{5 \times 3}{4 \times 3} = \frac{15}{12}
\]
Now add them together:
\[
\frac{22}{12} + \frac{15}{12} = \frac{22 + 15}{12} = \frac{37}{12}
\]
3. **Convert \( \frac{37}{12} \) hours back to a mixed number:**
- Divide 37 by 12, which gives 3 with a remainder of 1. Therefore:
\[
\frac{37}{12} = 3 \frac{1}{12} \text{ hours}
\]
4. **Determine if John met his goal:**
John's goal is \( 2 \frac{1}{2} \) hours, which can be converted to an improper fraction:
\[
2 \frac{1}{2} = \frac{5}{2}
\]
To compare, we can convert \( \frac{5}{2} \) to a fraction with a denominator of 12:
\[
\frac{5}{2} = \frac{5 \times 6}{2 \times 6} = \frac{30}{12}
\]
Now we compare:
- Total practice time: \( \frac{37}{12} \)
- Goal: \( \frac{30}{12} \)
Since \( \frac{37}{12} > \frac{30}{12} \), John has indeed met his goal by practicing \( 3 \frac{1}{12} \) hours, which is more than \( 2 \frac{1}{2} \) hours.
1. **Convert the time practiced into a common format (hours):**
- Saturday: \( \frac{11}{6} \) hours
- Sunday: \( 1 \frac{1}{4} \) hours = \( 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4} \) hours
2. **Add the hours together:**
- Total practice time = \( \frac{11}{6} + \frac{5}{4} \)
To add these fractions, we need a common denominator. The least common multiple of 6 and 4 is 12.
- Convert \( \frac{11}{6} \) to a denominator of 12:
\[
\frac{11}{6} = \frac{11 \times 2}{6 \times 2} = \frac{22}{12}
\]
- Convert \( \frac{5}{4} \) to a denominator of 12:
\[
\frac{5}{4} = \frac{5 \times 3}{4 \times 3} = \frac{15}{12}
\]
Now add them together:
\[
\frac{22}{12} + \frac{15}{12} = \frac{22 + 15}{12} = \frac{37}{12}
\]
3. **Convert \( \frac{37}{12} \) hours back to a mixed number:**
- Divide 37 by 12, which gives 3 with a remainder of 1. Therefore:
\[
\frac{37}{12} = 3 \frac{1}{12} \text{ hours}
\]
4. **Determine if John met his goal:**
John's goal is \( 2 \frac{1}{2} \) hours, which can be converted to an improper fraction:
\[
2 \frac{1}{2} = \frac{5}{2}
\]
To compare, we can convert \( \frac{5}{2} \) to a fraction with a denominator of 12:
\[
\frac{5}{2} = \frac{5 \times 6}{2 \times 6} = \frac{30}{12}
\]
Now we compare:
- Total practice time: \( \frac{37}{12} \)
- Goal: \( \frac{30}{12} \)
Since \( \frac{37}{12} > \frac{30}{12} \), John has indeed met his goal by practicing \( 3 \frac{1}{12} \) hours, which is more than \( 2 \frac{1}{2} \) hours.