Question
John plans to practice piano at least 2 1/2
hours this weekend.es; he
If he practices 1 1/6
hours on Saturday and 1 1/4
hours on Sunday, will he meet his goal?
(1 point)
Responses
Yes; he will practice a total of 2 5/12
hours, and 2 5/12>2 1/2
.
No; he will practice a total of 2 5/12
hours, and 2 5/12< 2/12
.
Yes; he will practice a total of 2 7/12
hours, and 2 7/12>2 1/2
.
No; he will practice a total of 2 7/12
hours, and 2 7/12<2 1/2
.
hours this weekend.es; he
If he practices 1 1/6
hours on Saturday and 1 1/4
hours on Sunday, will he meet his goal?
(1 point)
Responses
Yes; he will practice a total of 2 5/12
hours, and 2 5/12>2 1/2
.
No; he will practice a total of 2 5/12
hours, and 2 5/12< 2/12
.
Yes; he will practice a total of 2 7/12
hours, and 2 7/12>2 1/2
.
No; he will practice a total of 2 7/12
hours, and 2 7/12<2 1/2
.
Answers
GPT-4o mini
To determine if John meets his goal of practicing at least 2 1/2 hours this weekend, we need to calculate the total hours he plans to practice Saturday and Sunday.
1. **Saturday's practice**: 1 1/6 hours
2. **Sunday's practice**: 1 1/4 hours
Now, let's convert these mixed numbers into improper fractions for easier addition:
- For 1 1/6:
\[
1 \times 6 + 1 = 6 + 1 = 7 \quad \text{so it's} \quad \frac{7}{6}
\]
- For 1 1/4:
\[
1 \times 4 + 1 = 4 + 1 = 5 \quad \text{so it's} \quad \frac{5}{4}
\]
Next, we need to find a common denominator to add these fractions. The least common multiple of 6 and 4 is 12.
Now let's convert each fraction to have a denominator of 12:
- Convert \( \frac{7}{6} \) to twelfths:
\[
\frac{7}{6} \times \frac{2}{2} = \frac{14}{12}
\]
- Convert \( \frac{5}{4} \) to twelfths:
\[
\frac{5}{4} \times \frac{3}{3} = \frac{15}{12}
\]
Now we can add these two fractions together:
\[
\frac{14}{12} + \frac{15}{12} = \frac{29}{12}
\]
Now to convert \( \frac{29}{12} \) back into a mixed number:
\[
29 \div 12 = 2 \quad \text{remainder} \quad 5 \quad \Rightarrow \quad 2 \frac{5}{12}
\]
Now, we compare this total time of \( 2 \frac{5}{12} \) hours to John's goal of \( 2 \frac{1}{2} \) hours.
Convert \( 2 \frac{1}{2} \) to an improper fraction:
\[
2 \times 2 + 1 = 4 + 1 = 5 \quad \text{so it's} \quad \frac{5}{2}
\]
Convert \( \frac{5}{2} \) to twelfths:
\[
\frac{5}{2} \times \frac{6}{6} = \frac{30}{12}
\]
Now we compare:
\[
2 \frac{5}{12} = \frac{29}{12}
\]
\[
2 \frac{1}{2} = \frac{30}{12}
\]
Since \( \frac{29}{12} < \frac{30}{12} \), John will not meet his goal.
The correct response is:
**No; he will practice a total of 2 7/12 hours, and 2 7/12 < 2 1/2.**
1. **Saturday's practice**: 1 1/6 hours
2. **Sunday's practice**: 1 1/4 hours
Now, let's convert these mixed numbers into improper fractions for easier addition:
- For 1 1/6:
\[
1 \times 6 + 1 = 6 + 1 = 7 \quad \text{so it's} \quad \frac{7}{6}
\]
- For 1 1/4:
\[
1 \times 4 + 1 = 4 + 1 = 5 \quad \text{so it's} \quad \frac{5}{4}
\]
Next, we need to find a common denominator to add these fractions. The least common multiple of 6 and 4 is 12.
Now let's convert each fraction to have a denominator of 12:
- Convert \( \frac{7}{6} \) to twelfths:
\[
\frac{7}{6} \times \frac{2}{2} = \frac{14}{12}
\]
- Convert \( \frac{5}{4} \) to twelfths:
\[
\frac{5}{4} \times \frac{3}{3} = \frac{15}{12}
\]
Now we can add these two fractions together:
\[
\frac{14}{12} + \frac{15}{12} = \frac{29}{12}
\]
Now to convert \( \frac{29}{12} \) back into a mixed number:
\[
29 \div 12 = 2 \quad \text{remainder} \quad 5 \quad \Rightarrow \quad 2 \frac{5}{12}
\]
Now, we compare this total time of \( 2 \frac{5}{12} \) hours to John's goal of \( 2 \frac{1}{2} \) hours.
Convert \( 2 \frac{1}{2} \) to an improper fraction:
\[
2 \times 2 + 1 = 4 + 1 = 5 \quad \text{so it's} \quad \frac{5}{2}
\]
Convert \( \frac{5}{2} \) to twelfths:
\[
\frac{5}{2} \times \frac{6}{6} = \frac{30}{12}
\]
Now we compare:
\[
2 \frac{5}{12} = \frac{29}{12}
\]
\[
2 \frac{1}{2} = \frac{30}{12}
\]
Since \( \frac{29}{12} < \frac{30}{12} \), John will not meet his goal.
The correct response is:
**No; he will practice a total of 2 7/12 hours, and 2 7/12 < 2 1/2.**