John plan to practice piano at least 2 1/2 hour this weekend it he practice 1 1/6hours on Saturday and 1 1/4 hours on Sunday will he meet his goal
1 1/6 + 1 1/4 = ___
is that at least 2 1/2?
To determine if John will meet his goal of practicing piano for at least 2 1/2 hours this weekend, we need to add up the amount of time he practiced on Saturday and Sunday.
On Saturday, John practiced for 1 1/6 hours.
On Sunday, John practiced for 1 1/4 hours.
To calculate the total time John practiced, we need to find a common denominator for 6 and 4, which is 12.
Converting 1 1/6 to twelfths: 1 1/6 = 1 + 2/12 = 1 + 1/6 = 12/12 + 2/12 = 14/12.
Converting 1 1/4 to twelfths: 1 1/4 = 1 + 3/12 = 12/12 + 3/12 = 15/12.
Now, we can add the two fractions together:
14/12 + 15/12 = 29/12.
This means that John practiced for a total of 29/12 hours.
To convert the fraction back to a mixed number, we can divide the numerator (29) by the denominator (12):
29 รท 12 = 2 with a remainder of 5.
Therefore, John practiced for 2 5/12 hours.
Since John practiced for more than 2 1/2 hours (2 5/12 hours vs. 2 1/2 hours), he will meet his goal.
To determine if John will meet his goal of practicing the piano for at least 2 1/2 hours over the weekend, we need to add the hours he practiced on Saturday and Sunday.
On Saturday, John practiced 1 1/6 hours. To add this to our total, we convert 1 1/6 hours to a fraction with the same denominator as 2 1/2. The denominator is 2 since it is the smallest number that 6 and 2 have in common.
1 1/6 = 6/6 + 1/6 = 7/6
Now, let's add the hours John practiced on Sunday.
On Sunday, John practiced 1 1/4 hours. Again, we convert 1 1/4 hours to a fraction with the same denominator as 2 1/2.
1 1/4 = 4/4 + 1/4 = 5/4
Now, we can add the two fractions:
7/6 + 5/4
To add these fractions, we need to find a common denominator. The smallest number that 6 and 4 have in common is 12. So, we need to convert both fractions to have a denominator of 12.
7/6 = (7/6) * (2/2) = 14/12
5/4 = (5/4) * (3/3) = 15/12
Now that both fractions have a common denominator, we can add them together:
14/12 + 15/12 = 29/12
So, John practiced a total of 29/12 hours over the weekend.
However, since our goal is specified as 2 1/2 hours, we need to convert this mixed number to an improper fraction:
2 1/2 = 2 + 1/2 = 2 + 6/12 = 2 + 6/12 = 24/12 + 6/12 = 30/12
Now we can compare the total hours John practiced (29/12) with his goal (30/12).
Since 29/12 is less than 30/12, John did not meet his goal of practicing at least 2 1/2 hours over the weekend.