Brian was training to run a marathon. During the three day period before the race he decided he would train for 11 hours. If he trained for 2 3/5 hours first day and 2 9/10 second day, how many hours would he need to train third day.

This is the question

I solved it to the point where I got improper fraction of 13/5 +29/10 then I did
130/50 + 154/50 then I got 275/50 I simplified it to 5/2. The answer is however 5 1/2 I don't know how.

Take out your calculator, or do it by hand,

275/50=55/10=5 1/2

why use 50 for the common denominator, when 10 works just as well?

13/5 + 29/10
= 26/10 + 29/10
= 55/10

Now subtract that total from the 11 hours (110/10) needed, and you still need 55/10 = 5 1/2

275/50 is 5 1/2, not 5/2.

To find the total amount of training time Brian will need on the third day, you can add the training times from the first and second day.

First, let's convert the mixed numbers to improper fractions:

2 3/5 = (5*2 + 3)/5 = 13/5
2 9/10 = (10*2 + 9)/10 = 29/10

Now, let's add the fractions:

13/5 + 29/10 = (13*2 + 29)/10 = 55/10

To simplify the fraction, you can divide both the numerator and denominator by their greatest common divisor, which is 5 in this case:

55/10 ÷ 5/5 = 11/2

Now, we have the fraction 11/2. To express it as a mixed number (a whole number and a proper fraction), we divide the numerator (11) by the denominator (2):

11 ÷ 2 = 5 remainder 1

So, the result is 5 1/2 hours. Brian would need to train for 5 1/2 hours on the third day.

To find the total training time for the three days, you correctly added the fractions 13/5 and 29/10. However, to compare and add fractions, it is important to have a common denominator. In this case, the least common multiple of 5 and 10 is 10.

To convert 13/5 to the denominator 10, you can multiply both the numerator and denominator by 2. This gives you (13/5) * (2/2) = 26/10.

Now you can add the fractions: (26/10) + (29/10) = 55/10.

To simplify the fraction 55/10 into a mixed number, you divide the numerator (55) by the denominator (10). The quotient is the whole number, and the remainder becomes the numerator of the fraction part.

55 divided by 10 equals 5 with a remainder of 5. This means the mixed number is 5 and 5/10. Since 5/10 simplifies to 1/2, the final answer is 5 1/2 hours for the third day of training.