Question

Eli practices for a piano recital 3 3 /4 hours in one week. In the same week, he practices basketball 1 2/ 3 hours. How much longer does he practice for his piano recital?

Answer 1

3 3/4 - 1 2/3=15/4 -5/3=45/12 - 20/12=25/12

Answer 2

To answer a question of "how much longer", you need to find the difference between the two times. That is, you subtract the basketball practice time from the piano practice time:

... 3 3/4 hours - 1 2/3 hours

There are many ways to do this subtraction. Since these are time values, you can convert the fractional hours to minutes. You know that an hour is 60 minutes, so 3/4 hour is (3/4)·(60 min) = 45 minutes, and 2/3 hour is (2/3)·(60 minutes) = 40 minutes. Now the difference can be computed to be ...

... 3:45 hours - 1:40 hours = 2:05 hours, or 2 hours and 5 minutes

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Another way to do this subtraction is to convert the fractions to ones with the same denominator. You know that 12 is a multiple of both 4 and 3, so a denominator of 12 can be used for each of the fractions:

... 3/4 = (3/4)·(3/3) = 9/12

... 2/3 = (2/3)·(4/4) = 8/12

Then the time difference is ...

... 3 9/12 hours - 1 8/12 hours = 2 1/12 hours

Sine 1/12 hour is 5 minutes, these two computations are in agreement.

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Yet another way to subtract these mixed numbers is to let your calculator do it. Many graphing calculators have the ability to display answers either as a decimal or as a fraction. The attachment shows a fraction display. I'm not using a mixed-number input for this calculator, so I'm just adding the fraction to the integer part.

Summary: Eli practiced piano 2 1/12 hours longer.