Question

On Monday billy spent 4 1/4 hours studying.On Tuesday he spent another 3 5/9 hours studying what is the combined time he spent studying answer as a mixed number

Answer 1

`7(29)/(36)\ hours`

Explanation:

Given:

Time spent on Monday (M) =
`4(1)/(4)\ hours`

Time spent on Tuesday (T) =
`3(5)/(9)\ hours`

Now, the total combined time spent on study is equal to the sum of the times spent on Monday and Tuesday.

So, we need to add both the times to get the combined time spent on studying.

The combined study time is given as:

Total time spent = Time spent on Monday + Time spent on Tuesday

`Total\ time=4(1)/(4)+3(5)/(9)\\\\Total\ time = (4* 4+1)/(4)+(3* 9+5)/(9)\\\\Total\ time = (17)/(4)+(32)/(9)\\\\\textrm{Taking LCD of 9 and 4 as 36, we get:}\\\\Total\ time = (17* 9)/(4* 9)+(32* 4)/(9* 4)\\\\Total\ time = (153)/(36)+(128)/(36)\\\\\textrm{Since the denominators are same, we add the numerators.}\\\\Total\ time = (153+128)/(36)\\\\Total\ time = (281)/(36)\ hours`

Divide 281 by 36. The quotient is the whole number part, the remainder is the numerator part and the denominator remains the same.

So, on dividing, we get 7 as quotient and 29 as remainder. So, converting to mixed fractions, we get:

`Total\ time = 7(29)/(36)\ hours`

Therefore, the the combined time he spent studying is
`7(29)/(36)\ hours`