Question

Today, a bicycle rider rode her bike 5 1/2 miles. Yesterday, she rode 6 1/4 miles. The difference in length between the two rides is what fraction of the longer ride?

Answer 1

`(3)/(25)`

Explanation

First we need to find the difference of the tow fractions. But to find it, we need to convert the mixed fraction to improper fraction so we can ease our calculation.

Remember that to convert a mixed fraction to an improper fraction, we just need to multiply the denominator of the fraction part by the whole number and add the result to the numerator of the fraction part; the denominator of the improper fraction will be the same denominator of the fraction part of the mixed fraction:

`5(1)/(2) =((5*2)+1)/(2) =(10+1)/(2)=(11)/(2)`

`6(1)/(4) =((4*6)+1)/(4) =(24+1)/(4) =(25)/(4)`

Now we can find the difference:

`(25)/(4) -(11)/(2)`

Remember that to add or subtract fractions, both fraction must have the same denominator, so we are multiplying both numerator and denominator of our second fraction by 2:

`(25)/(4) -(11)/(2)*(2)/(2)`

`(25)/(4) -(22)/(4)=(25-22)/(4) =(3)/(4)`

Now to find what fraction of our difference is to the longer ride, we just need to divide our difference by the longer ride:

`((3)/(4))/(6(1)/(4) ) =((3)/(4))/((25)/(4) ) =(3)/(4) *(4)/(25) =(3)/(25)`

We ca conclude the difference in length between the two rides is
`(3)/(25)` of the longer ride.