Question

A road is 5/7 of a mile long. A crew needs to repave 5/6 of the road. How long is the section that needs to be repaved?

Answer 1

Answer:
`0.59\ mi`

Explanation:

For this exercise let "x" represents the length in miles of the section of the road that needs to be repaved.

According to the information given in the exercise, you know that the total length of the road is the following:

`Total\ length=(5)/(7)\ mi`

Now, knowing that
`(5)/(6)` of the total length needs to be repaved, you can say that the value of "x" can be calculated by multiplying those fractions.

But first, it is important to remember that, by definition, the procedure to multiply fractions is:

`((a)/(b))((d)/(c))=(ad)/(bc)`

Therefore, you must multiply the numerators and multiply the denominators of each fraction.

You get that the product is:

`x=((5)/(7)\ mi)((5)/(6))\\\\x=(25)/(42)\ mi\\\\x=0.59\ mi`