Question

A construction crew must build 3 miles of road in one week. On Monday, they build 2/3 mile of road. On Tuesday, they build 1/4 mile of a road. How many miles of road do they still have to build thus week?

Answer 1

So first we need to find how much road they have built already this week (on Monday and Tuesday).

We are told that Monday they built
`(2)/(3)` mile and on Tuesday they built
`(1)/(4)` mile. So let's add them together. We'll use a denominator of 12, since that is a common factor to both of them. What you do to the bottom of the fraction you must do to the top:

`(2)/(3)=(8)/(12)`

`(1)/(4)=(3)/(12)`

So now that we have a common denominator, we can add them together:

`(8)/(12)+(3)/(12)=(8+3)/(12)=(11)/(12)`

They built
`(11)/(12)` mile of road so far this week. If they need to build 3, we need to subtract
`(11)/(12)` from 3 to find how much remains. Let's get 3 to a number of 12 so we have a common denominator:

`(3)/(1)=(36)/(12)`

Now let's subtract:

`(36)/(12)- (11)/(12)= (25)/(12)=2(1)/(12)`

So now we know that the amount of road left that they must build this week is
`2(1)/(12)` mile.