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 $\frac{2}{3}$ mile and on Tuesday they built $\frac{1}{4}$ 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:

$\frac{2}{3}=\frac{8}{12}$

$\frac{1}{4}=\frac{3}{12}$

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

$\frac{8}{12}+\frac{3}{12}=\frac{8+3}{12}=\frac{11}{12}$

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

$\frac{3}{1}=\frac{36}{12}$

Now let's subtract:

$\frac{36}{12}- \frac{11}{12}= \frac{25}{12}=2\frac{1}{12}$

So now we know that the amount of road left that they must build this week is $2\frac{1}{12}$ mile.