Question

Divide. Write the quotient in lowest terms.5 2/3 divided by 4Your answer should bea simplified proper fraction, like 3/5a simplified improper fraction, like7/4a mixed number, like 13/4

Answer 1

We want to calculate the following division

`5\text{ }(2)/(3)\text{ / 4}`

First, to do so, we will transform the mixed number to its equivalent fraction, so the division is easier. Given a mixed number of the form a b/c, its equivalent fraction is of the form

`a\text{ }(b)/(c)\text{ = }(a\cdot c+b)/(c)`

In our case, a = 5, b = 2 and c =3, so the equivalent fraction is

`5\text{ }(2)/(3)\text{ = }(5\cdot3+2)/(3)\text{ = }(17)/(3)`

Now, we will use the fact that the number 4 could be written as the fraction 4/1 and we will divide both fractions.

If we have one fraction a/b and we want to divide it by c/d we can do as follows

`(a)/(b)/((c)/(d))\text{ = }(a)/(b)\cdot(d)/(c)\text{ = }(a\cdot d)/(b\cdot c)`

which is equivalent to"flip" the fraction that we are using to divide and then multiply. So we have the fraction 17/3 and we want to divide it by 4/1. So, we proceed as follows:

`(17)/(3)/((4)/(1))\text{ = }(17)/(3)\cdot(1)/(4)\text{ = }(17)/(12)`

Since this fraction can not be simplified further, the final answer is 17/12