To solve this problem, we will illustrate how to proceed with the fraction 30/12 . At first, recall that a fraction is a number of the form
where a and b are integers and b is not zero. One way to represent a quotien is by using fractions. If we have the number a / b, we simply put the a on top of the b.
In this case the quotien 30 /12 is written as a fraction as follows:
however, in this case, we can reduce the fraction by factoring each number as follows
So another fraction that represent the quotient 30/12 is given by
Also, whenever the number on top (which is called the numerator) is greater than the number on the bottom (which is called the denominator), then we can write the fraction as a mixed number. Recall that a mixed number is a number that has a whole part and a fractional part. They look like this
where a is the whole number, and b/c is a proper fraction. That is, b is less than c.
Now, let us consider the fraction we found before
to find its mixed number representation, first, we take as reference the number on top. Then, we try to find the multiple of the number on the bottom that is the closest to the number on top, and that is less than the number on top. In this case, we have on top the number 5 and on the bottom the number 2. Note that 4 is the multiple of 2 that is the closest to 5 that is less than 5.
Now, we proceed to write 5 as a sum of 4 and something else. So we have
Now, we will split the fraction on the right into two fractions as follows:
Note that 4/2 =2. So this is the same as having
In this case, we have that the whole number is 2 and the fraction part is 1/2. So the mixed number representation of 5/2 is
