What Is an Improper Fraction?
An improper fraction is a fraction where the numerator is larger than the denominator. An example of this would be the fraction ƒ12/8.
Improper fractions represent a value that is greater than the total value of one set. Often times, it's easier to leave your fraction in the improper fraction form to work with fractions. When multiplying and dividing fractions, you must use an improper fraction rather than mixed numbers.
What Is a Mixed Number?
Mixed numbers are fractions that contain a numerator, a denominator, and a whole number. These types of fractions contain whole sets and a fraction of the remaining set. An example of a mixed number would be 4 3/4.
Mixed numbers are used to represent the final answer when working with fractions. They are also helpful when adding and subtracting fractions.
Changing From an Improper Fraction to a Mixed Number
The challenge with these two different forms of fractions is being able to convert between them easily. When converting an improper fraction to a mixed number, we will think of the fraction bar as division. For example, using the improper fraction 12/8, we would divide the numerator 12 by the denominator 8.
To convert an improper fraction to a mixed number, we will start by dividing the numerator by the denominator. Once you are finished dividing, your quotient will become your whole number. Your remainder will also become your numerator, and you will keep the same denominator.
Looking at the example, 12 will divide into 8 one time, with 4 left as our remainder. This will make our mixed number 1 4/8.
Improper to Mixed Example
Let's check with a friend of mine, Adam, who works at a local cookie factory. Adam spends his day stacking delicious cookies into boxes that can hold 10 cookies each.
As he works steadily, the machine suddenly speeds up. Adam realizes that he has run out of boxes. In a panic, he presses the emergency stop button. Adam must go get enough boxes to pack the overflow of cookies. He counts the cookies and sees that there are 78 cookies to fit in the boxes that only hold 10 cookies each. Adam knows that the fraction to represent this would be 78/10.
Adam needs to change this improper fraction to a mixed number so that he can see how many boxes he needs. Adam begins by dividing the numerator 78 by the denominator 10. 10 will divide into 78 7 times. After subtracting, the remainder will be 8.
Adam can now see that the quotient 7 will become his whole number, the remainder 8 will become the numerator, and the denominator will stay 10.
Adam's mixed number is 7 8/10. Adam can see that he will be able to fill 7 full boxes and 8 out of 10 cookies in the next box. As he packs the last cookie, he presses the start button, and the machine starts sending more cookies down the line.