Finding the Whole Number With a Fraction

Instructor: Tammy Galloway

Tammy teaches business courses at the post-secondary and secondary level and has a master's of business administration in finance.

In this lesson, we will define a fraction and identify the parts of a fraction: numerator and denominator. Then, you will learn the difference between a proper and improper fraction and how to simply an improper fraction into a whole number.

What Is A Fraction?

Jose has been the number one student in math since kindergarten. Although he's now in third grade, his teacher Ms. Jimenez expects him to shine and tutor other students in simplifying fractions into whole numbers.

A fraction is a number that represents part of the number. Even though Jose has always been successful in math, he cannot grasp fractions. His mom enrolls him in an evening math class where his tutor, Mr. Rosa, introduces him to the parts of a fraction: numerator and denominator. After this, he will explain to his class how to simplify fractions into a whole number. Let's take a closer look at his explanations.

Numerator & Simplification

Mr. Rosa writes the following fraction on the board, 6/12. He tells Jose the top part of the fraction is called a numerator. The numerator shows how many parts of the bottom number are taken. In sum, 6 out of the 12 parts are represented by the numerator.

Let's think of a pizza that has a total 12 slices, and 6 of them are mine. Basically, 6/12 of the pizza is taken. If we want to further simply 6/12, we find a common number that will go into the 6 and 12, which is 6. 6 ÷ 6 = 1; while 12 ÷ 6 = 2. Therefore, 6/12 can be simplified to 1/2. Mr. Rosa asks Jose to explain this concept without using fractions. Jose states, if we receive 6 pieces of pizza, and there are 12 pieces, we're allowed to eat half of the pizza.


Mr. Rosa then explains the denominator is the number at the bottom of the fraction. He asks Jose to identify the denominator in the pizza example; Jose states it's 12. 'Exactly', exclaims Mr. Rosa, 'the denominator represents the total number of parts'. Therefore, a fraction where the numerator is smaller than the denominator is called a proper fraction. Mr. Rosa asks Jose if he knows the name of a fraction when the numerator is larger than the denominator. Of course, Jose answers no.

Finding The Whole Number

Mr. Rosa asks Jose to define improper. Jose says improper means out of order and not following the rules. Mr. Rosa smiles widely and says, 'That's correct; now throw out all the rules and definitions I just shared with you about the numerator and denominator'. When a fraction is improper, it doesn't follow the typical rules; the numerator is now larger or equal to the denominator, which will result in a whole number. If we simplify 12/6, 12 ÷ 6 = 2, a whole number.

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