Fractions Basics

Slicing a Cake into Fractions

This is a simple example, if you cut a cake into two equal pieces, each piece represents half of the cake. In other words, the half of the cake you took is one of the two parts. Mathematically, we express this division by which is a fraction number where 1 represents the piece you took and 2 represents the number of portions the cake was divided into.

Definition of Fraction

Every fraction number is a real number consisting of two integers separated by a "fraction bar", which can be written horizontally or diagonally. For example, we can write or .

A fraction is a "part" of a "whole":

  • The upper part (PART) of a fraction is called a numerator. This number tells us how many parts we took;

  • the lower part (WHOLE) is called a denominator. This number tells us the total number of parts;

Now suppose that if you divide this cake into 6 pieces and eat 5 pieces of it, what is the number that represents all the cake you ate? I think it has become easy now, we divided the cake into 6 parts which means the denominator is 6, and you ate five parts which means the numerator is 5, so what you ate is of the cake.


Let and two integers with .

The expression or called a Fractional Number.

  • The number is called a Numerator;

  • The number is called a Denominator which is always non-zero number.

Types of Fractions

There are 3 types of fractions:

  • Proper Fractions: The numerator is less than the denominator. ()

    Exemples: ; ;

  • Improper Fractions: The numerator is greater than, or equal to, the denominator. ()

    Exemples: ; ;

  • Mixed numbers: There is a whole number and a fraction.

    Exemples: ; ;

Remainder of Fraction

Going back to the previous example, remember you ate 5 cookies out of 6. How many do you have left? This is very clear that the rest is only one piece. From this example, we can draw the following conclusion:


REMAINDER part, quantity, or number left over after division

Fraction Word Problems


In my fruit basket, there are 9 pieces of fruit, 5 of which are apples.

How can we express the number of apples as a fraction?


Total pieces: 9, corresponds to the Denominator

Apple pieces: 5, corresponds to the numerator


Maria spent of the money her grandparents gave her on an adventure book.

What fraction number represents the remainder?


Maria spent three quarters of her money, Then, she had only one quarter left.


What fraction of the colored part of each figure?

fractions of colored parts in cercle and shapes


Figure 1:

Figure 2:

Figure 3:


What fraction of the colored part of the two circles?

mixed fractions of colored parts in cercle and shapes


In this figure, we took all the eight parts of the left circle, and we also took 5 parts out of the eight from the right circle. Which means we took of the parts.