Not only in maths, but fractions also come in handy in our daily lives. Take the example of dividing a pizza among your siblings into perfectly equal parts so that you get to relish the flavor as much as them. Based on the number of siblings, you would have divided the pizza into different but equal pieces.
To understand it even better, head over to Numbers Tips and Tricks first. It will speed up your learning process in numerous ways. You will understand that every fraction can also be represented as a rational number, which can be written as a/b, where a and b are natural numbers.
Simplification is the premise of establishing an equation, solving a mathematical problem, or implementing their daily routine principles. A fraction is considered a part of a whole number, a number between the whole numbers. Before we learn how to simplify fractions, let us delve into the aspects of it. Let us understand the numbers between two whole numbers and learn to simplify them along the way.
What Is a Fraction?
There are numerous daily life examples to define fractions more practically. Ordinarily, we entail dividing different objects into equal parts to share that among ourselves. Each part that is divided equally will be considered the fraction of the whole object that has been divided. It also denotes how many parts we can divide a whole into.
A fraction is identified by a slash (/) or a line in between two natural numbers. The two parts of the fraction separated by a slash or a line have different values based on their nomenclature. The left to the slash or above the line is called the numerator. The number right to the slash or below the line is called the denominator. The numerator represents the number of equal parts taken from the whole. Denominator defines the total number of equally divided parts in a whole.
For example, 8/10 is a fraction. Where the numerator 8 represents the number of equal parts taken from a whole. Whereas the denominator 10 represents the total number of equally divided parts in a whole.
Recall your last birthday. Your parents bought you a delicious cake. You have your friends gathered around when you blow the candles and cut the cake. You cut slices and give each slice to your friends to eat.
Consider your cake as a whole object, and each slice you took out of it is a fraction of that object. Depending upon the total number of slices you made and the number of slices you shared with your friends, the numerator’s values and the denominator will be defined. Suppose you carved five equal slices and gave away each slice to five different friends. Subsequently, each of your friends will receive 1/5th portion of your birthday cake. Here, the value 1 is the numerator, and the value 5 is the denominator.
From the above example, we have established that the slices or the parts of a whole object need to be equal to be called a fraction of that object. If the parts are unevenly divided, they can’t be considered fractions.
A Fraction On a Number Line
Mathematically, a number line is defined as a straight line segment with numbers placed at equal intervals or distance along its length. The line segment can be extended in any direction infinitely. Usually, we draw it horizontally. As we move from left to right along the number line, the value of the numbers increases. The value decreases as we move from right to left. The increasing and decreasing values are separated by a zero (0) at the center.
To define fractions even precisely, we can represent them on a number line.
As we now understand that a fraction is a part of a whole. The value of it can also be defined as less than 1.
To represent the value of a fraction on a number line, we have to first draw a line with whole numbers placed on it at equal intervals. Now, before placing the value of fractions on it, we have to look for the denominators. If the denominator’s value is 4, we will have to divide the number line into four parts between each whole number at equal intervals. This way, we can show the fourths along the number line.
Alternately, the numerator’s values need to be placed from right to left in increasing order along the number line.
For example, to represent the fraction 2/4 on a number line, we need to divide the number line into four equal parts between the whole numbers 0 and 1. Assign the values of the denominator of each equal part, i.e., 4. To assign the numerator’s values, we have to follow along the line from left to right. The numerator for the first part will be 1, the value of the numerator of the second part will be 2, and so on.
As we have to represent the fraction 2/4 on the number line, the second part between the whole numbers 0 and 1 is our answer.
Types of fraction
In maths, the numerator and the denominator define the types of fractions. Majorly, there are three different types of fractions. Apart from three major types, the fractions are also defined as three other types.
Let us look at each type and try to understand them one at a time.
- Proper fraction: As the name suggests, a proper form of a fraction where the numerator’s value is less than the denominator is called a proper fraction. The most significant example of a proper fraction is an object that is divided into two equal parts.
We can write the fraction numerically as 1/2, or we can call that a whole object has been divided into two equal halves.
In the above example, we can see that the numerator of the fraction 1/2 is smaller than the denominator.
In other words, a fraction whose value is less than 1 is called a proper fraction. This means, after further simplification of a proper fraction, the value will always be less than 1.
Some other examples of proper fractions are 2/4, 5/7, 8/9, 11/20.
- Improper fraction: On the contrary to the proper fraction, an improper fraction will have a numerator that is greater than the denominator. It will be an improper fraction even if the values of both the numerator and the denominator are equal.
In other words, if we simplify such a fraction, we will get 1 since every natural number can be defined as a fraction where the value of the denominator is always 1. Likewise, the simplification of an improper fraction will give a value that is either greater than or equal to 1.
- Mixed fraction: Going by the name itself, a mixed fraction is a blend of a whole number and a proper fraction. It is a special kind of improper fraction.
For example, to write a mixed fraction, we have to place a whole number adjacent to a proper fraction. It is written as 1½, 21/2, or 1 + ½, 2 + ½, etc.
In addition to an improper fraction, upon further simplification, the value of a mixed fraction is always greater than 1. Likewise, we can always convert a mixed fraction into an improper fraction and vice versa.
- Like fraction: If we place a set of fractions with different values, but with the same denominator, adjacent to each other, it will be called a like fraction.
1/4, 6/4, 8/4, 10/4, and so on.
In the above example, where the fractions of different values are put adjacent to each other, the denominator’s values are the same. It can be a mixture of proper and improper fractions. The simplification of such fractions is simple. If we are asked to add the above fractions, then:
We get, 1/4 + 6/4 + 8/4 + 10/4 = (1 + 6 + 8 + 10)/4 = 25/4
- Unlike fraction: A set of fractions with different values of denominators placed adjacent to each other are called unlike fractions. The numerator of such fractions need not be alike. It can also have a mixture of proper and improper fractions.
5/9, 6/15, 12/3, 7/12, and so on.
Contrary to the like fractions, simplification of the above fractions is a bit lengthy. In the case of addition or subtraction, we need to find the lowest common factor or the LCM of the denominators.
Supposedly, if we are asked to find the sum of two unlike factors, 3/4 and 4/12.
We have to find the LCM for the denominators of both the fractions, which is 12.
Now, we have to multiply both the numerator and the denominator of 3/4 by 12 and 4/12 by 4.
We will get,
36/48 and 16/48.
By adding both the fractions, we will get:
36/48 + 16/48 = 52/48
- Equivalent fraction:When we simplify two or more fractions representing the same portion of the whole and find the same result, they will be called equivalent fractions.
3/12 and 1/4; 5/10 and 1/2.
Both the examples are equivalent fractions. When we simplify them, we find the exact result equivalent to each other: – 1/4 and 1/4; 1/2 and 1/2.
Fractions are a fun way to learn about maths and life in general. We hope you learned to simplify the fractions in easy steps.