How to Reduce Fractions? Step by Step Methods to Reduce Fractions

How to reduce Fractions and how to simplify algebraic fractions, are described here. Hope, you remember your childhood days, during 3rd standard onwards, where most probably new terms such as fractions and decimals are introduced. It’s fun playing with integers.  But most of the times, when you cannot solve the fraction problem,  you think it as the most difficult chapter. But as your standard goes on increasing, it lets you know that it is nothing but division only. A common fraction is a numeral which represents a rational number. That same number can also be represented as a decimal, a percentage, or with a negative exponent. The set of all numbers that can be expressed in the form a/b, where a and b are integers and b is not zero, is called the set of rational numbers and is represented by the symbol Q . There are two type of fractions ,a. Proper fraction , b. Improper fraction.

A proper fraction is a fraction whose denominator is greater than numerator and an improper fraction are those in which the numerator is greater than the denominator.

 

In the above picture, the circle is divided into some parts, In the first figure the circle is divided into 8 equal parts and thus the selected area(in grey) is 2/8 of the circle. But in second figure the circle is divided into 4 equal parts and 1 part(in grey) is selected, hence the fraction is 1/4. But both the result are same as it depends on the no. of equal parts, the figure is divided into.

But if you have any problem in reducing and solving the fractions, then you are at right place and get ready to know more about fractions and some simple ways to reduce them.

How to Reduce Fractions?

There are many ways to reduce a fraction. But the most common method that is followed by most people is described below:-

  • First, find the factors of the numerator and do same with the denominator.
  • Find the highest common factor(H.C.F) among those factors in the numerator and denominator.
  • Divide both numerator and denominator with HCF, and the result we get is the lowest term to which the fraction can be reduced.

How to Reduce Fractions Step by Step?

So in this case 2/3 is the answer after diving both numerator and denominator with the GCF.

Reducing Fractions Examples

A fraction is reduced to lowest terms or simplified when its numerator and denominator have no common factors. It’s easier to multiply, divide, add and subtract fractions when they are simplified. To simplify a fraction, we find an equivalent fraction where the numerator and denominator have no common factors.

How to Simplify Algebraic Fractions?

Ok, till now you have learned how to reduce normal fractions, But do you know how to simplify algebraic fractions? If no, don’t worry, listed below are the steps to simplify algebraic fractions:-

For e.g;

  • Factorise the numerator and denominator to its smallest factor and find the common factors.
  • Now divide both numerator and denominator with the common factors.
  • The simplified result is the answer.

How to Simplify Improper Fractions?

An improper fraction is a fraction which has a greater numerator than denominator and thus it’s value is always greater than 1. Solving improper fractions is not too different from solving proper fractions.

The steps to simplify these kinda fractions are as follows:-

  • First, check whether the numerator is greater than denominator or not.
  • If yes, then divide the numerator and denominator with their common highest factor.
  • Now the reduced form is achieved.
  • To convert it into a mixed function, take the remainder and quotient out after dividing the numerator with the denominator.

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