How to Reduce Fractions: Step by Step Methods

How to Reduce Fractions: Step by Step Methods

How to Reduce Fractions and how to simplify algebraic fractions, are described here. I Hope, you remember your childhood days, during the 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 time, when you cannot solve the fraction problem,  you think of 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 that 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 types of fractions, a. Proper fraction, b. Improper fraction.

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

How to Reduce Fractions

 

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 the 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 is the 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 the 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 the 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?

How to Reduce Fractions Step by StepSo 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 the 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.

Reducing Fractions Examples

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.;

How to Simplify Algebraic Fractions

  • Factorize 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 that has a greater numerator than the denominator and thus its value is always greater than 1. Solving improper fractions is not too different from solving proper fractions.

How to Simplify Improper Fractions

The steps to simplify these kind of fractions are as follows.

  • First, check whether the numerator is greater than the 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.