Simplifying Fractions Algebra
Fractions are part of a whole number written as numerator/denominator, the numerator and the denominators are numbers that have factors other than 1 and itself, in short composite numbers. The process of simplifying fractions is a simple method of reducing fractions. Let us now learn how to simplifying fractions which leads to a reduced fraction. In simplifying fractions following are the steps to be followed:
• First we need to find the common factor of the numerator and the denominator. For instance, the common factor of 4 and 8 is 4 as 4 divides both 4 and 8 evenly.
• Next step is to divide the numerator and also the denominator with the common factor of the numerator and the denominator
• The process is to be repeated till there are no common factors for the numerator and the denominator
• Once the composite numbers of the numerator and denominator have no common factors left, the fraction is a reduced fraction or a simplified fraction
Consider the following Simplifying Fractions Examples
Simplify the fraction 48/108,
The common factor of 48 and 108 is 2, dividing 48 and 108 with 2, 48/2=24 and 108/2=54,
The common factor of 24 and 54 is 2, dividing 24 and 54 with 2, 24/2=12 and 54/2=27,
The common factor of 12 and 27 is 3, dividing 12 and 27 with 3, 12/3=4 and 27/3=9.
There are no common factors of 4 and 9 other than 1 and hence the simplified fraction is 4/9
There is another method used in Reducing Fractions or simplifying fractions, it is the GCF method. In this method, the greatest common factor of the numerator and the denominator are found. Then the numerator and the denominator are divided by the greatest common factor which gives the reduced fraction. So, in this method first the largest number that goes exactly into the numerator and the denominator is found, 9/27, here the largest number that divided 9 and 27 exactly is 9 and hence the reduced fraction would be 9x1/9x3= 1/3
Examples of Simplifying Fractions
Simplify the fraction 48/108
The greatest common factor of 48 and 108 is,
48= 2 x 2 x 2 x 2 x 3
108= 2 x 2 x 3 x 3 x 3
The greatest common factor is, 2 x 2 x 3= 12
The numerator and the denominator are divided with the greatest common factor
48/12 = 4 and 108/12=9, the simplified fraction is 4/9 which has no other common factor other than 1
Fractions are part of a whole number written as numerator/denominator, the numerator and the denominators are numbers that have factors other than 1 and itself, in short composite numbers. The process of simplifying fractions is a simple method of reducing fractions. Let us now learn how to simplifying fractions which leads to a reduced fraction. In simplifying fractions following are the steps to be followed:
• First we need to find the common factor of the numerator and the denominator. For instance, the common factor of 4 and 8 is 4 as 4 divides both 4 and 8 evenly.
• Next step is to divide the numerator and also the denominator with the common factor of the numerator and the denominator
• The process is to be repeated till there are no common factors for the numerator and the denominator
• Once the composite numbers of the numerator and denominator have no common factors left, the fraction is a reduced fraction or a simplified fraction
Consider the following Simplifying Fractions Examples
Simplify the fraction 48/108,
The common factor of 48 and 108 is 2, dividing 48 and 108 with 2, 48/2=24 and 108/2=54,
The common factor of 24 and 54 is 2, dividing 24 and 54 with 2, 24/2=12 and 54/2=27,
The common factor of 12 and 27 is 3, dividing 12 and 27 with 3, 12/3=4 and 27/3=9.
There are no common factors of 4 and 9 other than 1 and hence the simplified fraction is 4/9
There is another method used in Reducing Fractions or simplifying fractions, it is the GCF method. In this method, the greatest common factor of the numerator and the denominator are found. Then the numerator and the denominator are divided by the greatest common factor which gives the reduced fraction. So, in this method first the largest number that goes exactly into the numerator and the denominator is found, 9/27, here the largest number that divided 9 and 27 exactly is 9 and hence the reduced fraction would be 9x1/9x3= 1/3
Examples of Simplifying Fractions
Simplify the fraction 48/108
The greatest common factor of 48 and 108 is,
48= 2 x 2 x 2 x 2 x 3
108= 2 x 2 x 3 x 3 x 3
The greatest common factor is, 2 x 2 x 3= 12
The numerator and the denominator are divided with the greatest common factor
48/12 = 4 and 108/12=9, the simplified fraction is 4/9 which has no other common factor other than 1
