Reducing the Fractions to their Lowest Terms.

REDUCING A FRACTION:

Reducing a fraction means making the fraction as simple as possible.

Reducing a fraction is called as simplifying the fraction. We say the fraction in its Lowest terms.       

We need to divide the numerator and denominator by a common factor.

We can keep reducing a fraction till the numerator and the denominator in the reduced fraction have no common factor other than 1.

 

Simplify (or) Reduce the Fractions (or) the fractions to their Lowest Terms:

1) 48/108 =

Solution:

(i) We need to find out the common factor of both Numerator and Denominator. The Common factor is 2.

(ii) Divide the numerator and denominator with that common factor:2

Numerator: N = 48 ÷ 2 = 24.

Denominator:D = 108 ÷ 2 = 54.

(iii) We need to simplify the fraction with their common factor, till we get the common factor as 1.

Numerator: N    = 48 ÷ 2  =  24 ÷ 2  = 12 ÷ 3  = 4.

Denominator: D = 108 ÷ 2 =  54 ÷ 2  = 27 ÷ 3  = 9.

The Simplified or Reduced fraction is: 4/9, for which the common factor is 1.   

     

2) 168/144 =

Solution:

(i) The common factor of the given fraction numerator, N: 168 and denominator, D: 144 is 4.

(ii) Divide the numerator and denominator with the common factor in each step.

(iii) Reduced the fraction till the common factor of the fraction is 1.

Numerator: N    = 168 ÷ 4 = 42 ÷ 3 = 14 ÷ 2 = 7.

Denominator: D = 144 ÷ 4 = 36 ÷ 3 = 12 ÷ 2 = 6.

The Common factor of the Reduced fraction: 7/6  is 1.   

Thus, the simplified or Reduced fraction of the given fraction is:

168/144 =  42/36  =  14/12 =  7/6.

 

3) 20/24 =

Solution:

(i) The common factor of the given fraction is: 4.

(ii) Dividing the given fraction with their common factor at each step till the common factor of the reduced fraction is 1.

Numerator: N    = 20 ÷ 4 = 5.

Denominator: D = 24 ÷ 4 = 6. 

Thus, the Reduced fraction = 20/24 = 5/6.

                             (OR)

If we choose the common factor for the given fraction as 2, then

Numerator: N    = 20 ÷ 2 = 10 ÷ 2 = 5.

Denominator: D = 24 ÷ 2 = 12 ÷ 2 = 6.

The Reduced fraction = 20/24 = 10/12 = 5/6.

 

Note: We can choose different common factor in reducing the fraction, the Reduced fraction is same.

 

4) 32/60 =

Solution:

Let the common factor of the given fraction =  4.

Numerator: N    = 32 ÷ 4 = 8.

Denominator: D = 60 ÷ 4 = 15.   

Thus, the Reduced Fraction is : 32/60 = 8/15.

                             (OR)

Let the common factor of the given fraction = 2.

Numerator: N     = 32 ÷ 2  =  16 ÷ 2  =  8.

Denominator: D = 60 ÷ 2  =  30 ÷ 2  = 15.

Thus, the Reduced fraction in its lowest terms:

32/60 = 16/30 = 8/15.

 

 5) 27/81=

Solution:

If the common factor of the given fraction is: 9.

Numerator: N    =  27 ÷ 9  =  3 ÷ 3  =  1.

Denominator: D =  81 ÷ 9  =  9 ÷ 3  =  3.

Thus, the given fraction in its Lowest terms = 27/81 = 3/9 = 1/3.

                          (OR)

If the common factor of the given fraction is: 3.

Numerator: N    =  27 ÷ 3  =  9 ÷ 3    =  3 ÷ 3  =  1.

Denominator: D =  81 ÷ 3  =  27 ÷ 3  =  9 ÷ 3  =  3.

Thus, the given fraction in its Lowest terms =

27/81  =   9/27  =  3/9  =  1/3.