Solved Examples based on Complex Fractions

Example 1: Simplify {(1 + 1/x) / (1 -1/x) } ?

Solution:

Given: {(1 + 1/x) / (1 -1/x) } 

Step 1: Create a single fraction from both the denominator and the numerator.

             =   {(1 + 1/x) / (1 -1/x) } 

             = [{(x+1)/x } / {(x-1)/x}]

Step 2: Apply the division rule by multiplying the top of the fraction by the reciprocal of the denominator 

          = [{(x+1)/x } / {(x-1)/x}]                        { Reciprocal of denominator {(x-1)/x} is {x /(x-1)}   } 

Therefore , 

          =  [{(x+1)/x } × {x /(x-1)} ]

          =  {(x+1)x / {x(x-1) }

Step 3:  Reduce the result to the simplest terms feasible.

          = {(x+1)x / {x(x-1) }

          = (x+1)/(x-1)

Example 2: Simplify Complex fraction (40/3)/(10/12).

Solution:

Given: (40/3)/(10/12)

Now , Follow above steps:

Step 1: Create a single fraction from both the denominator and the numerator.

Step 2: Apply the division rule by multiplying the top of the fraction by the reciprocal of the bottom

         = (40/3)/(10/12)                                          { Reciprocal of denominator 10/12 = 12/10 }

Therefore ,

         = 40/3 × 12/10

         =  480 /30

Step 3: Simplify the fraction to its simplest terms.

         = 480/30

         = 16

Example 3: Simplify {(4+2x)/x}/ (2/x).

Solution:

Given fraction: {(4+2x)/x}/ (2/x)

Apply the division rule by multiplying the top of the fraction by the reciprocal of the bottom

     =  {(4+2x)/x}/ (2/x)

     =  (4+2x)/x} × (x/2)

     =  (4+2x)/2

     =  {2(2+x)}/2

     = 2+x

Example 4: Simplify Complex fraction (5)/(15/6).

Solution: 

Given: (5)/(15/6)

Now, Follow above steps:

Step 1: Create a single fraction from both the denominator and the numerator.

Step 2: Apply the division rule by multiplying the top of the fraction by the reciprocal of the bottom

        = (5/1)/(15/6)                                       { Reciprocal of denominator 15/6 = 6/15 }

Therefore ,

        = 5/1 × 6/15

        =  30/15

Step 3: Simplify the fraction to its simplest terms.

        = 30/15

        = 2

Fractions are defined as numerical figure that represents a portion of a whole. A fraction is a portion or section of any quantity taken from a whole, which might be any number, a specified value, or an item.

Every fraction has a numerator and a denominator separated by a horizontal bar known as the fractional bar.

• The number of parts into which the whole has been divided is indicated by the denominator. It is placed below the fractional bar at the fraction lower part.
• The numerator indicates how many fractional parts are depicted or selected. It is placed above the fractional bar at the fraction upper part.

Examples: 2/3, 5/4, 9/8 etc