Answer: Complex Fractions can be solved using two methods. The two methods are by creating a single fraction and by calculating the Least Common Multiple of the denominator.
Fractions are defined as a 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
Complex Fraction
A complex fraction is one in which the denominator and numerator, or both, include fractions. A complex rational expression is a complex fraction with a variable.
For Example:
- 4/(1/3) is a complex fraction in which 4 is the numerator and 1/3 is the denominator.
- (2/7)/8 is also a complex fraction, with the numerator and denominator being 2/7 and 8, respectively.
- (5/4)/(2/10) is another complicated fraction having a numerator of 5/4 and a denominator of 2/10.
How to Simplify Complex Fractions?
Solution: To simplify complex fractions, we have two methods:
Method 1
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.
Step 3: Simplify the fraction to its simplest terms.
Example: Simplify Complex fraction (5/2)/(2/4). (Method 1)
Solution:
Given: (5/2)/(2/4)
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
= (5/2)/(2/4) { Reciprocal of denominator 2/4 = 4/2 }
Therefore,
= 5/2 × 4/2
= 20/4
Step 3: Simplify the fraction to its simplest terms.
= 20/4
= 5
Method 2
Step 1: Begin by calculating the Least Common Multiple of each denominator in the complex fractions.
Step 2: Multiply the complex fraction's numerator and denominator by this L.C.M.
Step 3: Reduce the result to the simplest terms feasible.
Example: Simplify Complex fraction (5/2)/(2/4). (Method 2)
Solution:
Given: (5/2)/(2/4)
Step 1: Begin by calculating the Least Common Multiple of each denominator in the complex fractions.
So we have (5/2)/(2/4)
LCM of denominator 2 and 4 is 4
Step 2: Multiply the complex fraction's numerator and denominator by this L.C.M i.e 4
= {(5/2) × 4 } / {(2/4) × 4}
= (5×2)/(2)
= 10/2
Step 3: Reduce the result to the simplest terms feasible.
= 10/2
= 5
Related Articles:
Similar Questions on Solving 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
