Simplifying rational numbers
Simplifying rational numbers is reducing the given rational number into its simplest form. Before learning about simplifying a given rational number,we should have an idea of Rational numbers.
Define Rational Number :
Rational numbers mean in math is number of the from `a/b` where a and b are integers and b`!=`0 are known as rational number. Q={`a/b` | a `in` z, b `in` z and b `!=` 0} is the set of all rational numbers. Rational number is the quotient of two integers. Therefore, a rational number is a number that can be write down in the form `S/T`, where S and T are integers, and T is not equal to zero. A rational number note in this way is frequently called a fraction . `S/T` Where
S `rArr` an integer
T `rArr` a nonzero integer
`11/5`,`(19)/(3)` `rArr` Rational numbers in math
An integer can be marking it as the quotient of the integer and 1, every integer is a rational number in math.
i .e :- 5 is an integer it can be written as `5/1` so it is a rational number Basic rule for solve rational number operations:
How to Simplify Rational Numbers
Rational Numbers Examples
Below are the examples on how to simplify rational numbers -
Example1 :
Simplify the rational number `50/20`
Solution:
numerator = 50 , denominator = 20
Least common divisor of 50 and 20 =2
`50/ 20 = (50/2)/(20/2)`
`= 25/10`
Least common divisor of 25 and 10 = 5
`25/10 = (25/5)/(10/5)`
`= 5/2`
Least common divisor of 5 and 2 =1
So the simplified form of `50/20 = 5/2`
Example 2:
Simplify the rational number `121/11`
Solution:
numerator = 121 , denominator = 11
Least common divisor of 121 and 11 = 11
`121/ 11 = (121/11)/(11/11)`
`= 11/1`
` = 11`
So the simplified form of `121/11 = 11`
Example 3:
Simplify the rational number `6/12`
Solution:
numerator = 6 , denominator = 12
Least common divisor of 6 and 12 =2
`6/ 12 = (6/2)/(12/2)`
` = 3/6`
Least common divisor of 3 and 6 = 3
`3/6 = (3/3)/(6/3)`
` = 1/2`
Least common divisor of 1 and 2 =1
So the simplified form of `6/12 = 1/2`
Example 4:
Simplify the rational number `3/5`
Solution:
numerator = 3 , denominator = 5
Least common divisor of 5 and 3 =1
So the simplified form of `3/5` is itself
Define Rational Number :
Rational numbers mean in math is number of the from `a/b` where a and b are integers and b`!=`0 are known as rational number. Q={`a/b` | a `in` z, b `in` z and b `!=` 0} is the set of all rational numbers. Rational number is the quotient of two integers. Therefore, a rational number is a number that can be write down in the form `S/T`, where S and T are integers, and T is not equal to zero. A rational number note in this way is frequently called a fraction . `S/T` Where
S `rArr` an integer
T `rArr` a nonzero integer
`11/5`,`(19)/(3)` `rArr` Rational numbers in math
An integer can be marking it as the quotient of the integer and 1, every integer is a rational number in math.
i .e :- 5 is an integer it can be written as `5/1` so it is a rational number Basic rule for solve rational number operations:
- If “a” and “b” are both of the same sign, then `a/b` is a positive rational number in math
- If “a” and “b” are opposite sign, then `a/b` is a negative rational number in math.
- Every integer “a” can written as `a/1`. Therefore, every integer is a rational number in math.
How to Simplify Rational Numbers
Rational Numbers Examples
Below are the examples on how to simplify rational numbers -
Example1 :
Simplify the rational number `50/20`
Solution:
numerator = 50 , denominator = 20
Least common divisor of 50 and 20 =2
`50/ 20 = (50/2)/(20/2)`
`= 25/10`
Least common divisor of 25 and 10 = 5
`25/10 = (25/5)/(10/5)`
`= 5/2`
Least common divisor of 5 and 2 =1
So the simplified form of `50/20 = 5/2`
Example 2:
Simplify the rational number `121/11`
Solution:
numerator = 121 , denominator = 11
Least common divisor of 121 and 11 = 11
`121/ 11 = (121/11)/(11/11)`
`= 11/1`
` = 11`
So the simplified form of `121/11 = 11`
Example 3:
Simplify the rational number `6/12`
Solution:
numerator = 6 , denominator = 12
Least common divisor of 6 and 12 =2
`6/ 12 = (6/2)/(12/2)`
` = 3/6`
Least common divisor of 3 and 6 = 3
`3/6 = (3/3)/(6/3)`
` = 1/2`
Least common divisor of 1 and 2 =1
So the simplified form of `6/12 = 1/2`
Example 4:
Simplify the rational number `3/5`
Solution:
numerator = 3 , denominator = 5
Least common divisor of 5 and 3 =1
So the simplified form of `3/5` is itself