Equivalent rational numbers

The equivalent rational numbers are the term in the mathematics. The equivalent rational number definesthe equivalent definition fractions math and the equivalent ratio for the numbers. The ratios of the two numbers have the equal ratios for theratios of other two numbers. Here we are going to see about the equivalent forms of rational numbers for the two numbers. Two rational numbers are said to be equivalent if we divide each decimal value will be the same.that is if a/b is equivalent to c/d if a/b=p then c/d=p.

Properties of rational Number

The numbers of the from a/b where a and b are integers and b`!=` 0( b is not equal to zero) are known as rational numbers.

                 `Q = { a/b | a in z , b in z and b!=0 }`

is the set of all rational numbers.

If ‘a’ and ‘b’ are both of the same sign, then a/b is known as a positive rational number.

If ‘a’ and ‘b’ are of opposite signs, then a/b is known as a negative rational number.

Every integer ‘a’ can be written as a/1. So every integer is a rational number


Equivalent rational numbers examples


Below are the examples on equivalent rational numbers  -

Example 1 

 Find two equivalent rational number for `14/9` .

 Solution:

 The given rational number is  `14/9` .

We have to find the equivalent rational number by multiplying or dividing the given rational number by the common number.

First multiply the given rational number by 2 on numerator and denominator.

 `14/9` = `(14*2)/(9*2)` 

 `14/9` =  `28/18` .

To find the next rational number multiply the given ratio by the number 5.

`14/9`  = `(14*5)/(9*5)` 

 `14/9` =  `70/45` 

The equivalent ratios of  `14/9`  are  `28/18`  `70/45` . 


Example 2 

Determine three equivalent rational number for `4/10` .

Solution:

The given rational number is  `4/10` .

We have to find the equivalent ratio by multiplying or dividing the given rational number by the common number.

First multiply the numerator and denominator of given rational number by 10 .

 `4/10` =  `(4*10)/(10*10)` 

 `4/10` =   `40/100` 

To find the next rational number by dividing number 2 in numerator and denominator.

 `4/10`  =   `(4/2)/(10/2)` 

 `4/10`  =   `2/5` 

To find the next rational number ,multiply the number 5 on numerator and denominator.  

 `4/10`  =  `(4*5)/(10*5)`  `4/10`  =   `20/50` 

The equal ratios of   `4/10`  are   `4/10` ,  `4/10`   `4/10` 


Example 3 

Determine the least equivalent rational number for the ratio `50/100` .

Solution:

The given rational number is `50/100` .

The denominator is a multiple of numerator

100 = 2*50

So to get the least equivalent rational number we divide numerator and denominator by 50

`50/100` = `(50/50)/(100/50)` 

`50/100` = `50/100 = 1/2`

So the least equivalent rational number of `50/100 = 1/2`


Practice problems


  • Evaluate two equivalent rational number for `1/9` .

Answer: `2/18, 5/45`

  • Determine the least equivalent rational number for the ratio `16/ 49` .

Answer: `4/7` .