## Ordering Real Numbers

Let us study about ordering real numbers. In common real numbers are defined as the combined form of both rational and irrational numbers in the branch of mathematics.

Rational numbers are commonly termed to be as the form of simple

Irrational numbers are commonly termed to be as the numbers that are not in the form of simple ratios. Some examples for ordering real numbers are below.

Jain is having 3 forks, `5/7` cakes and `2/7` breads, Jimmi is having `1/3 ` forks, 2 cakes and `3/5 ` breads and Nithi is having `2/5 ` forks, `2/7` cakes and 2 breads. Find the total number of forks, cakes and breads and order them from the smallest to the greatest?

Jain having 3 forks,` 1/3` cakes and `2/7 ` breads

Jimmi is having `2/3 ` forks, 3 cakes and `3/5` breads

Nithi is having `1/3` forks, `2/3` cakes and 2 breads

To calculate the total number of fruits, chocolates and nuts follow the steps as below:

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= 3 + `2/3` + `1/3` (the total number of forks are added)

= 3 `(3/3)` + `2/3 ` + `1/3` (to get common denominator multiply and divide 3 by ‘3’)

= `9/3` + `2/3` + `1/3`

= `(9 + 2 + 1)/3` (‘3’ is taken as common divisor)

= `12/3`

= 4 (total real numbers of forks)

= `5/7 ` + 2 + `2/7` (the total number of cakes are added)

=` 5/7` + 2 `(7/7)` + `2/7 ` (to get common denominator multiply and divide 2 by ‘7’)

= `5/7` + `14/7` + `2/7`

= `(5 + 14 + 2)/7` (‘7’ is taken as common divisor)

= `21/7`

= 3 (total real numbers of cakes)

= `2/7` + `3/5` + 2 (the total number of breads are added)

= `(2/7) (5/5)` + `(3/5) (7/7)` + 2 `(35/35)` (to get common denominator multiply and divide `(2/7)` by ‘5’, `(3/5)` by ‘7’ and 2 by ’35’)

= `10/35 + 21/35 + 70/35`

= `(10 + 21 + 70)/35` (‘35’ is taken as common divisor)

= `101/35` (total real numbers of breads)

My previous blog post was on

List all the real numbers in the order that largest to the smallest numbers from the following series of real numbers: (`sqrt(3), 1/2, -3/5,` 0.432317.. and `45/10` )

Associative Property of Real Numbers

List all the real numbers in the order that largest to the smallest numbers from the following series of real numbers: (`sqrt(3), 1/2, -3/5,` 0.432317.. and `45/10` )

Rational numbers are commonly termed to be as the form of simple

**ratios**with two integer values.Irrational numbers are commonly termed to be as the numbers that are not in the form of simple ratios. Some examples for ordering real numbers are below.

**Ordering real numbers:****Ordering real numbers - example 1:**Jain is having 3 forks, `5/7` cakes and `2/7` breads, Jimmi is having `1/3 ` forks, 2 cakes and `3/5 ` breads and Nithi is having `2/5 ` forks, `2/7` cakes and 2 breads. Find the total number of forks, cakes and breads and order them from the smallest to the greatest?

**Solution:****1. Given:**Jain having 3 forks,` 1/3` cakes and `2/7 ` breads

Jimmi is having `2/3 ` forks, 3 cakes and `3/5` breads

Nithi is having `1/3` forks, `2/3` cakes and 2 breads

To calculate the total number of fruits, chocolates and nuts follow the steps as below:

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**Symbol for all Real Numbers**. Keep checking my blog.**2. Forks:**= 3 + `2/3` + `1/3` (the total number of forks are added)

= 3 `(3/3)` + `2/3 ` + `1/3` (to get common denominator multiply and divide 3 by ‘3’)

= `9/3` + `2/3` + `1/3`

= `(9 + 2 + 1)/3` (‘3’ is taken as common divisor)

= `12/3`

= 4 (total real numbers of forks)

**3. Cakes:**= `5/7 ` + 2 + `2/7` (the total number of cakes are added)

=` 5/7` + 2 `(7/7)` + `2/7 ` (to get common denominator multiply and divide 2 by ‘7’)

= `5/7` + `14/7` + `2/7`

= `(5 + 14 + 2)/7` (‘7’ is taken as common divisor)

= `21/7`

= 3 (total real numbers of cakes)

**4. Breads:**= `2/7` + `3/5` + 2 (the total number of breads are added)

= `(2/7) (5/5)` + `(3/5) (7/7)` + 2 `(35/35)` (to get common denominator multiply and divide `(2/7)` by ‘5’, `(3/5)` by ‘7’ and 2 by ’35’)

= `10/35 + 21/35 + 70/35`

= `(10 + 21 + 70)/35` (‘35’ is taken as common divisor)

= `101/35` (total real numbers of breads)

**1.**Therefore the total number of forks, cakes and breads in their ascending are as follows:**2.**`101/35` breads, 3 cakes and 4 forksMy previous blog post was on

**Associative Property of Real Numbers**please express your views on the post by commenting.**Ordering real numbers - example 2:**List all the real numbers in the order that largest to the smallest numbers from the following series of real numbers: (`sqrt(3), 1/2, -3/5,` 0.432317.. and `45/10` )

**Solution:****1.**The given real number series is (`sqrt(3), 1/2, -3/5` , 0.432317.. and `45/10` )**2.**The arrangement of largest to the smallest number order of the given real number series is as follows:**3.**(`45/10, sqrt(3), 1/2` , 0.432317…, `-3/5` ).**Ordering real numbers – exercises:****1.**List all the real numbers in the order that smallest to the largest numbers from the following series of real numbers: (`sqrt(5), 7/2, -1/5` , 1.336767.. and `5/10` ) (Answer: `-1/5, 5/10` , 1.336767…., `sqrt(5), 7/2` )Associative Property of Real Numbers

**Ordering real numbers - example 2:**List all the real numbers in the order that largest to the smallest numbers from the following series of real numbers: (`sqrt(3), 1/2, -3/5,` 0.432317.. and `45/10` )

**Solution:****1.**The given real number series is (`sqrt(3), 1/2, -3/5` , 0.432317.. and `45/10` )**2.**The arrangement of largest to the smallest number order of the given real number series is as follows:**3.**(`45/10, sqrt(3), 1/2` , 0.432317…, `-3/5` ).**Ordering real numbers – exercises:****1.**List all the real numbers in the order that smallest to the largest numbers from the following series of real numbers: (`sqrt(5), 7/2, -1/5` , 1.336767.. and `5/10` ) (Answer: `-1/5, 5/10` , 1.336767…., `sqrt(5), 7/2` )**2.**List all the real numbers in the order that largest to the smallest numbers from the following series of real numbers: (`sqrt(2), 3/2, -3/7` , 0.00017.. and `4/100` ) (Answer: `3/2, sqrt(2)` , `4/100` , 0.00017, `-3/7` )