Introduction to Ordering rational numbers:
To compare the ordering rational numbers using the number line, the rational numbers should have the same denominator. Arrange these rational numbers on the number line in the ascending order left from left to right and compare.Since there lies a rational number between any two ordering rational number, it is clear that there lies an infinite number of rational between two given rational numbers.
Definition of Rational Numbers(ordering Rational Numbers):
The numbers of the from a/b where a and b are integers and b1=0( b is not equal to zero) are known as rational numbers.
` Q = {a/b | ainz, binz and b!=o}`
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.
Therefore,
`NsubWsubZsubQ`
Ascending order and Descending order:
When two or more numbers are given, if we arrange these numbers on such a way that each number is greater than the previous number, then we say that the numbers are arranged in ascending order.
On the other hand if we arrange the numbers in such a way that each number is lesser than the previous number, then the numbers are said to be in descending order.
I am planning to write more post on prime factorization chart 1-100, experimental probability formula. Keep checking my blog.
Examples of Ordering Rational Numbers:
Let us see the some examples of ordering rational numbers:
Example 1:
Arrange the rational numbers `(-7)/10` ,` 5/(-8)` , `(-2)/3` in ascending order.
Solution:
We first write the given numbers as `(-7)/10, (-5)/8, (-2)/3`
2 |10, 8, 3
5,4 ,3
L.C.M of 10, 8, 3 is `5xx4xx3xx2=120`
We convert the numbers into equivalent rational numbers with a common denominator.
`(-7)/10 = (-7xx12)/(10xx12) = (-84)/120`
`(-2)/3 = (-2xx40)/( 3xx40) =(-80)/120`
Let us compare the numerators -84, -75, -80
Since -84 < -80 < -75
`(-84)/120 < (-80)/120 <(-75)/120`
(i.e) `(-7)/10 < (-2)/3 < (-5)/8`
`(-7)/10 < (-2)/3 < 5/-8`
The numbers arranged in ascending order are `(-7)/10,` `(-2)/3` and `5/-8`
Example 2:
Arrange the rational numbers `(-2)/3` , `4/-5` , `(-1)/6` in descending order.
Solution:
We first write the given numbers as -2/3,4/-5, -1/6
2 |3, 5, 6
1,5,2
L.C.M of 3,5 and 6 is `2xx5xx3` =30
We convert the numbers into equivalent rational numbers with a common denominator.
`(-2)/3=(-2xx10)/(3xx10)=(-20)/30`
`(-4)/5=(-4xx6)/(5xx6)=(-24)/30`
` (-1)/6 = (-1xx5)/(6xx5)=(-5)/30`
Let us compare the numerators -20, -24 and -5
`-5 > -20 > -24`
`(-5)/30 >( -20)/30 > (-24)/30`
`(-1)/6 > (-2)/3 > (-4)/5`
(i.e) `(-1)/6 > (-2)/3 > 4/-5 `
The numbers arranged in ascending order are `(-1)/6` , `(-2)/3` and `4/-5`
These are some examples of ordering rational numbers.
To compare the ordering rational numbers using the number line, the rational numbers should have the same denominator. Arrange these rational numbers on the number line in the ascending order left from left to right and compare.Since there lies a rational number between any two ordering rational number, it is clear that there lies an infinite number of rational between two given rational numbers.
Definition of Rational Numbers(ordering Rational Numbers):
The numbers of the from a/b where a and b are integers and b1=0( b is not equal to zero) are known as rational numbers.
` Q = {a/b | ainz, binz and b!=o}`
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.
Therefore,
`NsubWsubZsubQ`
Ascending order and Descending order:
When two or more numbers are given, if we arrange these numbers on such a way that each number is greater than the previous number, then we say that the numbers are arranged in ascending order.
On the other hand if we arrange the numbers in such a way that each number is lesser than the previous number, then the numbers are said to be in descending order.
I am planning to write more post on prime factorization chart 1-100, experimental probability formula. Keep checking my blog.
Examples of Ordering Rational Numbers:
Let us see the some examples of ordering rational numbers:
Example 1:
Arrange the rational numbers `(-7)/10` ,` 5/(-8)` , `(-2)/3` in ascending order.
Solution:
We first write the given numbers as `(-7)/10, (-5)/8, (-2)/3`
2 |10, 8, 3
5,4 ,3
L.C.M of 10, 8, 3 is `5xx4xx3xx2=120`
We convert the numbers into equivalent rational numbers with a common denominator.
`(-7)/10 = (-7xx12)/(10xx12) = (-84)/120`
`(-2)/3 = (-2xx40)/( 3xx40) =(-80)/120`
Let us compare the numerators -84, -75, -80
Since -84 < -80 < -75
`(-84)/120 < (-80)/120 <(-75)/120`
(i.e) `(-7)/10 < (-2)/3 < (-5)/8`
`(-7)/10 < (-2)/3 < 5/-8`
The numbers arranged in ascending order are `(-7)/10,` `(-2)/3` and `5/-8`
Example 2:
Arrange the rational numbers `(-2)/3` , `4/-5` , `(-1)/6` in descending order.
Solution:
We first write the given numbers as -2/3,4/-5, -1/6
2 |3, 5, 6
1,5,2
L.C.M of 3,5 and 6 is `2xx5xx3` =30
We convert the numbers into equivalent rational numbers with a common denominator.
`(-2)/3=(-2xx10)/(3xx10)=(-20)/30`
`(-4)/5=(-4xx6)/(5xx6)=(-24)/30`
` (-1)/6 = (-1xx5)/(6xx5)=(-5)/30`
Let us compare the numerators -20, -24 and -5
`-5 > -20 > -24`
`(-5)/30 >( -20)/30 > (-24)/30`
`(-1)/6 > (-2)/3 > (-4)/5`
(i.e) `(-1)/6 > (-2)/3 > 4/-5 `
The numbers arranged in ascending order are `(-1)/6` , `(-2)/3` and `4/-5`
These are some examples of ordering rational numbers.
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