We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.
We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.
Affiliations with Schools & Educational institutions are also welcome.
Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit
We will be happy to post videos as per your requirements also. Do write to us.
A Rational Number of the form
or a number which can be expressed in the form of
, where p and q are integers and q ≠ zero, is called a
Rational - Number.
Example : 2 / 3 , -5 / 7, -10 / -3 are Rational Number.
| Some useful results
1) Every natural number is a Rational No.but a rational no. need not be a natural number.
2) Zero is a rational no.
3) Every integer is a rational no. but a rational no. need not be an integer.
4) Every fraction is a rational no. but a rational no. need not be a fraction.
If p /q is a rational no., then p - > Numerator and q - > denominator.
If both numerator and denominator are positive or negative then that rational no.called Positive rational no.
If either numerator or denominator is negative then the rational no. is called a Negative rational no.
The rational no. zero is neither positive nor negative.
Some solved examples
|Properties of rational no.
1) If p / q is a rational no.and m is non- zero integer then
p / q = ( p x m) / ( q x m)
This ( p x m) / ( q x m) is rational no. equivalent to p / q.
2) If p / q is a rational number and m is non- zero integer then
p / q = ( p ÷ m) / ( q ÷ m)
1) Express 3 / 4 as a rational no. with denominator 36.
In order to express 3 / 4 as rational no. with denominator 36, we first find a number which when multiplied with 4 gives 36.
So, that number is 9. So multiply numerator and denominator both by 9.
3 / 4 = ( 3 x 9) / (4 x 9)
3 /4 = 27 / 36
2) Express -4 / 5 as rational no. with denominator -30.
In order to express -4 / 5 as rational no. with denominator - 30, we first find a number which when multiplied with 5 gives - 30.
So, that number is - 6. So multiply numerator and denominator both by - 6.
-4 / 5 = ( - 4 x – 6 ) / (5 x - 6 )
-4 / 5 = 24 / - 30
3) Express 42 / -63 as a rational no. of denominator 3.
In order to express 42 / -63 as rational no. with denominator 3, we first find a number which when divide with -63 gives 3.
So, that number is -21. So divide numerator and denominator both by - 21.
42 / - 63 = ( 42 ÷ - 21) / (- 63 ÷ -21)
42 / - 63 = -2 / 3
Lowest form of rational no. :
Every rational no. can be put in the lowest form by using the following steps :
1) Obtain the rational no. p / q .
2) Find the GCF or HCF
of p and q.
3) If m = 1 then p / q is the lowest form.
4) If m ≠ 1, then ( p ÷ m) / ( q ÷ m) is the lowest form of p / q.
Some solved example
1) Write in lowest form : i) 17 / 79 ii) -60 / 72
i) 17 / 79
As GCF of 17 and 79 is 1 so 17 / 79 is in the lowest form.
ii) -60 / 72
GCF of 60 and 72 is 12.
-60 ÷ 12 = - 5 and 72 ÷ 12 = 6.
∴ -60 / 72 = - 5 / 6.
• Representation of rational-number on number line
• Comparison of rational-number
• Addition rational-numbers
• Subtraction of rational-numbers
• Conversion of rational-numbers to decimal
• Irrational Numbers
Number system Page
7th grade math
8th grade math
Russia-Ukraine crisis update - 3rd Mar 2022
The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.