Chap
1
Rational
Numbers
Some
Important Facts :-
1.
The numbers which can be expressed in the
form of p , when P/q and q both are natural numbers, are called fractions, like
2/5 , 7/3 etc. Here, p is numerator and
q is denominator
of fraction.
2.
If
the denominator of fraction is greater than its numerator then the fraction is
known as proper fraction, but if numerator is greater than its denominator then
the fraction is known as improper fraction.
- If the
numbers p and q in a fraction P/ Q have no common factor other
than 1, then P / Q is in
its simplest or lowest form. Suppose k is the other common factor of p and q,
then we take p = mk and q = nk, hence P/ Q = m x k = m/ n Here, p/n and m/n are said
to be equivalent fractions. nx k
4. (i) If the denominators of
fractions are not equal, then we make their numerator will be greater. For
example:
In 3/ 5 and 1 / 5 , 3 /5 is greater. i.e. 3/ 5 > 1/5 \ 3 > 1
(ii) If the denominators of fractions are not
equal, then we make their denominators
equal and compare them.
5. In fraction p /q , p and q are positive
integers. If we take p and q be any integers and q are positive than zero i.e.,
q ≠ 0, then p/q is known as rational number.
6.
Two rational numbers p/q and r/s are
said to be equivalent if p x s = q x r.
7. Every rational number can be
represented on the number line.
8. If p/q and r/s are two rational
numbers and q, s ≠ 0 then p/q > r/s if p x s > q x r
9. If p/q and
r/s are two rational numbers and q, s ≠ 0 then p/q < r/s if p x s < q x r
10. The
absolute value of a number is equal to or greater than the
number
itself. 