je one exam
valent rational numbers?
c)
- 1 and 22
irs of rational numbers:
Answers
Answer:
A number that can be expressed in the form p
q
, where p and q are
integers and q ≠ 0, is called a rational number.
• All integers and fractions are rational numbers.
• If the numerator and denominator of a rational number are multiplied
or divided by a non-zero integer, we get a rational number which is
said to be equivalent to the given rational number.
• Rational numbers are classified as positive, zero or negative rational
numbers. When the numerator and denominator both are positive
integers or both are negative integers, it is a positive rational number.
When either the numerator or the denominator is a negative integer,
it is a negative rational number.
• The number 0 is neither a positive nor a negative rational number.
• There are unlimited number of rational numbers between two rational
numbers.
• A rational number is said to be in the standard form, if its
denominator is a positive integer and the numerator and
denominator have no common factor other than 1.
• Two rational numbers with the same denominator can be added by
adding their numerators, keeping with the same denominator.
• Two rational numbers with different denominators are added by first
taking the LCM of the two denominators and then converting both
the rational numbers to their equivalent forms having the LCM as
the denominator and adding them as above.
• While subtracting two rational numbers, we add the additive inverse
of the rational number to be subtracted to the other rational number.
• Product of rational numbers = Product of numerators
Product of denominators
• The reciprocal of a non-zero rational number p
q
is q
p
.
• To divide one rational number by the other non-zero rational number,
we multiply the first rational number by the reciprocal of the other.
(B) Solved Examples
In Examples 1 to 4, there are four options, out of which one is correct.
Choose the correct one.
Example 1: Which of the following rational numbers is equivalent
to
2
3
?
(a)
3
2
(b)
4
9
(c)
4
6
(d)
9
4
Solution: Correct answer is (c).
Example 2: Which of the following rational numbers is in standard
form?
(a)
20
30 (b)
10
4
(c)
1
2
(d)
1
–3
Solution: Correct answer is (c).
Example 3: The sum of
3
2
−
and
1
2
is
(a) –1 (b) –2 (c) 4 (d) 3
Solution: Correct answer is (a).
Example 4: The value of
4 –1
–
3 3
− is
(a) – 2 (b) – 3 (c) 2 (d) –1
Solution: Correct answer is (d).
hope it helps you