This document discusses rational and irrational numbers. It defines rational numbers as numbers that can be written as p/q where p and q are integers and q is not equal to 0. Rational numbers include fractions, integers, and natural numbers. The document describes the different types of rational numbers such as positive, negative, and in standard form. It also discusses how to perform operations like addition, subtraction, multiplication, and division on rational numbers. Irrational numbers are defined as real numbers that cannot be expressed as a ratio of integers like the roots of prime numbers or pi.

1. HOLIDAY HOMEWORK
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SUBMITTED BY-
LAKSHMI SINGH
SUBMITTED TO-

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3. RATIONAL NUMBERS
 A rational number is a number that can be written in the form p/q , where
p and q are integers and q is not equal to 0. EXAMPLES- 2/5, -3/4
 The collection of numbers in the form of p/q, where q ≠ 0, is represented
by Q.
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Rational numbers include natural numbers, whole
numbers, integers and all negative and positive
fractions.

4. TYPES OF RATIONAL NUMBERS
Positive rational number
Rational number is positive if its numerator and denominator are both
either positive integers or negative integers. Eg : 2/5 , -8/-5.
Negative rational number
If either the numerator or the denominator of a rational number is a
negative integer ,then the rational number is called a negative rational
number. Eg: -2/5
Standard form
A rational number is said to be in its standard form if its numerator and
denominator have no common factor other than 1,and its denominator is
a positive integer . Eg: 4/7
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5. 5Representation of Rational Numbers on
the Number Line
To express rational numbers appropriately on
the number line, divide each unit length into as
many number of equal parts as the denominator
of the rational number and then mark the given
number on the number line.

6. OPERATION ON RATIONAL NUMBERS
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1. ADDITION OF RATIONAL NUMBERS
To add rational numbers that have a common denominator, we add the
numerators, but we do not add the denominators
NOTE: To add rational numbers that have a common denominator, we add the
numerators, but we do not add the denominators

7. 2. SUBTRACTION OF RATIONAL NUMBERS
Subtraction is the inverse operation of addition. To subtract rational numbers that
have a common denominator, we subtract the numerator, but we do not subtract
the denominators.
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8. 3. MULTIPLYING TWO RATIONAL NUMBERS
To multiply two rational numbers, we multiply the numerators to get the new
numerator and multiply the denominators to get the new denominator
4. DIVISION OF TWO RATIONAL NUMBERS
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9. IRRATIONAL NUMBERS
 An irrational number is any real number that cannot be expressed as a
ratio a/b, where a and b are integers, with b non-zero, and therefore
not a rational number.
 All numbers which cannot be written as an integer upon integer where the
denominator is zero and both integers are co-primes are irrational numbers.
 They are non - terminating non-repeating decimal expansions.
 The roots of prime number are irrational.
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10. EXAMPLES OF IRRATIONAL NUMBERS
 𝜋 = 3.1415926535897932384626433
 e= 2.71828182845904523536
 2 =1.41421356237309504
 3 =1.732050807568877293527
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