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Ratno

This document discusses rational numbers. It begins by recapping natural numbers, whole numbers, and integers. It then defines rational numbers and discusses their standard form and absolute value. Some key properties of rational numbers are also defined, including closure property, commutative property, associative property, distributive property, additive identity, additive inverse, multiplicative inverse, and multiplicative identity. Examples are provided to illustrate these concepts and properties.

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Kartik chaudhary
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106 views26 pages

Ratno

This document discusses rational numbers. It begins by recapping natural numbers, whole numbers, and integers. It then defines rational numbers and discusses their standard form and absolute value. Some key properties of rational numbers are also defined, including closure property, commutative property, associative property, distributive property, additive identity, additive inverse, multiplicative inverse, and multiplicative identity. Examples are provided to illustrate these concepts and properties.

Uploaded by

Kartik chaudhary
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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CLASS

VIII
Concepts to be covered in this session-
• Recap Natural Numbers, Whole Numbers and
Integers
• Define Rational Numbers, Standard Form and
Absolute Value of Rational Numbers
• Properties of Rational Numbers-
❑ Closure Property
❑ Associative Property
❑ Commutative Property
❑ Additive Identity
❑ Multiplicative Identity
❑ Reciprocal
❑ Additive Inverse
RECAP
• ____________ are the numbers used for
counting and ordering.
• The smallest natural number is ________.
• The set of numbers starting from 0,1,2…..
and so on are called the ___________.
• The smallest whole number is __________.
• All natural numbers along with 0 form a
group of numbers called _____________.
• __________ includes positive and negative
natural numbers along with zero.
Answers
• Natural Numbers
• 1
• Whole Numbers
• 0
• Whole Numbers
• Integers
The Number Family

INTEGERS …-2,-1,0,1,2….

WHOLE NUMBERS
0,1,2,3……

NATURAL
NUMBERS
1,2,3….
Number Set Symbols
N – Natural/Counting Numbers
W – Whole Numbers
Z – Integers
Q – Rational Numbers
RATIONAL NUMBERS- 2, 0.4, -7/3

INTEGERS …-2,-1,0,1,2….

WHOLE NUMBERS
0,1,2,3……

NATURAL
NUMBERS
1,2,3….
1
= 0.333
3
HOTS
❖A fraction is always a rational number
whereas a rational number may or may not
be a fraction.
❖
−2 2
or are not fractions
3 −3
Why?
Fractions are part of a whole. They are of the
form a/b, where a and b belong to Whole
Numbers.
ABSOLUTE VALUE OF A RATIONAL NUMBER
❖Absolute value of a rational number is its
numerical value with no regards to its sign.

❖ 3 3
= ,
7 7
❖
3 3
− =
7 7
STANDARD FORM
• A rational number pis said to be in
standard form if q
(i) The denominator q is positive
(ii) p and q have no common factor other than
1 i.e. they are co-primes.
12 2
=
−18 −3
To write in standard form we make
denominator as positive.
2  ( −1) −2
=
−3  ( −1) 3
Properties of Rational Numbers
•
Closure Property
Commutative Property
Associative Property
Associative Property for Multiplication and
Division
DISTRIBUTIVE PROPERTY OF
MULTIPLICATION OVER ADDITION

p r u  p r  p u
 +  =    +   
q s v q s q v
Additive inverse
Additive Identity
• Additive Identity is that number when
added to a rational number, the sum is the
rational number itself.
• p/q + 0= 0 + p/q = p/q
Multiplicative inverse

• If p/q is a rational number then there exist a


number q/p such that
• p/q x q/p = 1
• p/q is called the multiplicative inverse or
reciprocal of p/q.

• Which number does not have a reciprocal?


0
•
p  p  p
  1  = =  1 
q  q  q

Where 1 is called the multiplicative identity .


p q  q p
•   =1=   
 q p p q
q
where is the multiplicative inverse
p
p
(or reciprocal) of
q
For for queries online
Contact:Anjna goswami
8057660066

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