Numbers- Whole, Rational, Integers
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Transcript of Numbers- Whole, Rational, Integers
Project Work
Mathematics
TWO KIND OF NUMBERS
Rational Numbers Irrational Numbers
RATIONAL NUMBERSA rational number is a real number that can be written as a ratio of two integers.
A rational number written in decimal form is terminating or repeating.
EXAMPLES OF RATIONAL NUMBERS-81.3333…- 3/4161/23.56
IRRATIONAL NUMBERSAn irrational number is a number that cannot be written as a ratio of two integers.
Irrational numbers written as decimals are non-terminating and non-repeating.
EXAMPLES OF IRRATIONAL NUMBERS
Square roots of non-perfect “squares”
Pi
π√17
Integers One of the subsets of
rational numbers
WHAT ARE INTEGERS?Integers are the whole numbers and their opposites.
Examples of integers are i. 6ii. -12iii. 0iv. 186v. -934
INTEGERSIntegers are rational numbers because they can be written as fraction with 1 as the denominator
WHOLE NUMBERSWhole numbers one of the subsets of rational numbers
WHAT ARE WHOLE NUMBERS?
Whole numbers are rational numbers because they can be written as fraction with 1 as the denominator
Examples Of whole numbers:i. 1ii. 2iii. 3
WHOLE NUMBERSWhole numbers are rational numbers because they can be written as fraction with 1 as the denominator
COMMUTATIVITYWhole NumbersOperation Numbers Remarks
Addition 0+7=7+0=7,2+3=3+2=5For any two whole numbers a and b,a+b = b+a
Addition is commutative.
Subtraction 4-6 ≠ 6-4 Subtraction is not commutative
Multiplication 2×6 = 6×2 = 12,4×5 = 5×4 = 20
Multiplication is commutative
Division 7÷3 ≠ 3÷7 Division is not commutative
COMMUTATIVITYIntegersOperation Numbers Remarks
Addition -6+5 = (-1)-7+(-5) = (-12)
Addition is commutative
Subtraction 7-5 = 25-7= (-2)
Subtraction is not commutative
Division 5÷8 = 8÷5=
Division is not commutative
Multiplication 5×8 = 40(-5) ×(-8)= 40
Multiplication is commutative
COMMUTATIVITY Rational Numbers Addition-i. +()= =
Subtraction-
We find that subtraction is not commutative.
COMMUTATIVITY Multiplication-
So, we find that multiplication is commutative.
Division-
So, we find that division is not commutative.
ASSOCIATIVITY Whole numbers-Operation Numbers Remarks
Addition 7+(2+5)=(7+2)+5LHS= 7+(7)=14RHS= (9)+5=14
So, we find addition is associative with whole numbers.
Subtraction 8-(9-11)=11-(9-8)LHS= 8-2=6RHS= 11-1=10
So, we find subtraction is associative with whole numbers.
Division 3÷(2÷9)≠ 9÷(3÷2)LHS= 3÷[]=RHS= 9÷[=
So, we find division is associative with whole numbers.
Multiplication
7×(2×5)=(7×2) ×5LHS= 7×10=70RHS= 14×5=70
So, we find multiplication is associative with whole numbers.
ASSOCIATIVITY IntegersOperation
Numbers Remarks
Addition (-2)+[3+(-4)]=[(-2)+3]+(-4)LHS=(-2)+(-1)=(-3)RHS=1+(-4)=(-3)
Addition is associative.
Subtraction
5-(7-3)= (5-7)-3LHS= 5-10= (-5)RHS= (-2)-3= (-5)
Subtraction is not associative.
Division [(-10)2](-5)=(-10)[2(-5)]LHS=(-5)(-5)= (-1)RHS= (-10)=(-25)
Division is not associative.
Multiplication
5×[(-7) ×(-8)]=[5((-7)]×(-8)LHS=5×56=280RHS=(-35)×(-8)=280
Multiplication is associative.
ASSOCIATIVITY Rational numbers- Addition-
Addition is associative with rational numbers.
Subtraction-
[ Subtraction is associative with rational
numbers.
ASSOCIATIVITY Division-
LHS= = =
Division is associative with rational number.
ASSOCIATIVITY Multiplication-
( Multiplication is associative with
rational numbers.
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