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Grade 6 | Maths | Integers, Integers, Olympiad, CBSE, ICSE, Maths Olympiad, Science Olympiad, English Olympiad
Integers: All number whether it is positive, negative including zero is called Integers.
Note* Zero is an integer which is neither positive or negative"
There is no greatest or smallest integer.
Addition of Integers:
i)Having the same sign:
i)if both are having the +ive sign, add the number and put the +ive sign.
ii)if both are having -ve sign, add the number and put -ve sign.
2)Having the opposite sign: If the integers are having opposite signs we just subtract the number and put the sign of greater no.
Properties of Addition:
a)Closure Property: Sum of two integers is always an integer.
In the above case, all numbers are integers.
b)Commutative Property: If we add two integers but if we change the order of no answer will be the same.
Example: 8+9=9+8
17=17
c) Associative Property: If we change the order of three number, the addition will remain unchanged.
Example: a+(b+c)=(a+b)+c
2+(3+5)=(2+3)+5
10=10
d) Additive Identity: When we add 0 to any number ,addition remains same .In this case 0 is the additive identity.
Example: a+0=a
4+0=4
e) Additive Inverse: When we add two same number with an opposite sign, the answer comes to zero.
Exampl9+(-9)=0
Subtraction of Integers:
Subtraction is the inverse operation of integers.
Properties of Subtraction of Integers:
a) Closure Property: Difference of two integers is always an integer.
Example: 6-4=2
in the above example, all are integers.
b) Commutative Property: This property is not followed in subtraction.
Example 6-5 is not equal to 5-6.
c) Associatative Property: This property is not followed in subtraction.
Example: 6-(5-8) is equal to (6-5)-8.
Multiplication of Integers:
Multiplication means to calculate the product of two numbers but in multiplication sign plays an important role.
i) If the sign of both numbers is same(++,--), the sign of product is positive.
ii) If the sign of both numbers(-+,+-), the sign of product is negative.
Properties of Multiplication of Integers:
a) Closure Property: Product of two integers is also an integer.
Example: 7X8=72 all are integers.
b) Commutative Property: Product of two numbers is the same if we change the order of number.
Example: 14X5=5X14
70=70
c) Associatative Property: If we have three numbers a,b,c
aX(bXc)=(aXb)Xc
Example: 2X(3X4)=(2X3)X4
2X12=6X4
24=24
d) Distributive Property law of multiplication over Addition: This law is a combination of multiplication and Addition.
aX(b+c)=aXb+axc
Example: 5X(6+8)=5X6+5X8
5X14=30+40
70=70
c)Multiplicative Property: If 1 is multiplied by any number answer will be that number only.
aX1=a
Example: 25X1=25
d)Multiplicative Inverse: When integers is multiplied by its reciprocal then the answer will be 1. This property is known as a multiplicative inverse.
Example: Multiplicative inverse of 25=1/25.
e)Property of Zero: Any integer multiplied by zero gives an answer equal to zero.
Division of Integers:
The division is an inverse operation of multiplication
i) If having the same sign: Both having be positive or negative sign, answer will be positive.
ii) Having the opposite sign: If sign are opposite (+ and - or - and +), then answer will be negative.
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