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Grade 7 | Maths | Addition and Subtraction of Integers, Integers, Olympiad, CBSE, ICSE, Maths Olympiad, Science Olympiad, English Olympiad
The numbers which can be written as non-fractions are called integers. They include all natural numbers, zero and negative numbers.
E.g. -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 etc.
Integers which carry negative sign are called negative integers like -1, -5, -8 etc.
Integers which do not carry negative sign are called positive integers except for zero. E.g. 2, 8, 21 etc.
Integers extend on both sides of a number line.
Important points:
Rules for the addition of integers:
Properties of Addition of Integers:
1) Closure Property: The sum of two integers is always an integer. Thus we can say that integers are closed under addition.
eg 2 + 3 = 5, here 2 and 3 are an integer and 5 is also an integer.
2) Commutative Property: If we add two integers and then we change the order of the numbers but the sum will remain the same. If P and Q are two integers then P + Q = Q + P.
eg: i) 8+9 = 9+8
17 = 17
ii) -7+(-12) = -12+(-7)
-19 = -19
Associative Property: If we change the order of number the sum remains unchanged.
eg: a+(b+c)=(a+b)+c
7+(6+2)=(7+6)+2
7+8=13+2
15=15
4)Additive Identity:When we added 0 to any integer,sum remains same.In this case 0 is the additive Identity.
eg: a+0=a
12+0=12
5)Additive Inverse:When we add the same number with opposite sign,answer comes to zero.
Same number with opposite sign are called Additive Inverse.
Subtraction of Integer:
Subtraction is inverse operation of addition of Integers.
Properties of Subtraction of Integers:
1)Closure Property:Difference of two integer is always an integer.
All are integer in above example.
2)Commutative Property:This property is not followed in subtraction.
Eg: 5-4 is not equal to 4-5
3)Associative Property:This property is not followed in subtraction.
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