Are you one of those candidates looking eagerly to learn about the concept of Integers? If yes, you must check this page to know the complete details about Integers. Integers is a basic and important concept that lays a stronger foundation for your maths. Know definition, rules, numbers, solved questions, symbols, etc.\u00a0 Go through the below sections to find various methods and formulae.<\/p>\n
The integer word is derived from the Latin word “Integer” which represents the whole. Integers are the positive, negative numbers, or zero. Integer values cannot be in decimals, fractions, percents, and we can perform various operations(arithmetic operations) like subtraction, addition, multiplication, division, etc. Examples of integers are 1,2,3,-4,-5, etc.\u00a0 Integers also include various sets like<\/p>\n
Integers also include various sets like zero, whole numbers, natural numbers, additive inverses, etc. These are the subset of real numbers.
\nExample of integer set: -5,-3, -1, 0, 2, 5<\/p>\n
As integers contain various numbers and sets and are the subset of real numbers, they are represented with the letter “Z”.<\/p>\n
Example:<\/strong> Types of numbers in Integers<\/strong><\/p>\n While adding 2 positive or negative integers(with the same sign), add the absolute values and note down the sum of those numbers with the sign provided with numbers.<\/p>\n Example:<\/strong><\/p>\n (+6)+(+5) = +11 While adding 2 integers with a different sign, subtract the absolute values and note down the difference of those numbers with the sign provided with numbers.<\/p>\n Example:<\/strong><\/p>\n (-5)+(+2)= -3 While subtracting we follow the rules of addition but change the 2nd number which is being subtracted.<\/p>\n Example:<\/strong><\/p>\n (-4)+(-3)= (-4)-(+3) = -11 The rule is simple while dividing and multiplying 2 integer numbers.<\/p>\n Example:<\/strong><\/p>\n (+3)*(-4) = -12 There are 7 properties of integers. The major properties are<\/p>\n 1. Associative Property This property refers to grouping and rules can be applied for addition and multiplication.<\/p>\n Associative Property of Addition<\/strong><\/p>\n Associative property enables the special feature of grouping the numbers in your own way and still, you get the same answer.<\/p>\n (a+b)+c = a+(b+c)<\/strong><\/p>\n Example: <\/strong><\/p>\n (-4+2)+3= -2+(3+4)<\/p>\n In the above example, if we consider the first equation you can solve it in either way i.e., First you take the difference of 4 and 2 and then add 3 to it or you can first add 2 and 3 and then subtract 4 from it. In both ways, you get a constant answer.<\/p>\n Associative Property of Multiplication<\/strong><\/p>\n This property also refers to the same as the addition property. In whatever way you group numbers, you still get the same answer.<\/p>\n (ab)c= a(bc)<\/strong><\/p>\n Example: <\/strong><\/p>\n -2(4)*3=-2(4*3)<\/p>\n In the above example, you can solve it 2 ways and still find the same answer. First, you can multiply 2,4 and then multiply that with 3 or you can first multiply 4,3 and then multiply it with 4.<\/p>\n The distributive property is used when the expression involving addition is then multiplied by a number. This property tells us that we can multiply first and then add or add first and multiply then. In both ways, the multiplication is distributed for all the terms in parentheses.<\/p>\n a(b+c) = ab+ac<\/strong><\/p>\n Example:<\/strong><\/p>\n -4(2+3)= (-4*2)+(-4*3)<\/p>\n In the above example, we can first add 2 and 3, then multiply it with 4 or we can multiply 4 with 2 and 3 separately and then add it, still you get the same answer.<\/p>\n Closure property for addition or subtraction states that the sum or difference of any 2 integers will be an integer value.<\/p>\n a + b = integer<\/strong> Example: <\/strong><\/p>\n 6-3= 3 The closure property for multiplication also states that the product of any two integer numbers is an integer number.<\/p>\n Example: <\/strong><\/p>\n 5*5=25 The closure property for division does not hold true that the division of two integers is an integer value.<\/p>\n Example:<\/strong><\/p>\n (-3)\/(-12)=1\/4, which is not an integer<\/p>\n The commutative property for addition states that when two integer numbers undergo swapping, the result remains unchanged.<\/p>\n a+b=b+a<\/strong> Example:<\/strong><\/p>\n 28+5+43=5+43+28=76<\/p>\n The commutative property for multiplication also states the same that if two integers are swapped, the result remains unchanged.<\/p>\n Example:<\/strong><\/p>\n 5*4*2=2*4*5=40<\/p>\n The commutative property doesn’t hold true for subtraction.<\/p>\n Identity Property states that any number that is added with zero will give the same number. Zero is called additive identity.<\/p>\n a+0=a<\/strong> Example:<\/strong><\/p>\n 5+0=5<\/p>\n The identity property for multiplication also states the same that the integer number multiplied by 1 will give the same number. 1 is called the additive identity.<\/p>\n Example:<\/strong><\/p>\n 5*1=5<\/p>\n Consider “a” as an integer, then as per the multiplicative inverse property of integers,<\/p>\n a*(1\/a)=1<\/p>\n Here, 1\/a is the multiplicative inverse of integer a.<\/p>\n Consider “a” as an integer, then as per the additive inverse property of integers,<\/p>\n a+(-a)= 0<\/p>\n Here, “-a” is the additive inverse of the integer a<\/p>\n Integers have many real-life applications. We use them in different situations to quantify things. For example, to check the temperature, positive numbers are used to indicate the temperature above zero and negative numbers are used to indicate the temperature below zero. Integers are also mainly used in real-life situations like hockey, football tournaments, rating for a movie, bank credits and debits, etc.<\/p>\n We have mentioned all the important information about Integers. Hope, the above-provided details will help you in your preparation. Stay tuned to our site to get instant updates on various mathematical concepts.<\/p>\n","protected":false},"excerpt":{"rendered":" Are you one of those candidates looking eagerly to learn about the concept of Integers? If yes, you must check this page to know the complete details about Integers. Integers is a basic and important concept that lays a stronger foundation for your maths. 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\nZ= {5,-3, -1, 0, 2, 5}<\/p>\n\n
Integers Rules<\/h3>\n
\n
Addition of Integer Numbers<\/h3>\n
\n(-5)+(-5)= -10<\/p>\n
\n(+6)+(-3)= -3<\/p>\nSubtraction of Integer Numbers<\/h3>\n
\n(+5)-(+4)=(+5)+(-4)= +1<\/p>\nDivision and Multiplication of Integer Numbers<\/h3>\n
\n
\n(+4)*(+3) = 12
\n(+16)\/(+4) = +4
\n(-6)\/(+2) = -3<\/p>\nInteger Properties<\/h3>\n
\n2. Distributive Property
\n3. Closure Property
\n4. Commutative Property
\n5. Identity Property
\n6. Multiplicative Inverse Property
\n7. Additive Inverse Property<\/p>\n1. Associative Property<\/h4>\n
2. Distributive Property<\/h4>\n
3. Closure Property<\/h4>\n
\na x b = integer<\/strong><\/p>\n
\n6+(-3)= 3<\/p>\n
\n(-5)*(-5)=25<\/p>\n4. Commutative Property<\/h4>\n
\na*b=b*a<\/strong><\/p>\n5. Identity Property<\/h4>\n
\na*1=a<\/strong><\/p>\n6. Multiplicative Inverse Property<\/h4>\n
7. Additive Inverse Property<\/h4>\n
Applications of Integers in Real Life<\/h3>\n