Many students are afraid of math but this fear in them is because they haven’t understood the basics of math. When they will join the math program of Cuemath they will start loving math. It is an online platform that easily clears the math concepts. In the below-given article, we have explained the properties of integer.
What are integers in mathematics?
The term ‘integer’ in mathematics was adapted from a Latin word that means intact or whole. Integers are just like whole numbers except for the fact that they also include negative numbers. Integers are the numbers having no decimal or fraction part. In other words, integer includes positive numbers, negative numbers, and zero but can’t be in the form of decimal and fraction. The symbol by which integers are indicated is ‘Z’. The integers are used to perform different arithmetic operations such as addition, subtraction, multiplication, and division. The examples of integers are: Z = -6, -5, -4, 0, 2, 6, 11, 4044 and so on.
What are the properties of integers?
- Closure Property:
This property under addition, subtraction, and multiplication state that the sum, difference, and product of any two integers, say x and y will be integer only.
For example, in case of addition, 5 + (-6) = -1;
in case of subtraction, 4 – 2 = 2;
in case of multiplication, -6 × -8 = 48
The results are integer in all cases.
This property doesn’t hold any good under the division of any two integers.
For example, (-4) / (-8) = ½ , the result is not integer.
- Commutative Property:
According to this property, swapping the positions of integers under addition and multiplication doesn’t matter, the results will be the same.
For example,
- a + b = b + a = (-3) + 4 = 1 = 4 + (-3)
- a × b = b × a = 2 × (-6) = -12 = (-6) × 2
But under subtraction and division, swapping the positions of integers changes the result.
For example,
- a – b ≠ b – a = 5 – (-7) = 12, (-7) – 5 = -12
5 – (-7) ≠ (-7) – 5
- a / b ≠ b /a = 12 / 4 = 3, 4 / 12 = 1/3
12 / 4 ≠ 4 / 12
- Associative Property:
According to this property, under addition and multiplication, the way of grouping integers doesn’t matter. The results will be the same. But it is not the case in subtraction and division.
For example,
- a + (b + c) = (a + b) + c = 2 + (3 + 5) = 10 = (2 + 3) + 5
- a × (b × c) = (a × b) × c = 2 × (3 × 5) = 30 = (2 × 3) × 5
- a – (b – c) ≠ (a – b) – c = 2 – (3 – (-5)) = -6, (2 – 3) – (-5) = 4
2 – (3 – (-5)) ≠ (2 – 3) – (-5)
- Distributive Property:
This property explains the ability of distribution of operation over the other mathematical operation within a bracket. For instance, it can be the distributive property of multiplication over addition or multiplication over subtraction.
For example,
- a × (b + c) = a × b + b × c
- a × (b – c) = a × b – b × c
- Identity Property:
According to the additive identity property when any integer is added to zero then the result will be integer itself. And multiplicative identity property states that any integer is multiplied with 1 then the result will be integer itself; when an integer is multiplied by zero, then the result will be zero; and when an integer is multiplied by -1 then the result will be opposite of integer.
For example,
- a + 0 = a
- a × 1 = a
- a × 0 = 0
- a × -1 = -a
An integer involves four operations and five properties. Go through the article and understand integers in the best possible way. Many students are afraid of math but this fear in them is because they haven’t understood the basics of math. When they will join the math program of Cuemath they will start loving math.