# Maths Number System

by Dasa . 08 Dec 2020

The test below has 118 basic questions in the number system, including real numbers, rational numbers, irrational numbers, integers, fractions, and decimals.

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## Properties of Numbers

### Closure

Property Operation Symbol Natural Numbers Whole Numbers Integers
Closure (A Sense of Conclusion)
Addition a+b = c If a & b are Natural numbers. c is also a Natural numbers Closure 2+3 = 5 If a & b are Whole numbers. c is also a Whole numbers Closure "2+3 = 5
0+3 = 3"
If a & b are Integers. c is also a Integer. Closure 2+3 = 5
0+3 = 3
Subtraction a-b = c "If a & b are Natural numbers.
c can be Natural numer or an Integers"
Not Closure 2-3 = -1 "If a & b are Whole numbers.
c can be a Whole numer or an Integer"
Not Closure "2-3 = -1
3-3 = 0
4-0 = 4"
"If a & b are Integers.
c is also a Integer."
Closure "2-3 = -1
3-3 = 0
4-0 = 4
-2-3 = -5"
Multiplication axb = c "If a & b are Natural numbers.
c is also a Natural numbers"
Closure 2x3 = 6 "If a & b are Whole numbers.
c is also a Whole numbers"
Closure "2x3 = 6
0x3 = 0"
"If a & b are Integers.
c is also an Integer."
Closure "2x3 = 6
0x3 = 0
-2x-3 = 6
-2x3 = -6"
Division a/b = c "If a & b are Natural numbers.
c can be a Fraction"
Not Closure 2÷3 = 2/3 "If a & b are Whole numbers.
c can be a Whole number, Fraction or Not defined"
Not Closure "2÷3 = 2/3
0÷2 = 0
3÷0 = Not defined"
"If a & b are Integers.
c can be a Integer, Fraction, Rational Number or Not defined"
Not Closure "2÷3 = 2/3
-2÷3 = - (2/3)
0÷2 = 0
3÷0 = Not defined"

### Commutative

Property Operation Symbol Result Example
Commutative (A relation to an exchange)
Addition a+b = b+a Commutative 2+3 = 3+2 = 5
0+2 = 2+0 = 2
Subtraction a-b ≠ b-a Not Commutative 2-3 ≠ 3-2
2-0 ≠ 0-2
Multiplication axb = bxa Commutative 2x3 = 3x2 = 6
0x2 = 2x0 = 0
Division a/b ≠ b/a Not Commutative 2÷3 ≠ 3/2

### Associative

Property Operation Symbol Result Example
Associative (A co-operative link between numbers)
Addition (a+b)+c = a+(b+c) Associative (2+3)+5 = 2+(3+5)
=> 5+5 = 2+8
=> 10 = 10"
Subtraction (a-b)-c ≠ a-(b-c) Not Associative (8-5)-2 = 8-(5-2)
=> 3-2 = 8-3
=> 1 ≠ 5"
Multiplication (axb)xc = ax(bxc) Associative (2x3)x5 = 2x(3x5)
=> 6x5 = 2x15
=> 30 = 30"
Division (a/b)/c = a/(b/c) Not Associative (16÷4)÷2 = 16÷(4÷2)
=> 4÷2 = 16÷2
=> 2 ≠ 8"

### Distributive

Property Operation Symbol Result Example
Distributive (The action of sharing)
Multiplication ax(b+c) = (axb)+(axc) Distributive 2x(3+5) = (2x3)+(2x5)
=> 6 + 10
=> 16

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