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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| 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" |
|
| 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 |
| 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" |
| 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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