Natural numbers

• All numbers starting from 1 upwards. e.g., 1, 2, 3, 4, .....

Whole numbers

• Includes all Natural numbers, plus 0. e.g., 0, 1, 2, 3, 4, .....

Intergers

• All whole numbers, plus negative numbers. e.g., ..., -2, -1, 0, 1, 2, ...
  

Rational numbers

• All intergers, plus fractions and decimals. However, fractions must be made up of intergers and the denominator should not be zero (0).

Irrational numbers

• Numbers that cannot be represented as simple fractions. e.g., √2, √5, π = 3.14..., e = 2. 718281.., Phi = 1,618033.., i = √-1, etc. All rational numbers are not Irrational numbers.

Real numbers

• All Rational and Irrational numbers.

Even Numbers

• Even numbers are numbers that give you an Interger (All numbers including negative and positive numbers, and zero (0), no fractions. E.g., ...-3, -2, -1, 0, 1, 2, 3...), when divided by 2. for example, ...-6, -4, -2, 0, 2, 4, 6, ...

Odd numbers

• Numbers that does not give you an interger when divided by 2. E.g., 1, 3, 5, 6, ...

Adding Even and Odd Numbers

• EVEN + EVEN = EVEN
  E.g., 4 + 4 = 8
  6 + 6 = 12
  EVEN + ODD = ODD
  3 + 4 = 7
  17 + 24 = 41
  ODD + ODD = EVEN
  3 + 3 = 6
  13 + 13 = 26
  

Multiplying Even and Odd numbers

• EVEN x EVEN = EVEN
  2 x 2 = 4
  12 x 12 = 144
  ODD x EVEN = EVEN
  3 x 4 = 12
  9 X 10 = 90
  ODD x ODD = ODD
  3 x 3 = 9
  15 x 15 = 225
  

Multiplying intergers with the same sign

• The Product (The number you get when you multiply numbers together.), should have a positive sign. e.g.,
  -3 x -3 = 9
  3 x 3 = 9
  

Multiplying intergers with different signs

• The product should is always negative. E.g.,
  -3 x 3 = -9
  -5 x 5 = -25
  

Diving intergers with the same sign

• The Quotient (The number you get when you diving numbers together.), is always positive, just like when multiplying. E.g.,
  -3 ÷ -3 = 1
  10 ÷ 2 = 5
  

Diving intergers with different signs

• The quotient is always negative, just like when multiplying. E.g.,
  -3 ÷ 3 = -1
  10 ÷ -2 = -5
  

Adding Intergers

If the signs are the same

• Add the absolute (A number that is neither negative or positive), values and the sum should therefore have the sign of both values.
  5 + 5 = ?
• Absolute values are 5 and 5, the Sum (The number you get when you add numbers together.) of that is 10 and they both positive(+)
  Therefore, the final answer is 10.
  -3 + (-7) = ?
• absolute values are 3 and 7, the sum of that is 10 and they both negative(-)
  Therefore, the final answer is -10.

If the signs are different

• Substract the smaller absolute value from the greater absolute value and the difference should carry the sign of the greater value.
  5 + (-3) = ?
  
• absolute values are 5 and 3, 3 is smaller than 5, therefore substract 3 from 5 ( 5 - 3 = 2).
  Since 5 is positive, the difference (The number you get when you substract numbers together.), is therefore also positive (+2).
  
  3 + (-5) = ?
• absolute values are 5 and 3, 3 is smaller than 5, therefore substract 3 from 5 ( 5 - 3 = 2).
  Since 5 is negative, the difference is therefore also negative (-2).

Substracting Intergers

When substracting intergers with different signs, having the negative interger on the right.

• Add the absolute values and the sum should be positive e.g.:
  5 - (-3) = ?

absolute values are 5 and 3, the sum of that is 8 and the value on the left is positive(+)
Therefore, the final answer is +8.

Substracting intergers with different signs, having the negative interger on the left.

• Add the absolute values and the sum should be negative e.g.:
  -3 - (+5) = ?
  
• Simply, add absolute values (5 and 3), the sum of that is 8 and the value on the left is negative(-)
  Therefore, the final answer is -8.
  

When substracting intergers with same signs, having the greater interger on the left.

• Substract the smaller absolute value from the greater absolute value and the difference should be negative.
  -5 - (-3) = ?
  
• absolute values are 5 and 3, 3 is smaller than 5, therefore substract 3 from 5 ( 5 - 3 = 2).
  S, the difference is therefore negative (-2).
  
  

When substracting intergers with same signs, having the greater interger on the right.

• Substract the smaller absolute value from the greater absolute value and the difference should be positive.
  -3 - (-5) = ?
• absolute values are 5 and 3, 3 is smaller than 5, therefore substract 3 from 5 ( 5 - 3 = 2).
  The difference is therefore also positive (+2).