# What Type of Number Will You Get?

This Web page is about the types of numbers you get as __solutions/correct answers__ to math problems depending on the arithmetic operation used. (Except *division;* out of all 4 arithmetic operations, division is the most unpredictable & tends to gives you random types of **quotients!**) For more information about number types, see the page entitled "Types of Numbers".

__You can select the 3 Different Pairs of Directly Opposite Number Types here:__

- Even Numbers & Odd Numbers
- Positive Numbers & Negative Numbers
- Real Numbers & Imaginary Numbers

## First, Even Numbers & Odd Numbers

## Even + Even = Even

## Odd + Odd = Even

## Even + Odd = Odd

(Addition is Commutative!)

## Even - Even = Even

## Odd - Odd = Even

## Even - Odd = Odd

## Odd - Even = Odd

## Even × Even = Even

## Odd × Odd = Odd

## Even × Odd = Even

(Multiplication is Commutative!)
## Positive Numbers & Negative Numbers

## Positve + Positive = Positive

## Negative + Negative = Negative

## Positive + Negative = Sign That's Greater In *Absolute Value* or Zero If They're *Additive Inverses*

(Addition is Commutative!)

## Positive - Positive = Positive or Zero If Both Numbers Are Equal or Negative If 2nd Number Is Greater In *Absolute Value*

## Negative - Negative = Negative or Zero If Both Numbers Are Equal or Positive If 2nd Number Is Greater In *Absolute Value*

## Positive - Negative = Positive

## Negative - Positive = Negative

## Positive × Positive = Positive

## Negative × Negative = Positive

## Positive × Negative = Negative

(Multiplication is Commutative!)
## Finally, Real Numbers & Imaginary Numbers

## Real + Real = Real

## Imaginary + Imaginary = Imaginary

## Real + Imaginary = Complex

(Addition is Commutative!)

## Real - Real = Real

## Imaginary - Imaginary = Imaginary

## Real - Imaginary = Complex

## Imaginary - Real = Complex

## Real × Real = Real

## Imaginary × Imaginary = Real

## Real × Imaginary = Imaginary

(Multiplication is Commutative!)
### Note: Imaginary numbers can flip positivity & negativity around in the multiplication of complex numbers!

In conclusion, these are **the only 3 different pairs of directly opposite number types** because with *indirectly opposite* types, the number type of the solution is __random!__ Multiplying an *irrational* number by an *irrational* number, for example, could give you either a *rational* product or an *irrational* product. *The square root of *2 multiplied by itself gives you **2,** which is *rational;* however, *the square root of *2 multiplied by *the square root of *3 = *the square root of *6, which is *irrational!* Also, *the square root of *2 + *the square root of *3 ≠ *the square root of* (2 + 3), which is 5; but yes, the sum of those 2 *irrational* numbers is also *irrational;* it's approximately equal to **π + .0046717164...** But adding 2 *irrational* numbers might give you a *rational* number! (*The square root of *2 + **(1 - ***the square root of *2) = **1!**)

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© Derek Cumberbatch