## Abridged Glossary of Terms

Absolute value
The absolute value of a number is the number's value if it were positive (the number's distance from zero on the real number line). For example, the absolute value of -4 is 4. The absolute value of 4 is also 4.

To indicate the absolute value of a variable, we put a vertical line on both sides of the variable. For example, ``|x|`` means the absolute value of ``x``. If ``x = 5`` or ``x = -5``, the value of ``|x|`` will be 5.

Base
In the expression ``x^y``, ``x`` is the *base* and ``y`` is the *exponent*.

Commutative property
A math operation (such as multiplication) is *commutative* if reversing the order of the input numbers, called *operands*, doesn't change the result. For example, ``5 \times 2 = 2 \times 5``.

Of the four basic arithmetic operations (addition, subtraction, multiplication, and division), multiplication and addition are commutative, and subtraction and division are not.

Examples:

- Multiplication (commutative): ``2 \times 3 = 3 \times 2``
- Addition (commutative): ``2+3 = 3+2``
- Division (non-commutative): ``3 \div 2 \ne 2 \div 3``
- Subtraction (non-commutative): ``3-2 \ne 2-3``

Distributive property
Distributive describes a relation between one math operation and another. We say that multiplication is *distributive over addition* because when we are multiplying a value with the sum of some other values (for example ``5 \times (2+4)``), we can *distribute* the multiplication to the various parts of the addition:
```5 \times (2+4) = (5 \times 2) + (5 \times 4) ```

Multiplicative inverse
A number's *multiplicative inverse* or *reciprocal* is equal to 1 divided by the number: the reciprocal of ``x`` is ``1 \over{x}``.

If you multiply a number by its reciprocal, the result will always be 1. Example: ``4 \times \frac{1}{4} = 1`` Or: ``\frac{1}{3} \times 3 = 1``.

If a number is negative, its reciprocal will be negative; if it is positive, its reciprocal will be positive too.

If a number's *absolute value* is greater than 1, the absolute value of its reciprocal will always be between 0 and 1, and vice versa.

For fractions, the reciprocal is just the reverse fraction. For example, the reciprocal of ``2\over{3}`` is ``3\over{2}``.

The reciprocal of a number can also be written as an exponent: ``n^{-1} = \frac{n}{1}``

*Note: these rules apply consistently to real number only*