## 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