The absolute value of a real number is its numerical value without regard to its sign. In other words, it’s the distance of the number from zero on the number line.

Explanation: For example:

The absolute value of 5 is 5. The absolute value of -5 is also 5.

Mathematically, the absolute value of a number x is denoted as \$|x|\$ and is defined as:

\$|x| = x, if x ≥ 0\$
\$|x| = -x, if x < 0\$

Grouping symbols, also known as parentheses, brackets, and braces, are used in math to clarify the order of operations and group terms in an expression. They show which operations to perform first, ensuring correct calculations. Grouping symbols include:

Explanation: This image shows different types of symbols.

The Order of Operations is a set of rules used in math to solve expressions. The rules are as follows: first, solve inside parentheses, then solve any exponents, next, perform multiplication and division, and finally, perform addition and subtraction. Following these rules will help you solve expressions correctly.

Explanation: This image shows BODMAS stands for Brackets(or Parentheses) Orders(or Exponents and Roots, etc.) Division and Multiplication(from left to right) Addition and Subtraction(from left to right) This image shows PEMDAS stands for Parentheses Exponents Multiplication and Division(from left to right) Addition and Subtraction(from left to right)

The commutative Property states that the order of numbers added or multiplied does not affect the outcome. Thus, for addition, a + b = b + a, for multiplication, \$ a \times b = b \times a \$. In both cases, interchanging a and b does not affect the result.

Explanation: The image shows the commutative property: swapping the order of numbers doesn’t change the sum (addition) or product (multiplication).