set 2

Grouping Symbols

Used to group parts of an expression or sentence.

Parentheses

( )

Brackets

[ ]

Braces

{ }

Syntax

Refers to the rules for combining symbols to form a meaningful mathematical statement. Just as English has grammar rules, mathematics has its own set of rules that must be followed to avoid nonsense.

Expressions

A combination of numbers, variables, and operators that represents a single value. ___ do NOT contain an equal sign.

Expressions

Example: 2x+5

Equations

A statement that two expressions are equal. An ___ always contains an equal sign (=).

Equations

Example: 2x+5=11

Inequalities

A statement that one expression is not equal to another. It uses symbols like

Inequalities

Example: 3y-2<7

PEMDAS

The order of operations, often remembered by the acronym ___, is a fundamental rule of mathematical syntax. It ensures everyone gets the same answer when evaluating an expression.

PEMDAS

Parentheses, Exponents, Multiplication or Division (from left to right), Addition or Subtraction (from left to right).

Commutative Rule

The order of numbers doesn’t change the result for addition and multiplication.

Commutative Rule

Addition: a+b=b+a / Multiplication: a×b=b×a

Associative Rule

The way you group numbers doesn’t change the result for addition and multiplication.

Associative Rule

Addition: (a+b)+c=a+(b+c) / Multiplication: (a×b)×c=a×(b×c)

Distributive Rule

This rule connects multiplication and addition/subtraction.

Distributive Rule

Example: a(b+c)=ab+ac

Variable

A letter that represents an unknown or changing numerical value. It’s a placeholder for a number.

Variable

Value can change depending on the problem or equation; represents an unknown.

Variable

Example: In the expression 2x+5, x is the ___. It could be any number. If x=3, the expression’s value is 11. If x=4, the value is 13.

Coefficient

The number that is multiplied by a variable. It’s the numerical factor in a term containing a variable.

Coefficient

Always a number; sits in front of the variable.

Coefficient

Example: In the expression 2x+5, the number 2 is the ___ of x. It tells us that the variable x is being multiplied by 2.

Coefficient

Note: If a variable is written without a number in front of it, the ___ is 1. For example, in the expression y+7, the ___ of y is 1.