Order of Operations

This page covers the essential concept of order of operations, which provides the rules for simplifying expressions with multiple steps.

The order of operations is represented by the acronym PEMDAS:

1. Parentheses
2. Exponents
3. Multiplication and Division (left to right)
4. Addition and Subtraction (left to right)

Definition: Order of operations refers to the rules that determine the sequence in which mathematical operations should be performed when simplifying expressions.

Vocabulary:

• Base: The number being multiplied in an exponent expression
• Exponent: The number indicating how many times to multiply the base
• Square root: A value that, when multiplied by itself, gives the number under the root
• Cube root: A value that, when multiplied by itself three times, gives the number under the root
• Absolute value: The distance between a number and zero on a number line

Example: Simplify 2$3 x 4 - 5$ + 6 x 10 + 4 using the order of operations

Evaluating Algebraic Expressions

This page focuses on the process of evaluating algebraic expressions by substituting values for variables and following the order of operations.

Steps to evaluate an algebraic expression:

1. Replace each variable with the given value (use parentheses)
2. Multiply when a variable is next to a number
3. Use the order of operations to simplify the expression

Definition: An algebraic expression is a mathematical sentence containing variables, numbers, and operations.

Vocabulary:

• Substitute: Replace a variable with a defined number
• Term: A number, variable, or number multiplied by variable$s$
• Constant: A fixed value without a variable being multiplied with it
• Coefficient: A number used to multiply a variable
• Like terms: Terms with the same variables and exponents

Example: Evaluate 3x² - 7 when x = 2

Simplifying Algebraic Expressions and Applications

This final page covers techniques for simplifying algebraic expressions, including combining like terms and using the distributive property. It also introduces geometry applications and translating word problems into expressions.

Steps to simplify expressions:

1. Distribute (if necessary)
2. Combine like terms

The distributive property states that multiplying a number by a group of numbers added together gives the same result as doing each multiplication separately.

Example: 4$2x + 1$ = 4(2x) + 4(1) = 8x + 4

Geometry application: To find the perimeter of a shape, add up the lengths of all sides.

Translating word problems into expressions:

• Addition: sum, total, all together, plus, increase, more than
• Subtraction: minus, difference, fewer, take away, decrease, less than
• Multiplication: product, times, per, each
• Division: quotient, average, per, each

Highlight: When simplifying expressions, remember to only combine like terms and keep the variables and exponents unchanged.

Vocabulary: Translate in mathematics means expressing a word problem or situation in mathematical language.

Integer Rules

This page introduces the fundamental rules of integers for addition, subtraction, multiplication, and division. Understanding these rules is crucial for working with positive and negative numbers in algebra.

Addition Rules for Integers:

• For same signs, add the numbers and keep the sign
• For different signs, subtract the numbers and keep the sign of the larger number

Subtraction Rule for Integers:

• Use the "keep-change-change" method: keep the first number, change subtraction to addition, and change the sign of the second number

Multiplication and Division Rules for Integers:

• Same signs result in a positive answer
• Different signs result in a negative answer

Example: 12 - $-5$ = 12 + 5 = 17 (using the keep-change-change method)

Vocabulary: An integer is defined as a positive or negative whole number, including zero.

Highlight: The "keep-change-change" method for subtraction is a key technique for working with negative numbers.