Integers and Operations

Flashcards covering key definitions and rules for integers and their operations, including exponents, absolute value, addition, subtraction, multiplication, and division, based on the provided lecture notes.

Exponents

Something that shows the number of times a base number is multiplied by itself.

Integers

Whole numbers and their opposites (positive whole numbers, negative whole numbers, and zero).

Positive Integers

All integers greater than 0 (e.g., 1, 2, 3, 4…).

Negative Integers

All integers less than 0 (e.g., -1, -2, -3…).

Zero

An integer that is neither positive nor negative.

Opposites of Numbers

Numbers that are the same distance from zero on a number line but in opposite directions (e.g., -9 and 9, 7 and -7).

Absolute Value

The distance a number is from zero, written as |x|, and always results in a non-negative value (e.g., |-6| = 6, |12| = 12).

Adding Integers (Same Sign)

Add their absolute values and then keep the common sign

Adding Integers (Unlike Signs)

Subtract their absolute values and keep the sign of the number with the larger absolute value.

Additive Inverse

Two numbers whose sum is zero; also known as opposites (e.g., -12 + 12 = 0).

Multiplying/Dividing Integers (Same Sign)

The product or quotient will be positive (e.g., 3 x 4 = 12, -3 x -4 = 12).

Multiplying/Dividing Integers (Different Signs)

The product or quotient will be negative (e.g., -3 x 4 = -12 , 12 / -3 = -4).

Product with Odd Number of Negative Factors

The final product will be negative.

Product with Even Number of Negative Factors

The final product will be positive.

Multiplication by Zero

Zero times any number is zero (0 * x = 0).

Division by Zero

Division of any number by zero is undefined (x / 0 = undefined).

Zero Divided by a Non-Zero Number

Zero divided by any number (except zero) is zero (0 / x = 0, where x
eq 0).

Multiplication by -1

Multiplying a number by -1 results in the opposite of that number (e.g., x •(-1)= -x).

Subtracting Integers

To subtract an integer, add its additive inverse (e.g., a - b = a + (-b)).

Evaluating Expressions

The process of finding the numerical value of an expression by copying the problem, substituting variable values, and then simplifying.