Pre-Algebra with Dino Rex

Integers include all whole numbers and their negatives: ..., −3, −2, −1, 0, 1, 2, 3, ...

Order of Operations (PEMDAS): Parentheses → Exponents → Multiplication/Division → Addition/Subtraction, always left to right.

Absolute Value |x| means the distance from 0, always ≥ 0. So |−5| = 5.

To add fractions, find a common denominator. Multiply each fraction by the other's denominator form.

To find a percent of a number: convert % to decimal (÷100), then multiply.
e.g., 15% of 80 = 0.15 × 80 = 12

A ratio compares two quantities. A proportion says two ratios are equal.
Use cross-multiplication to solve: if a/b = c/d, then ad = bc.

Like terms have the same variable and exponent. Combine by adding/subtracting coefficients.

To evaluate an expression, substitute the given values and compute using PEMDAS.

Solve by doing the opposite (inverse) operation to both sides of the equation.
Addition ↔ Subtraction  |  Multiplication ↔ Division

Solve in this order: (1) Add or subtract to isolate the variable term. (2) Multiply or divide to isolate the variable.

Solve like equations, but: flip the inequality sign when multiplying or dividing by a negative number!

Example: −3x ≤ 9 → divide by −3, flip → x ≥ −3

Slope = rise over run = (y₂ − y₁) / (x₂ − x₁)

Slope-intercept form: y = mx + b, where m = slope, b = y-intercept.

A function assigns exactly one output to each input.
f(x) is "f of x" — substitute x to find the output.

For number patterns, find the rule between consecutive terms.

Rectangle: Area = length × width  |  Perimeter = 2(l + w)

Triangle Perimeter: sum of all 3 sides

Pythagorean Theorem (right triangles only): a² + b² = c², where c is the hypotenuse (longest side, opposite the right angle).