DinoMath Pre-Algebra | Learn with Rex the Dinosaur

Study each concept carefully! memorize the formulas, then try the worked examples before heading to the quiz! 🌟

Integers & Absolute Value

Signed Numbers · Number Line

📖 Core Concept

Integers on the Number Line

Integers include all whole numbers and their opposites: …−3, −2, −1, 0, 1, 2, 3… The absolute value |n| is the distance from 0 on the number line — always non-negative.

⭐ MEMORIZE

|a| ≥ 0 always
|a| = a if a ≥ 0 ; |a| = −a if a < 0
Opposite of a = −a
Adding same sign → add, keep sign
Adding diff sign → subtract, take larger sign

💡 WORKED EXAMPLE

Q: Simplify |−7| + |3| − |−2|

|−7| = 7, |3| = 3, |−2| = 2
= 7 + 3 − 2 = 8

Fractions, Decimals & Percents

Conversion · Operations

📖 Core Concept

FDP Conversions & Operations

Every fraction can be written as a decimal and a percent. To convert: fraction → divide; decimal → move point 2 places right for %; percent → divide by 100.

⭐ MEMORIZE

a/b ÷ c/d = a/b × d/c (flip & multiply)
a/b × c/d = (a×c)/(b×d)
LCM needed for + and −
% = decimal × 100

💡 WORKED EXAMPLE

Q: 3/4 ÷ 1/2

= 3/4 × 2/1 = 6/4 = 3/2 = 1.5

Ratios, Proportions & Percents

Cross-multiplication · Percent Change

📖 Core Concept

Proportions & Percent Problems

A proportion states two ratios are equal. Cross-multiply to solve. Percent change compares how much a value changed relative to the original.

⭐ MEMORIZE

a/b = c/d → ad = bc (cross-multiply)
% change = (new − old)/old × 100
part = % × whole
% of n = (% ÷ 100) × n

💡 WORKED EXAMPLE

Q: A price rose from $40 to $50. % increase?

= (50 − 40)/40 × 100
= 10/40 × 100 = 25%

Exponents & Order of Operations

PEMDAS · Laws of Exponents

📖 Core Concept

Exponent Rules & PEMDAS

PEMDAS: Parentheses → Exponents → Multiply/Divide (left→right) → Add/Subtract (left→right). Exponent laws govern how powers combine.

⭐ MEMORIZE

a^m × a^n = a^(m+n)
a^m ÷ a^n = a^(m−n)
(a^m)^n = a^(mn)
a^0 = 1 (a ≠ 0)
a^(−n) = 1/a^n

💡 WORKED EXAMPLE

Q: Evaluate 3 + 4² ÷ 2 − 1

= 3 + 16 ÷ 2 − 1
= 3 + 8 − 1
= 10

Algebraic Expressions & Variables

Simplifying · Combining Like Terms

📖 Core Concept

Expressions, Terms & Like Terms

A term is a number, variable, or product. Like terms share the same variable(s) with the same exponent(s). Combine by adding/subtracting coefficients.

⭐ MEMORIZE

Like terms: same variable, same power
3x + 5x = 8x (add coefficients)
3x + 5y = 3x + 5y (unlike → leave)
Distributive: a(b+c) = ab + ac

💡 WORKED EXAMPLE

Q: Simplify 2x + 3y − x + 4y

= (2x − x) + (3y + 4y)
= x + 7y

Solving One & Two-Step Equations

Inverse Operations · Balance Method

📖 Core Concept

Equation Solving Strategy

An equation is balanced. Do the same operation to both sides to isolate the variable. Undo operations in reverse PEMDAS order.

⭐ MEMORIZE

One-step: x + a = b → x = b − a
One-step: ax = b → x = b/a
Two-step: ax + b = c → x = (c−b)/a
Always: whatever you do to one side,
do to the other side!

💡 WORKED EXAMPLE

Q: Solve 3x − 5 = 16

3x − 5 + 5 = 16 + 5
3x = 21
x = 21 ÷ 3 = 7

Inequalities

Graphing · Solving · Flip Rule

📖 Core Concept

Solving & Graphing Inequalities

Inequalities work like equations, with one critical rule: multiplying or dividing both sides by a negative number reverses the inequality symbol.

⭐ MEMORIZE

−2x < 6 → x > −3 (flip!)
< or > : open circle on graph
≤ or ≥ : closed circle on graph
Shade direction of solutions

💡 WORKED EXAMPLE

Q: Solve −3x + 1 ≥ 7

−3x ≥ 6
x ≤ −2 (flip: divided by −3)
Graph: closed circle at −2, shade left

Graphing on the Coordinate Plane

Quadrants · Slope · Linear Equations

📖 Core Concept

Slope and Linear Equations

The coordinate plane has 4 quadrants. Slope (m) measures steepness. Slope-intercept form y = mx + b gives slope m and y-intercept b directly.

⭐ MEMORIZE

slope m = (y₂−y₁)/(x₂−x₁) = rise/run
y = mx + b (slope-intercept form)
y − y₁ = m(x − x₁) (point-slope)
Parallel lines: same slope (m₁ = m₂)
Perpendicular: m₁ × m₂ = −1

💡 WORKED EXAMPLE

Q: Slope through (2, 5) and (6, 13)?

m = (13 − 5)/(6 − 2)
= 8/4 = 2

Concepts down? Ready for the challenge? Hit the Quiz tab! I believe in you! 🦕✨