Pre-Algebra with Dino 🦕

Hi! I'm Rex! 🦕 Let's conquer Pre-Algebra together! I'll guide you through every topic with tips and explanations!

Rex the Math Dino 🌟

📚 What You'll Master

Integers & Number Sense Fractions & Decimals Ratios & Proportions Percents Variables & Expressions Solving Equations Inequalities Coordinate Plane Linear Equations Geometry Basics

🎯 How It Works

✅ Study each concept + formula
📝 See a worked example
🧠 Solve 20 exam-style questions
⏱️ Race against a 40-minute timer
🎉 Get instant feedback on each answer
📖 Review the full answer key at the end
🖨️ Print a clean study copy

⏱️

TIME REMAINING

40:00

Question 0 / 20 Score: 0

📘 Unit 1 · Integers & Number Sense

Unit 1 is all about integers — positive and negative whole numbers. Remember: the number line is your best friend! 🦕

Integers

Absolute Value & Integer Operations

Absolute value |x| = distance from 0 (always ≥ 0).
When multiplying/dividing: same signs → positive; different signs → negative.

⭐ Memorize

|−7| = 7 | (−3)(−4) = +12 | (−3)(+4) = −12
(+) × (+) = (+) | (−) × (−) = (+) | (+) × (−) = (−)

📝 Example

Find: (−6) × (−3) + |−5|

= 18 + 5

= 23 ✓

Question 1 of 20 Basic

Which expression has the greatest value?

|−15| = 15; (−3)(−6) = 18 ✓; −(−12) = 12; |−10| + 1 = 11. So B = 18 is the greatest.

📗 Unit 2 · Fractions & Decimals

Fractions are just division in disguise! 🍕 And decimals are fractions with powers of 10 as denominators. 🦕

Fractions

Operations with Fractions

Add/Subtract: common denominator first.
Multiply: straight across. Divide: flip & multiply (KCF: Keep, Change, Flip).

⭐ Memorize

a/b ÷ c/d = a/b × d/c | LCD needed for + and −

📝 Example

2/3 ÷ 4/9 = 2/3 × 9/4 = 18/12

= 3/2 = 1.5 ✓

Question 2 of 20 Basic

What is 3/4 ÷ 3/8?

KCF: 3/4 ÷ 3/8 = 3/4 × 8/3 = 24/12 = 2. Answer C ✓

📙 Unit 3 · Ratios & Proportions

Proportions

Ratios, Rates & Cross-Multiplication

A ratio compares two quantities. A proportion says two ratios are equal: a/b = c/d → ad = bc (cross-multiply).

⭐ Memorize

If a/b = c/d, then ad = bc

📝 Example

Solve: 3/5 = x/20

5x = 60 → x = 12

x = 12 ✓

Question 3 of 20 Basic

If 5/8 = x/40, what is x?

Cross-multiply: 8x = 5 × 40 = 200, so x = 200 ÷ 8 = 25. Answer D ✓

📕 Unit 4 · Percents

Percents

Percent Change & Percent of a Number

Percent of a number: multiply by the decimal form.
Percent change: (new − old) / old × 100%

⭐ Memorize

% change = (New − Old) / Old × 100

📝 Example

Price goes from $40 to $50. % increase?

= (50 − 40)/40 × 100 = 10/40 × 100

= 25% increase ✓

Question 4 of 20 Intermediate

A jacket costs $80. It goes on sale for $60. What is the percent decrease?

(80 − 60) / 80 × 100 = 20/80 × 100 = 25%. Answer C ✓

📓 Unit 5 · Variables & Expressions

Variables are just mystery numbers waiting to be found! I love a good mystery! 🦕🔍

Algebra

Simplifying & Evaluating Expressions

Like terms have the same variable and exponent. Combine them by adding/subtracting coefficients.
Distributive property: a(b + c) = ab + ac

⭐ Memorize

a(b + c) = ab + ac

📝 Example

Simplify: 3(2x − 4) + 5x

= 6x − 12 + 5x

= 11x − 12 ✓

Question 5 of 20 Intermediate

Simplify: 4(3x − 2) − 5x + 7

Distribute: 4(3x−2) = 12x−8. Then: 12x−8−5x+7 = 7x − 1. Answer B ✓

📔 Unit 6 · Solving Equations

Equations

One-Step & Two-Step Equations

Use inverse operations to isolate the variable. Whatever you do to one side, do to the other.

⭐ Memorize

Step 1: Undo addition/subtraction
Step 2: Undo multiplication/division

📝 Example

Solve: 3x + 7 = 22

3x = 15 (subtract 7 both sides)

x = 5 (divide by 3) ✓

Question 6 of 20 Basic

Solve for x: 2x − 5 = 13

2x − 5 = 13 → 2x = 18 → x = 9. Check: 2(9)−5 = 18−5 = 13 ✓

Equations

Multi-Step Equations & Variables on Both Sides

Collect variable terms on one side, constants on the other. Combine like terms, then solve.

5x + 3 = 2x + 12 → 3x = 9 → x = 3

📝 Example

Solve: 4x − 3 = 2x + 9

2x = 12

x = 6 ✓

Question 7 of 20 Intermediate

Solve: 5x + 4 = 3x + 16

5x − 3x = 16 − 4 → 2x = 12 → x = 6. Check: 5(6)+4 = 34 = 3(6)+16 ✓

📒 Unit 8 · Inequalities

Inequalities

Solving & Graphing Inequalities

Solve like an equation, BUT: when you multiply or divide by a negative number, flip the inequality sign!

⭐ Memorize — Critical Rule!

Multiply/divide by negative → FLIP the sign!
−2x < 8 → x > −4

📝 Example

Solve: −3x + 6 ≤ 15

−3x ≤ 9 → x ≥ −3 (flip!)

x ≥ −3 ✓

Question 8 of 20 Intermediate

Solve the inequality: −4x + 3 > 11

−4x + 3 > 11 → −4x > 8 → x < −2 (flip sign when dividing by −4!). Answer C ✓

🗺️ Unit 9 · Coordinate Plane

Graphing

Plotting Points & Quadrants

Points are written (x, y). The coordinate plane has 4 quadrants. Quadrant I: (+,+), II: (−,+), III: (−,−), IV: (+,−).

⭐ Memorize

Q I: (+,+) | Q II: (−,+) | Q III: (−,−) | Q IV: (+,−)

📝 Example

Distance from (1,2) to (5,5):

d = √((5−1)² + (5−2)²) = √(16+9) = √25

d = 5 units ✓

Question 9 of 20 Basic

In which quadrant is the point (−4, 7) located?

x = −4 (negative), y = 7 (positive) → that's Q II: (−, +). Answer B ✓

📈 Unit 10 · Slope & Linear Equations

Slope = rise over run! Think of me climbing a hill — how steep is it? 🏔️🦕

Linear

Slope & Slope-Intercept Form

Slope (m) = rise/run = (y₂ − y₁)/(x₂ − x₁).
Slope-intercept form: y = mx + b, where m = slope, b = y-intercept.

⭐ Memorize

m = (y₂ − y₁)/(x₂ − x₁) | y = mx + b

📝 Example

Slope through (2,3) and (6,11):

m = (11−3)/(6−2) = 8/4

m = 2 ✓

Question 10 of 20 Intermediate

What is the slope of the line passing through (−1, 4) and (3, −4)?

m = (−4 − 4)/(3 − (−1)) = −8/4 = −2. Answer C ✓

Question 11 of 20 Intermediate

A line has slope m = 3 and passes through (0, −5). What is its equation?

The point (0, −5) is the y-intercept, so b = −5. With m = 3: y = 3x − 5. Answer A ✓

⚡ Unit 12 · Exponents & PEMDAS

Exponents

Exponent Rules & PEMDAS

PEMDAS: Parentheses → Exponents → Multiply/Divide (left to right) → Add/Subtract (left to right).

⭐ Memorize Exponent Rules

xᵃ · xᵇ = xᵃ⁺ᵇ | xᵃ/xᵇ = xᵃ⁻ᵇ | (xᵃ)ᵇ = xᵃᵇ
x⁰ = 1 | x⁻ⁿ = 1/xⁿ

📝 Example

Simplify: 2³ + 4 × (6 − 2)

= 8 + 4 × 4 = 8 + 16

= 24 ✓

Question 12 of 20 Intermediate

Simplify: 3² × 2³ − 4 × (5 − 2)

Step by step: 3² = 9, 2³ = 8, (5−2) = 3. Then: 9 × 8 − 4 × 3 = 72 − 12 = 60. Answer C ✓

📐 Unit 13 · Geometry Basics

Geometry

Perimeter, Area & Volume Formulas

⭐ Memorize All

Rectangle: A = lw, P = 2(l+w)
Triangle: A = ½bh
Circle: A = πr², C = 2πr
Trapezoid: A = ½(b₁+b₂)h

📝 Example

Triangle: base = 8, height = 5

A = ½ × 8 × 5 = ½ × 40

A = 20 sq units ✓

Question 13 of 20 Intermediate

A circle has radius 6 cm. What is its area? (Use π ≈ 3.14)

A = πr² = 3.14 × 6² = 3.14 × 36 = 113.04 cm². Answer C ✓

Geometry

Pythagorean Theorem

In a right triangle, the square of the hypotenuse (c) equals the sum of squares of the legs (a and b).

⭐ Memorize

a² + b² = c²

📝 Example

Legs: a = 3, b = 4. Find c.

c² = 9 + 16 = 25

c = 5 ✓ (3-4-5 triple!)

Question 14 of 20 Intermediate

A right triangle has legs of length 5 and 12. What is the length of the hypotenuse?

c² = 5² + 12² = 25 + 144 = 169. c = √169 = 13. (5-12-13 Pythagorean triple!) Answer C ✓

📊 Unit 15 · Statistics

Statistics is about describing data! Mean = average, Median = middle value, Mode = most frequent! 📊🦕

Statistics

Mean, Median, Mode & Range

⭐ Memorize

Mean = sum ÷ count
Median = middle value (when sorted)
Mode = most frequent value
Range = max − min

📝 Example — Data: {3, 7, 7, 9, 14}

Mean = (3+7+7+9+14)/5 = 40/5 = 8

Median = 7 (middle), Mode = 7, Range = 11

Question 15 of 20 Intermediate

For the data set {4, 8, 6, 5, 3, 8, 9, 7}, what is the median?

Sorted: {3, 4, 5, 6, 7, 8, 8, 9}. 8 values → median = average of 4th & 5th = (6+7)/2 = 6.5. Answer B ✓

🔬 Unit 16 · Scientific Notation

Scientific Notation

Writing Numbers in Scientific Notation

Scientific notation: a × 10ⁿ, where 1 ≤ a < 10. Move the decimal to get a value between 1 and 10. Count the moves = exponent (positive = large number, negative = small number).

⭐ Memorize

a × 10ⁿ where 1 ≤ a < 10

📝 Example

4,500,000 = 4.5 × 10⁶

0.000072 = 7.2 × 10⁻⁵

Question 16 of 20 Hard

Which of the following equals (3 × 10⁴) × (2 × 10³)?

(3 × 2) × 10^(4+3) = 6 × 10⁷. Multiply coefficients, add exponents. Answer D ✓

🔢 Unit 17 · Number Properties

Properties

Commutative, Associative & Distributive

⭐ Memorize All Three

Commutative: a + b = b + a; ab = ba
Associative: (a+b)+c = a+(b+c)
Distributive: a(b+c) = ab + ac
Identity: a + 0 = a; a × 1 = a
Inverse: a + (−a) = 0; a × (1/a) = 1

Question 17 of 20 Hard

Which property justifies: 5 × (x + 3) = 5x + 15?

Distributing 5 across (x + 3) gives 5x + 15. This is the Distributive Property: a(b+c) = ab + ac. Answer C ✓

📝 Unit 18 · Word Problems

Word problems are like real-life adventures! Translate words → math, then solve! 🦕🌍

Question 18 of 20 Hard

Rex has twice as many stickers as Bella. Together they have 54 stickers. How many does Rex have?

Let Bella = x, Rex = 2x. Then x + 2x = 54 → 3x = 54 → x = 18. Rex = 2 × 18 = 36. Answer C ✓

🔄 Unit 19 · Functions

Functions

Functions & Function Notation

A function assigns exactly one output to each input. f(x) means "f evaluated at x." No x-value can have two different y-values (vertical line test).

⭐ Memorize

f(x) = expression in x
f(3) = substitute x = 3

📝 Example

f(x) = 2x² − 3. Find f(4).

f(4) = 2(16) − 3 = 32 − 3

f(4) = 29 ✓

Question 19 of 20 Hard

If f(x) = 3x − 7, what is f(−2)?

f(−2) = 3(−2) − 7 = −6 − 7 = −13. Answer B ✓

🏆 Unit 20 · Challenge Problem

Last one! This is a challenge — combine everything you know! You've got this! 🦕🏆

Question 20 of 20 Hard

A store sells notebooks for $3 each and pens for $1.50 each. Maya buys a total of 10 items and spends $21. How many notebooks did she buy?

Let n = notebooks, p = pens. System: n + p = 10 and 3n + 1.5p = 21. From first: p = 10 − n. Substitute: 3n + 1.5(10−n) = 21 → 3n + 15 − 1.5n = 21 → 1.5n = 6 → n = 4. Answer A ✓

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📖 Complete Answer Key

Detailed step-by-step solutions for all 20 questions

Answer: B — (−3)(−6) = 18

Evaluate each: |−15| = 15; (−3)(−6) = +18 (negative × negative = positive); −(−12) = 12; |−10|+1 = 11. The greatest value is 18.

Answer: C — 2

KCF rule: 3/4 ÷ 3/8 = 3/4 × 8/3 = 24/12 = 2. Flip the divisor and multiply.

Answer: D — x = 25

Cross-multiply: 5 × 40 = 8 × x → 200 = 8x → x = 200/8 = 25.

Answer: C — 25%

% decrease = (Old − New)/Old × 100 = (80 − 60)/80 × 100 = 20/80 × 100 = 25%.

Answer: B — 7x − 1

Distribute: 4(3x−2) = 12x−8. Then: 12x−8−5x+7 = (12x−5x)+(−8+7) = 7x − 1.

Answer: C — x = 9

2x − 5 = 13 → add 5: 2x = 18 → divide by 2: x = 9. Check: 2(9)−5 = 13 ✓

Answer: B — x = 6

5x + 4 = 3x + 16 → subtract 3x: 2x + 4 = 16 → subtract 4: 2x = 12 → x = 6. Check: 5(6)+4 = 34 = 3(6)+16 ✓

Answer: C — x < −2

−4x + 3 > 11 → −4x > 8 → divide by −4 and flip the sign → x < −2. This is the most common error: always flip when dividing by a negative!

Answer: B — Quadrant II

(−4, 7): x is negative, y is positive. Quadrant II contains all points (−, +). Remember: Q I=(+,+), Q II=(−,+), Q III=(−,−), Q IV=(+,−).

Answer: C — −2

m = (y₂−y₁)/(x₂−x₁) = (−4−4)/(3−(−1)) = −8/4 = −2. The line falls from left to right, so slope is negative.

Answer: A — y = 3x − 5

The point (0, −5) is on the y-axis, so b = −5 (y-intercept). With slope m = 3, the equation is y = 3x + (−5) = y = 3x − 5.

Answer: C — 60

PEMDAS: exponents first: 3² = 9, 2³ = 8. Parentheses: (5−2) = 3. Then multiply: 9×8 = 72, 4×3 = 12. Finally subtract: 72 − 12 = 60.

Answer: C — 113.04 cm²

A = πr² = 3.14 × 6² = 3.14 × 36 = 113.04 cm². Common mistake: using diameter (12) instead of radius (6).

Answer: C — 13

a² + b² = c² → 5² + 12² = 25 + 144 = 169 → c = √169 = 13. The 5-12-13 is a Pythagorean triple worth memorizing!

Answer: B — 6.5

Sort the data: {3, 4, 5, 6, 7, 8, 8, 9}. With 8 values (even count), median = average of 4th and 5th values = (6 + 7)/2 = 6.5.

Answer: D — 6 × 10⁷

Multiply coefficients: 3 × 2 = 6. Add exponents: 10⁴ × 10³ = 10^(4+3) = 10⁷. Result: 6 × 10⁷.

Answer: C — Distributive Property

5 × (x + 3) = 5·x + 5·3 = 5x + 15. This is the Distributive Property: a(b+c) = ab + ac. It distributes multiplication over addition.

Answer: C — 36 stickers

Let Bella = x, Rex = 2x. Equation: x + 2x = 54 → 3x = 54 → x = 18. Rex has 2×18 = 36 stickers. Check: 18+36 = 54 ✓

Answer: B — −13

f(−2) = 3(−2) − 7 = −6 − 7 = −13. Substitute x = −2 into the function. The negative result makes sense since 3(−2) = −6.

Answer: A — 4 notebooks

System of equations: n + p = 10 and 3n + 1.5p = 21. From eq 1: p = 10−n. Substitute: 3n + 1.5(10−n) = 21 → 3n + 15 − 1.5n = 21 → 1.5n = 6 → n = 4. Check: 4+6=10 ✓ and 3(4)+1.5(6)=12+9=21 ✓