๐Ÿฆ• Pre-Algebra
with Dino Rex!
All Units ยท 20 Exam-Style Questions ยท Grades 6โ€“8
Hi! I'm Rex! ๐Ÿฆด Let's crush Pre-Algebra together!
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Rex will guide you through all 10 Pre-Algebra units.
Each unit has a concept review, memory tips, and 2 exam-style questions.

โฑ 30 min timer ๐Ÿ“Š Score tracking ๐ŸŽ‰ Confetti rewards ๐Ÿ“„ PDF print ๐Ÿ’ก Instant explanations

Unit 1 Integer Operations
๐Ÿ“˜ Concept
Adding, Subtracting, Multiplying & Dividing Integers
Integers include positive numbers, negative numbers, and zero.
โ€ข Adding: Same signs โ†’ add & keep sign. Different signs โ†’ subtract & take sign of larger absolute value.
โ€ข Subtracting: Add the opposite: a โˆ’ b = a + (โˆ’b)
โ€ข Multiplying/Dividing: Same signs โ†’ Positive. Different signs โ†’ Negative.
๐Ÿฆด Memorize This!
  • (+)(+) = + and (โˆ’)(โˆ’) = +
  • (+)(โˆ’) = โˆ’ and (โˆ’)(+) = โˆ’
  • Subtracting = Adding the opposite
  • |negative| = positive (absolute value)
โœ๏ธ Example
Solve: โˆ’8 + 3 = ?
Different signs โ†’ subtract: 8 โˆ’ 3 = 5. Larger absolute value is 8 (negative), so answer is โˆ’5.
Answer: โˆ’5
Question 1
What is the value of โˆ’15 + (โˆ’9)?
Question 2
Evaluate: (โˆ’4) ร— (โˆ’7)
Unit 2 Order of Operations (PEMDAS)
๐Ÿ“˜ Concept
PEMDAS / BODMAS Rule
Always solve in this exact order:
Parentheses โ†’ Exponents โ†’ Multiplication & Division (left to right) โ†’ Addition & Subtraction (left to right)
๐Ÿฆด Memorize This!
  • Please Excuse My Dear Aunt Sally
  • M and D have equal priority โ†’ go left to right
  • A and S have equal priority โ†’ go left to right
โœ๏ธ Example
Solve: 3 + 4 ร— 2 = ?
Multiplication first: 4 ร— 2 = 8. Then addition: 3 + 8 = 11.
Answer: 11
Question 3
Simplify: 2 + 3 ร— (8 โˆ’ 5)ยฒ รท 9
Question 4
What is the value of 18 รท 3 ร— 2 โˆ’ 4?
Unit 3 Fractions & Decimals
๐Ÿ“˜ Concept
Operations with Fractions
โ€ข Add/Subtract: Find LCD, then add/subtract numerators.
โ€ข Multiply: Numerator ร— Numerator, Denominator ร— Denominator. Simplify.
โ€ข Divide: Multiply by the reciprocal (flip the second fraction).
๐Ÿฆด Memorize This!
  • Add/Subtract fractions โ†’ Common denominator first!
  • Multiply: straight across
  • Divide: Keep ยท Change ยท Flip (KCF)
  • Always simplify your final answer
โœ๏ธ Example
Solve: 3/4 รท 1/2 = ?
Keep 3/4 ยท Change รท to ร— ยท Flip 1/2 to 2/1 โ†’ 3/4 ร— 2/1 = 6/4 = 3/2 = 1ยฝ
Answer: 3/2
Question 5
What is 2/3 + 3/4?
Question 6
Simplify: 5/6 รท 5/12
Unit 4 Ratios & Proportions
๐Ÿ“˜ Concept
Ratios, Rates & Cross-Multiplication
A ratio compares two quantities. A proportion says two ratios are equal.
To solve: a/b = c/d โ†’ cross multiply โ†’ ad = bc.
Unit rate: rate per 1 unit (e.g., miles per hour).
๐Ÿฆด Memorize This!
  • Proportion: a/b = c/d โ†’ cross multiply: ad = bc
  • Unit rate = total รท number of units
  • Simplify ratios like fractions (divide by GCF)
โœ๏ธ Example
If 3 apples cost $1.50, how much do 7 apples cost?
Unit rate: $1.50 รท 3 = $0.50 per apple. 7 ร— $0.50 = $3.50
Answer: $3.50
Question 7
Solve the proportion: x/5 = 12/20
Question 8
A car travels 180 miles in 3 hours. At the same rate, how far does it travel in 5 hours?
Unit 5 Percents
๐Ÿ“˜ Concept
Percent, Discount, Tax & Change
Percent means "per 100." Key formulas:
โ€ข Part = Percent ร— Whole (as decimal)
โ€ข Percent Change = (Change รท Original) ร— 100
โ€ข Discount: Sale Price = Original โˆ’ (% ร— Original)
๐Ÿฆด Memorize This!
  • Percent โ†’ decimal: divide by 100 (move decimal left 2)
  • Part / Whole = Percent / 100
  • % increase = (new โˆ’ old) / old ร— 100
  • % decrease = (old โˆ’ new) / old ร— 100
โœ๏ธ Example
A $40 jacket is 25% off. What is the sale price?
Discount = 25% ร— 40 = 0.25 ร— 40 = $10. Sale price = 40 โˆ’ 10 = $30.
Answer: $30
Question 9
A score of 36 out of 48 is what percent?
Question 10
A price increased from $50 to $65. What is the percent increase?
Unit 6 Expressions & Variables
๐Ÿ“˜ Concept
Writing & Evaluating Algebraic Expressions
Variables (like x, y) represent unknown values.
โ€ข Like terms: same variable and exponent โ†’ can be combined (3x + 5x = 8x)
โ€ข Evaluate: substitute the value and compute
โ€ข Distributive Property: a(b + c) = ab + ac
๐Ÿฆด Memorize This!
  • Coefficient: the number in front of a variable (in 5x, 5 is the coefficient)
  • Like terms have the same variable AND same exponent
  • Distribute: multiply the outside term to EVERY term inside
โœ๏ธ Example
If x = 3, evaluate: 4xยฒ โˆ’ 5
4(3)ยฒ โˆ’ 5 = 4(9) โˆ’ 5 = 36 โˆ’ 5 = 31
Answer: 31
Question 11
Simplify: 3(x + 4) โˆ’ 2x + 1
Question 12
If a = โˆ’2 and b = 5, what is 3aยฒ โˆ’ 2b?
Unit 7 Solving Equations
๐Ÿ“˜ Concept
One-Step & Two-Step Equations
Goal: isolate the variable using inverse operations.
โ€ข One-step: undo one operation (add/subtract or multiply/divide)
โ€ข Two-step: 1st undo addition/subtraction, then undo multiplication/division
โ€ข Check: substitute your answer back in!
๐Ÿฆด Memorize This!
  • Inverse of + is โˆ’ and inverse of โˆ’ is +
  • Inverse of ร— is รท and inverse of รท is ร—
  • Whatever you do to one side, do to the other side
โœ๏ธ Example
Solve: 2x โˆ’ 5 = 11
Add 5 to both sides: 2x = 16. Divide both sides by 2: x = 8. Check: 2(8)โˆ’5 = 11 โœ“
Answer: x = 8
Question 13
Solve for x: 3x + 7 = 28
Question 14
If x/4 โˆ’ 3 = 5, what is x?
Unit 8 Inequalities
๐Ÿ“˜ Concept
Solving & Graphing Inequalities
Inequalities use <, >, โ‰ค, โ‰ฅ symbols.
โ€ข Solve like equations โ€” but: flip the inequality sign when multiplying or dividing by a negative number!
โ€ข Graph: open circle (strict < >) or closed circle (โ‰ค โ‰ฅ) on a number line.
๐Ÿฆด Memorize This!
  • Multiply/divide by negative โ†’ FLIP the sign!
  • < and > โ†’ open circle (not included)
  • โ‰ค and โ‰ฅ โ†’ closed circle (included)
โœ๏ธ Example
Solve: โˆ’3x < 12
Divide both sides by โˆ’3 and flip: x > โˆ’4
Answer: x > โˆ’4
Question 15
Solve the inequality: โˆ’2x + 4 โ‰ฅ 10
Question 16
Which value of x makes 5x โˆ’ 3 < 12 true?
Unit 9 Coordinate Plane & Linear Equations
๐Ÿ“˜ Concept
Slope, Intercepts & Slope-Intercept Form
โ€ข Slope (m) = rise รท run = (yโ‚‚ โˆ’ yโ‚) / (xโ‚‚ โˆ’ xโ‚)
โ€ข Slope-intercept form: y = mx + b, where m = slope, b = y-intercept
โ€ข Positive slope โ†’ line goes up left to right. Negative โ†’ goes down.
๐Ÿฆด Memorize This!
  • y = mx + b (m = slope, b = y-intercept)
  • Slope = rise / run = ฮ”y / ฮ”x
  • Horizontal line โ†’ slope = 0
  • Vertical line โ†’ slope = undefined
โœ๏ธ Example
Find the slope between (1, 3) and (4, 9).
Slope = (9 โˆ’ 3) / (4 โˆ’ 1) = 6 / 3 = 2
Answer: slope = 2
Question 17
What is the slope of the line passing through (2, 1) and (6, 9)?
Question 18
In the equation y = โˆ’3x + 7, what is the y-intercept?
Unit 10 Geometry: Area, Perimeter & Volume
๐Ÿ“˜ Concept
Key Geometry Formulas
โ€ข Rectangle: Area = lw, Perimeter = 2(l+w)
โ€ข Triangle: Area = ยฝbh
โ€ข Circle: Area = ฯ€rยฒ, Circumference = 2ฯ€r
โ€ข Rectangular Prism: Volume = lwh
๐Ÿฆด Memorize This!
  • Area of triangle = (base ร— height) / 2
  • Circle area = ฯ€ rยฒ (pi r squared)
  • Volume = length ร— width ร— height
  • ฯ€ โ‰ˆ 3.14 (use unless told otherwise)
โœ๏ธ Example
Find the area of a triangle with base 10 cm and height 6 cm.
Area = ยฝ ร— 10 ร— 6 = ยฝ ร— 60 = 30 cmยฒ
Answer: 30 cmยฒ
Question 19
A circle has a radius of 5 cm. What is its area? (Use ฯ€ โ‰ˆ 3.14)
Question 20
A rectangular box is 4 cm long, 3 cm wide, and 5 cm tall. What is its volume?
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๐Ÿ“– Complete Answer Key & Explanations