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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.
โฑ 30 min timer
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๐ก Instant explanations
Unit 1
Integer Operations
๐ Concept
Adding, Subtracting, Multiplying & Dividing Integers
Integers include positive numbers, negative numbers, and zero.
โข Adding: Same signs โ add & keep sign. Different signs โ subtract & take sign of larger absolute value.
โข Subtracting: Add the opposite: a โ b = a + (โb)
โข Multiplying/Dividing: Same signs โ Positive. Different signs โ Negative.
โข Adding: Same signs โ add & keep sign. Different signs โ subtract & take sign of larger absolute value.
โข Subtracting: Add the opposite: a โ b = a + (โb)
โข Multiplying/Dividing: Same signs โ Positive. Different signs โ Negative.
๐ฆด Memorize This!
- (+)(+) = + and (โ)(โ) = +
- (+)(โ) = โ and (โ)(+) = โ
- Subtracting = Adding the opposite
- |negative| = positive (absolute value)
โ๏ธ Example
Solve: โ8 + 3 = ?
Different signs โ subtract: 8 โ 3 = 5. Larger absolute value is 8 (negative), so answer is โ5.
Answer: โ5
Question 1
What is the value of โ15 + (โ9)?
Question 2
Evaluate: (โ4) ร (โ7)
Unit 2
Order of Operations (PEMDAS)
๐ 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)
Parentheses โ Exponents โ Multiplication & Division (left to right) โ Addition & Subtraction (left to right)
๐ฆด 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
โ๏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 โ 5)ยฒ รท 9
Question 4
What is the value of 18 รท 3 ร 2 โ 4?
Unit 3
Fractions & Decimals
๐ Concept
Operations with Fractions
โข Add/Subtract: Find LCD, then add/subtract numerators.
โข Multiply: Numerator ร Numerator, Denominator ร Denominator. Simplify.
โข Divide: Multiply by the reciprocal (flip the second fraction).
โข Multiply: Numerator ร Numerator, Denominator ร Denominator. Simplify.
โข Divide: Multiply by the reciprocal (flip the second fraction).
๐ฆด Memorize This!
- Add/Subtract fractions โ Common denominator first!
- Multiply: straight across
- Divide: Keep ยท Change ยท Flip (KCF)
- Always simplify your final answer
โ๏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
๐ 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).
To solve: a/b = c/d โ cross multiply โ ad = bc.
Unit rate: rate per 1 unit (e.g., miles per hour).
๐ฆด 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)
โ๏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
๐ Concept
Percent, Discount, Tax & Change
Percent means "per 100." Key formulas:
โข Part = Percent ร Whole (as decimal)
โข Percent Change = (Change รท Original) ร 100
โข Discount: Sale Price = Original โ (% ร Original)
โข Part = Percent ร Whole (as decimal)
โข Percent Change = (Change รท Original) ร 100
โข Discount: Sale Price = Original โ (% ร Original)
๐ฆด Memorize This!
- Percent โ decimal: divide by 100 (move decimal left 2)
- Part / Whole = Percent / 100
- % increase = (new โ old) / old ร 100
- % decrease = (old โ new) / old ร 100
โ๏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 โ 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
๐ Concept
Writing & Evaluating Algebraic Expressions
Variables (like x, y) represent unknown values.
โข Like terms: same variable and exponent โ can be combined (3x + 5x = 8x)
โข Evaluate: substitute the value and compute
โข Distributive Property: a(b + c) = ab + ac
โข Like terms: same variable and exponent โ can be combined (3x + 5x = 8x)
โข Evaluate: substitute the value and compute
โข Distributive Property: a(b + c) = ab + ac
๐ฆด 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
โ๏ธ Example
If x = 3, evaluate: 4xยฒ โ 5
4(3)ยฒ โ 5 = 4(9) โ 5 = 36 โ 5 = 31
Answer: 31
Question 11
Simplify: 3(x + 4) โ 2x + 1
Question 12
If a = โ2 and b = 5, what is 3aยฒ โ 2b?
Unit 7
Solving Equations
๐ Concept
One-Step & Two-Step Equations
Goal: isolate the variable using inverse operations.
โข One-step: undo one operation (add/subtract or multiply/divide)
โข Two-step: 1st undo addition/subtraction, then undo multiplication/division
โข Check: substitute your answer back in!
โข One-step: undo one operation (add/subtract or multiply/divide)
โข Two-step: 1st undo addition/subtraction, then undo multiplication/division
โข Check: substitute your answer back in!
๐ฆด Memorize This!
- Inverse of + is โ and inverse of โ is +
- Inverse of ร is รท and inverse of รท is ร
- Whatever you do to one side, do to the other side
โ๏ธ Example
Solve: 2x โ 5 = 11
Add 5 to both sides: 2x = 16. Divide both sides by 2: x = 8. Check: 2(8)โ5 = 11 โ
Answer: x = 8
Question 13
Solve for x: 3x + 7 = 28
Question 14
If x/4 โ 3 = 5, what is x?
Unit 8
Inequalities
๐ Concept
Solving & Graphing Inequalities
Inequalities use <, >, โค, โฅ symbols.
โข Solve like equations โ but: flip the inequality sign when multiplying or dividing by a negative number!
โข Graph: open circle (strict < >) or closed circle (โค โฅ) on a number line.
โข Solve like equations โ but: flip the inequality sign when multiplying or dividing by a negative number!
โข Graph: open circle (strict < >) or closed circle (โค โฅ) on a number line.
๐ฆด Memorize This!
- Multiply/divide by negative โ FLIP the sign!
- < and > โ open circle (not included)
- โค and โฅ โ closed circle (included)
โ๏ธ Example
Solve: โ3x < 12
Divide both sides by โ3 and flip: x > โ4
Answer: x > โ4
Question 15
Solve the inequality: โ2x + 4 โฅ 10
Question 16
Which value of x makes 5x โ 3 < 12 true?
Unit 9
Coordinate Plane & Linear Equations
๐ Concept
Slope, Intercepts & Slope-Intercept Form
โข Slope (m) = rise รท run = (yโ โ yโ) / (xโ โ xโ)
โข Slope-intercept form: y = mx + b, where m = slope, b = y-intercept
โข Positive slope โ line goes up left to right. Negative โ goes down.
โข Slope-intercept form: y = mx + b, where m = slope, b = y-intercept
โข Positive slope โ line goes up left to right. Negative โ goes down.
๐ฆด Memorize This!
- y = mx + b (m = slope, b = y-intercept)
- Slope = rise / run = ฮy / ฮx
- Horizontal line โ slope = 0
- Vertical line โ slope = undefined
โ๏ธ Example
Find the slope between (1, 3) and (4, 9).
Slope = (9 โ 3) / (4 โ 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 = โ3x + 7, what is the y-intercept?
Unit 10
Geometry: Area, Perimeter & Volume
๐ Concept
Key Geometry Formulas
โข Rectangle: Area = lw, Perimeter = 2(l+w)
โข Triangle: Area = ยฝbh
โข Circle: Area = ฯrยฒ, Circumference = 2ฯr
โข Rectangular Prism: Volume = lwh
โข Triangle: Area = ยฝbh
โข Circle: Area = ฯrยฒ, Circumference = 2ฯr
โข Rectangular Prism: Volume = lwh
๐ฆด Memorize This!
- Area of triangle = (base ร height) / 2
- Circle area = ฯ rยฒ (pi r squared)
- Volume = length ร width ร height
- ฯ โ 3.14 (use unless told otherwise)
โ๏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 3.14)
Question 20
A rectangular box is 4 cm long, 3 cm wide, and 5 cm tall. What is its volume?
๐ฆ
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