Subject
Pre-Algebra
Build the arithmetic and equation-solving foundations the rest of algebra rests on.
Begin at I if you’re new to Pre-Algebra.
Order of Operations
PEMDAS: parentheses, exponents, then multiplication/division and addition/subtraction left to right.
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Operations with Integers
Add, subtract, multiply, and divide positive and negative whole numbers using the sign rules.
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GCF, LCM, and Prime Factorization
Break numbers into prime factors, then find the greatest common factor and least common multiple.
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Operations with Fractions
Add, subtract, multiply, and divide fractions. Get common denominators when adding or subtracting; flip and multiply when dividing.
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Operations with Decimals
Add, subtract, multiply, and divide decimals. The trick is knowing where the decimal point goes for each operation.
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Converting Fractions, Decimals, and Percents
Three ways to write the same number. Learn to slide between fractions, decimals, and percents fluently.
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Ratios and Proportions
Set up and solve proportions using cross-multiplication. Use the same technique on real-world rate problems.
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Percents
Find a percent of a number, the original from a percent, and percent change. Used in tax, tips, discounts, and more.
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Intro to Geometry
Perimeter, area, and volume of basic shapes. Angle pairs and the triangle angle sum.
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Exponents and Powers
An exponent tells you how many times to multiply the base by itself. The foundation for everything from area to growth.
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Square Roots
The square root of n is the number that, when multiplied by itself, gives n. The inverse of squaring.
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Absolute Value
The distance of a number from zero. |x| is always zero or positive.
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The Coordinate Plane
Plot points, name quadrants, and find horizontal/vertical distances and midpoints. Foundation for graphing.
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Graphing Linear Equations
Read slope and y-intercept off y = mx + b. Plug in to find points. Find where the line crosses each axis.
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Combining Like Terms
Identify like terms and combine their coefficients to simplify expressions. The first big simplification skill.
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Distributive Property
Multiply an outside factor across each term inside parentheses. Watch the signs — they travel with the factor.
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Translating Words to Expressions and Equations
Turn an English sentence into a math expression or equation. The bridge that makes word problems solvable.
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Solving One-Step Equations
Use inverse operations to isolate the variable. Covers all four operations, negative answers, and equations with the variable on the right.
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Solving Two-Step Equations
Reverse-order undoing: subtract or add first, then multiply or divide. Builds on one-step equations.
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Solving Multi-Step Equations
Combine distributing, like terms, and inverse operations to isolate x. The 'put it all together' topic.
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Equations with Variables on Both Sides
Gather the variable terms onto one side, then solve as a multi-step equation.
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Solving One-Step Inequalities
Solve like a one-step equation, but flip the symbol when multiplying or dividing by a negative.
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Solving Two-Step Inequalities
Undo addition or subtraction first, then multiplication or division. Flip the symbol when you multiply or divide by a negative.
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