Pre-Algebra Honors Study Guide & Practice Review

Order of Operations

Use PEMDAS: Parentheses/Brackets, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

Signed Exponents

Pay close attention to parentheses; (-3)² = 9, while -3² = -9.

Absolute Value

Measures distance from 0, always non-negative; evaluate inside absolute value bars first.

Fraction Operations

Find a common denominator before adding/subtracting. Dividing fractions means multiplying by the reciprocal (Keep-Change-Flip).

Evaluating Expressions

Substitute negative numbers using parentheses to avoid sign errors.

Solving Multi-Step Equations

Distribute → Combine Like Terms → Move variables to one side → Isolate the variable using inverse operations.

Literal Equations

Treat all other letters as constants when solving for a target variable.

Cross-Multiplication

In proportions, a/b = c/d means a × d = b × c.

Scale Factor

To find the scale factor of quantities, divide the target amount by the original amount.

Inverse Proportions (Work Rate)

Total work done = (Workers) × (Time); if workers decrease, time increases proportionally.

Quadrants

Quadrant I (+, +), Quadrant II (-, +), Quadrant III (-, -), Quadrant IV (+, -). Points on axes are not in quadrants.

Slope Formula

m = (y₂ - y₁) / (x₂ - x₁) (Rise over Run).

Mean

(Sum of all data values) / (Total count of data values).

Median

Middle value when data is ordered least to greatest (average middle two if even count).

Range

Maximum value - Minimum value (measures spread/variability).

Outlier Effect

Extreme outliers pull the mean towards them, but the median remains resistant and stable.