Math Glossary
Clarify the vocabulary behind homework and workplace math—percent change, spreads, quadratics, and geometry—then jump into the matching tools.
12 terms · Linked from popular calculators on the hub
Categories
Percentage
ArithmeticDefinition
A ratio expressed per hundred. Percent change compares new vs old values; percent of answers “what fraction of the whole.”
Formula
Percent = (part ÷ whole) × 100Example
45 is what percent of 180? → (45 ÷ 180) × 100 = 25%.
Why it matters
Discounts, tax, tips, and growth rates all reduce to percent problems—pick the right base.
Common mistakes
- ✗Adding percents that don’t share the same base
- ✗Confusing percent increase with percent of
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Fraction
ArithmeticDefinition
Represents part of a whole as numerator/denominator. Operations need common denominators or multiplication rules.
Example
½ + ¼ = 2/4 + 1/4 = 3/4.
Why it matters
Recipes, probability, and algebra all lean on fraction fluency.
Common mistakes
- ✗Adding numerators and denominators directly (½ + ¼ ≠ 3/6)
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Ratio
ArithmeticDefinition
Compares two quantities (a : b). Equivalent ratios scale both sides by the same factor.
Example
Mixing 2:3 concentrate to water → 2 parts concentrate for every 3 parts water.
Why it matters
Maps, scale models, and dilution problems are ratio problems in disguise.
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Proportion
ArithmeticDefinition
States two ratios are equal: a/b = c/d. Cross-multiply to solve for an unknown when the relationship is linear.
Example
If 3 notebooks cost $12, then 5 notebooks cost x: 3/12 = 5/x → x = $20.
Why it matters
Direct and inverse variation show up in science, finance, and unit conversions.
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Standard deviation
StatisticsDefinition
Measures typical spread around the mean. Low σ = points cluster; high σ = more variability.
Formula
Population σ = √(Σ(x − μ)² / N); sample s uses (N − 1) in denominatorExample
Scores 80, 82, 78, 81, 79 have mean 80 and a modest standard deviation (~1.4 for this sample).
Why it matters
Compare consistency of investments, grades, or lab repeats—not just averages.
Common mistakes
- ✗Using population σ when you only have a sample
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Mean, median, mode
StatisticsDefinition
Mean is the average; median is the middle order statistic; mode is the most frequent value. Each resists outliers differently.
Why it matters
Income and home-price summaries often report median because means are skewed by extremes.
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Quadratic equation
AlgebraDefinition
Polynomial equation ax² + bx + c = 0 (a ≠ 0). Solutions may be two real roots, one repeated root, or complex.
Formula
x = (−b ± √(b² − 4ac)) / 2aExample
x² − 5x + 6 = 0 → (x − 2)(x − 3) = 0 → x = 2 or x = 3.
Why it matters
Projectile motion, area optimization, and parabola intersections all reduce to quadratics.
Common mistakes
- ✗Forgetting to check discriminant b² − 4ac
- ✗Sign errors on −b
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Slope
Geometry & algebraDefinition
Rise over run between two points: m = (y₂ − y₁) / (x₂ − x₁). Vertical lines have undefined slope.
Example
Points (2, 3) and (6, 11) → slope m = (11 − 3) / (6 − 2) = 2.
Why it matters
Slope is rate of change—speed, marginal cost, and trend lines.
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Triangle properties
GeometryDefinition
Angles sum to 180°. Right triangles obey Pythagoras: a² + b² = c². Area = ½ × base × height.
Example
Legs 3 and 4 → hypotenuse 5; area = 6 square units.
Why it matters
Surveying, graphics, and trigonometry start with triangle relationships.
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Scientific notation
ArithmeticDefinition
Writes numbers as a × 10ⁿ where 1 ≤ |a| < 10. Simplifies very large or small magnitudes.
Example
300,000,000 m/s → 3 × 10⁸ m/s.
Why it matters
Physics and chemistry use scientific notation to avoid counting zeros.
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Permutation & combination
ProbabilityDefinition
Permutations count ordered arrangements; combinations count unordered selections. nPr vs nCr depends on whether order matters.
Example
Choose 3 winners from 10 people (order doesn’t matter) → combination 10C3 = 120 ways.
Why it matters
Lottery odds, scheduling, and password-strength estimates use counting rules.
Common mistakes
- ✗Using combination when order matters (passwords, podiums)
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Matrix
Linear algebraDefinition
Rectangular array of numbers used for linear systems, transformations, and data. Dimensions are rows × columns.
Why it matters
Graphics, statistics (regression), and engineering models rely on matrix operations.
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