TEAS Math Formulas (TEAS 7)

A concise, printable cheat sheet of formulas you need for TEAS 7 Math. Grouped by lesson with quick practice links.

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Contents

Numbers & Algebra
Measurement & Data

Numbers & Algebra

Converting Fractions, Decimals, and Percents

Decimal → Percent $\text{percent} = (\text{decimal}) \times 100\%$
Percent → Decimal $\text{decimal} = (\text{percent}) \div 100$
Fraction → Decimal $\frac{a}{b} = a \div b$
Decimal → FractionWrite over 10, 100, 1000 … then simplify
Fraction → Percent $\text{percent} = \frac{a}{b} \times 100\%$

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Arithmetic with Rational Numbers

Add/Subtract $\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}$
Multiply $\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$
Divide $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$
Order of OperationsPEMDAS; left→right for × ÷ and + −

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Ordering & Comparing Rational Numbers

Compare Fractions (<) $\frac{a}{b} < \frac{c}{d} \iff ad < bc$
Compare Fractions (>) $\frac{a}{b} > \frac{c}{d} \iff ad > bc$
Compare DecimalsAlign place value; compare digits left→right
Sqrt estimate $k^{2} < n < (k+1)^{2} \Rightarrow k < \sqrt{n} < k+1$

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Percent Problems

Part $\text{part} = \text{percent} \times \text{whole}$
Percent $\text{percent} = \frac{\text{part}}{\text{whole}}$
Whole $\text{whole} = \frac{\text{part}}{\text{percent}}$
Percent Change $\frac{\text{new} - \text{old}}{\text{old}} \times 100\%$

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One‑Variable Linear Equations

Solve $ax + b = c \Rightarrow x = \frac{c - b}{a}$
Distribute $a(b + c) = ab + ac$
Combine like termsAdd coefficients of the same variable

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Ratios & Rates of Change

Ratio $a:b = \frac{a}{b}$
Unit RateValue per 1 unit (divide by the units)
Rate of Change $\frac{\Delta y}{\Delta x}$

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Multi‑Step Word Problems

Distance $d = r \times t$
Percent Error $\left| \frac{\text{measured} - \text{true}}{\text{true}} \right| \times 100\%$

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Estimation & Rounding

Rounding≥ 5 → round up; < 5 → round down (at chosen place)
Compatible numbersChoose close, easy numbers for mental math

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Setting Up & Solving Proportions

Proportion $\frac{a}{b} = \frac{c}{d} \iff ad = bc$
Dosage $\text{Dose} = \left( \frac{\text{Desired}}{\text{Have}} \right) \times \text{Volume}$
Concentration $C = \frac{\text{solute}}{\text{solution}}$

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Expressions, Equations & Inequalities in Context

Inequality flipMultiply/divide by a negative → reverse the inequality sign
Translate words → mathDefine variable; write expression/equation/inequality

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Measurement & Data

Reading Tables, Charts & Graphs

Percent of Whole $\frac{\text{category}}{\text{total}} \times 100\%$
Mean (freq. table) $\bar{x} = \frac{\sum (x_i f_i)}{\sum f_i}$

Bar chart

Pie chart

Red (40)

Blue (35)

Green (25)

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Basic Descriptive Statistics

Mean $\bar{x} = \frac{\sum x}{n}$
MedianMiddle value; even n → average the two middles
ModeMost frequent value
Range $\text{max} - \text{min}$

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Relationships Between Two Variables

Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$
Line $y = mx + b$
Correlationpositive / negative / none

Scatter plot (relationship)

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Geometry Essentials: Perimeter, Area, Volume & Pythagorean

Rectangle $P = 2(l + w),\ A = lw$
Triangle $A = \tfrac{1}{2}bh$
Trapezoid $A = \tfrac{1}{2}(b_1 + b_2)h$
Circle $C = 2\pi r,\ A = \pi r^{2}$
Right Triangle $a^{2} + b^{2} = c^{2}$
Rectangular Prism $V = lwh$
Cube $V = s^{3}$

Rectangle (A = lw)

Right Triangle (a²+b²=c²)

Circle (C = 2πr; A = πr²)

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US–Metric & Intra‑System Conversions

Metric1 km = 1000 m; 1 m = 100 cm = 1000 mm; 1 L = 1000 mL; 1 kg = 1000 g
US Length12 in = 1 ft; 3 ft = 1 yd; 5280 ft = 1 mi
US Volume8 oz = 1 cup; 2 cups = 1 pt; 2 pt = 1 qt; 4 qt = 1 gal
US Weight16 oz = 1 lb
Key Cross‑System1 in = 2.54 cm; 1 lb ≈ 0.454 kg; 1 oz ≈ 29.57 mL; 1 tsp = 5 mL
Temperature $F = \tfrac{9}{5}C + 32,\ \ C = \tfrac{5}{9}(F - 32)$

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