ATI TEAS 7 Math Formula & Conversion Sheet Notes

Fractions, Decimals, and Percents

• Fraction to Decimal Conversion:   $\text{Fraction} \rightarrow \text{Decimal}: \text{numerator} \div \text{denominator}$

• Decimal to Percent Conversion:   $\text{Decimal} \rightarrow \text{Percent}: \text{decimal} \times 100$

• Percent to Decimal Conversion:   $\text{Percent} \rightarrow \text{Decimal}: \text{percent} \div 100$

• Part Calculation:   $\text{Part} = \text{percent} \times \text{whole}$

• Percent Calculation:   $\text{Percent} = \frac{\text{part}}{\text{whole}} \times 100$

• Percent Change Formula:   $\text{Percent change} = \frac{\text{new} - \text{original}}{\text{original}} \times 100$

• Percent Increase / Decrease Formula:   $\text{Percent increase/decrease} = \frac{\text{amount of change}}{\text{original}} \times 100$

• Fraction Addition and Subtraction:   Find a common denominator, then add or subtract the numerators.

• Fraction Multiplication:   $\left(\frac{a}{b}\right)\left(\frac{c}{d}\right) = \frac{a \times c}{b \times d}$

• Fraction Division:   $\left(\frac{a}{b}\right) \div \left(\frac{c}{d}\right) = \left(\frac{a}{b}\right)\left(\frac{d}{c}\right)$

Ratios, Proportions, and Rates

• Proportion Equivalence and Cross-Multiplication:   $\frac{a}{b} = \frac{c}{d} \rightarrow a \times d = b \times c$

• Unit Rate Formula:   $\text{Unit rate} = \text{amount} \div 1\,\text{unit}$

• Distance Formula:   $d = r \times t$

• Rate Formula:   $r = \frac{d}{t}$

• Time Formula:   $t = \frac{d}{r}$

Algebra

• Distributive Property:   $a(b + c) = a \times b + a \times c$

• Slope Formula:   $m = \frac{y_2 - y_1}{x_2 - x_1}$

• Slope-Intercept Form:   $y = m \times x + b$

• Point-Slope Form:   $y - y_1 = m(x - x_1)$

• Quadratic Formula:   $x = \frac{-b \pm \sqrt{b^2 - 4 \times a \times c}}{2 \times a}$

• Exponent Rules:

  • Product Rule: $a^m \cdot a^n = a^{m + n}$
  • Quotient Rule: $\frac{a^m}{a^n} = a^{m - n}$
  • Power Rule: $(a^m)^n = a^{m \times n}$
  • Negative Exponent Rule: $a^{-n} = \frac{1}{a^n}$

Geometry: Area and Perimeter

• Rectangle Area:   $A = l \times w$

• Rectangle Perimeter:   $P = 2 \times l + 2 \times w$

• Square Area:   $A = s^2$

• Square Perimeter:   $P = 4 \times s$

• Triangle Area:   $A = \frac{1}{2} \times b \times h$

• Parallelogram Area:   $A = b \times h$

• Trapezoid Area:   $A = \frac{1}{2}(b_1 + b_2) \times h$

Circles

• Circle Area:   $A = \pi \times r^2$

• Circle Circumference:   $C = 2 \times \pi \times r$$C = \pi \times d$

• Circle Diameter:   $d = 2 \times r$

• Circle Radius:   $r = \frac{d}{2}$

Volume

• Rectangular Prism Volume:   $V = l \times w \times h$

• Cube Volume:   $V = s^3$

• Cylinder Volume:   $V = \pi \times r^2 \times h$

• General Prism Volume:   $V = B \times h$   Where $B$ equals the area of the base.

Right Triangles

• Pythagorean Theorem:   $a^2 + b^2 = c^2$

• Hypotenuse Properties:   $c$ is the longest side and is situated opposite the right angle.

• Common Pythagorean Triples:   $3-4-5$$5-12-13$

Statistics and Data

• Mean Formula:   $\text{Mean} = \text{sum of values} \div \text{number of values}$

• Median Definition:   Middle value after ordering the data.

• Mode Definition:   Most frequent value.

• Range Formula:   $\text{Range} = \text{maximum} - \text{minimum}$

• Weighted Average Formula:   $\text{Weighted average} = \frac{\Sigma(\text{value} \times \text{weight})}{\Sigma(\text{weights})}$

Simple Interest and Financial Mathematics

• Simple Interest Formula:   $I = P \times r \times t$

• Total Amount Formula:   $A = P + I$

• Discount Formula:   $\text{discount} = \text{original price} \times \text{discount rate}$

• Sale Price Formula:   $\text{Sale price} = \text{original price} - \text{discount}$

• Tax Formula:   $\text{Tax} = \text{price} \times \text{tax rate}$

• Total Price After Tax Formula:   $\text{Total after tax} = \text{price} + \text{tax}$

U.S. Customary Conversions

• Length Conversions:

  • $12\,\text{in} = 1\,\text{ft}$
  • $3\,\text{ft} = 1\,\text{yd}$
  • $5280\,\text{ft} = 1\,\text{mi}$

• Weight Conversions:

  • $16\,\text{oz} = 1\,\text{lb}$
  • $2000\,\text{lb} = 1\,\text{ton}$

• Volume Conversions:

  • $8\,\text{fl oz} = 1\,\text{cup}$
  • $2\,\text{cups} = 1\,\text{pint}$
  • $2\,\text{pints} = 1\,\text{quart}$
  • $4\,\text{quarts} = 1\,\text{gallon}$

• High-Yield Volume Equivalence:

  • $1\,\text{gallon} = 16\,\text{cups} = 128\,\text{fl oz}$

Metric Conversions

• Length Conversions:

  • $10\,\text{mm} = 1\,\text{cm}$
  • $100\,\text{cm} = 1\,\text{m}$
  • $1000\,\text{m} = 1\,\text{km}$

• Mass Conversions:

  • $1000\,\text{mg} = 1\,\text{g}$
  • $1000\,\text{g} = 1\,\text{kg}$

• Volume Conversions:

  • $1000\,\text{mL} = 1\,\text{L}$

• Metric Ladder Ordering (from largest to smallest prefix):

  • $\text{kilo} \rightarrow \text{hecto} \rightarrow \text{deka} \rightarrow \text{base} \rightarrow \text{deci} \rightarrow \text{centi} \rightarrow \text{milli}$

Measurement, Volume Equivalence, and Temperature

• Fahrenheit to Celsius Conversion Formula:   $C = (F - 32) \times \frac{5}{9}$

• Celsius to Fahrenheit Conversion Formula:   $F = \left(C \times \frac{9}{5}\right) + 32$

• Metric Volume Approximations and Equivalences:

  • $1\,\text{L} \approx 1000\,\text{mL}$
  • $1\,\text{mL} = 1\,\text{cm}^3$

Probability

• Probability Formula:   $P(\text{event}) = \frac{\text{favorable outcomes}}{\text{total possible outcomes}}$

• Probability Expressed as a Percent:   $\text{Probability percent} = \text{probability} \times 100$

• Complement Rule:   $P(\text{not } A) = 1 - P(A)$

• Independent Events Rule:   $P(A \text{ and } B) = P(A) \times P(B)$

Order of Operations and Number Rules

• PEMDAS Order of Operations Sequence:

  1. Parentheses
  2. Exponents
  3. Multiplication / Division (evaluated left-to-right)
  4. Addition / Subtraction (evaluated left-to-right)

• Absolute Value Definition:   $|x| = \text{distance from } 0$

• Parity Multiplication Rules:

  • $\text{even} \times \text{even} = \text{even}$
  • $\text{odd} \times \text{odd} = \text{odd}$
  • $\text{even} \times \text{odd} = \text{even}$

• Sign Multiplication Rules:

  • $\text{negative} \times \text{negative} = \text{positive}$
  • $\text{positive} \times \text{negative} = \text{negative}$

Must-Memorize Quick List and TEAS Strategy

• Core Formula and Fact Quick Reference:

  • Distance, rate, time: $d = r \times t$
  • Rectangle area: $A = l \times w$
  • Rectangle perimeter: $P = 2 \times l + 2 \times w$
  • Triangle area: $A = \frac{1}{2} \times b \times h$
  • Circle area: $A = \pi \times r^2$
  • Circle circumference: $C = 2 \times \pi \times r$
  • Rectangular prism volume: $V = l \times w \times h$
  • Right triangles: $a^2 + b^2 = c^2$
  • Slope: $m = \frac{y_2 - y_1}{x_2 - x_1}$
  • Linear equations: $y = m \times x + b$
  • Simple interest: $I = P \times r \times t$
  • Average: $\text{Mean} = \text{sum} \div \text{count}$
  • Data spread: $\text{Range} = \text{max} - \text{min}$
  • Proportions: $\frac{a}{b} = \frac{c}{d} \rightarrow a \times d = b \times c$
  • Volume conversion: $1\,\text{gal} = 16\,\text{cups}$
  • Length conversion: $1\,\text{ft} = 12\,\text{in}$
  • Weight conversion: $1\,\text{lb} = 16\,\text{oz}$
  • Metric volume: $1\,\text{L} = 1000\,\text{mL}$
  • Metric mass: $1\,\text{kg} = 1000\,\text{g}$

• TEAS Test Strategy and High-Yield Preparation Areas:

  • Know how to apply these formulas in word problems.
  • Pay special attention to fractions, decimals, percentages, ratios/proportions, unit conversions, equations, graphs, geometry, and data interpretation.