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31 results for “fraction”

Formulae (30)

Percentage

\% = \frac{\text{part}}{\text{whole}} \times 100

What fraction of a whole a part represents, out of 100.

Arithmetic & BasicsBasic

Fraction to Decimal

\frac{a}{b} = a \div b

Convert a fraction into a decimal by dividing.

Arithmetic & BasicsBasic

Adding Fractions

\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}

Add two fractions using a common denominator.

Arithmetic & BasicsBasic

Multiplying Fractions

\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}

Multiply numerators and denominators straight across.

Arithmetic & BasicsBasic

Dividing Fractions

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Divide by multiplying by the reciprocal (flip and multiply).

Arithmetic & BasicsBasic

Mixed Number to Fraction

a\frac{b}{c} = \frac{ac + b}{c}

Convert a mixed number to an improper fraction.

Arithmetic & BasicsBasic

Percent to Fraction

p\% = \frac{p}{100}

Convert a percentage to a fraction.

AlgebraIntermediate

Fractional Exponent

a^{m/n} = \sqrt[n]{a^m}

A fractional exponent is a root.

AlgebraIntermediate

Rational Exponent

a^{m/n} = \sqrt[n]{a^m}

A fractional exponent is a root and a power combined.

AlgebraAdvanced

Partial Fraction Setup

\frac{1}{(x-a)(x-b)} = \frac{A}{x-a} + \frac{B}{x-b}

Decompose a rational expression into simpler fractions.

Data Science & MLBasic

Classification Accuracy

Accuracy = \frac{TP + TN}{TP + TN + FP + FN}

Fraction of predictions that are correct.

Data Science & MLIntermediate

Precision

Precision = \frac{TP}{TP + FP}

Of all positive predictions, the fraction that were correct.

Data Science & MLIntermediate

Recall (Sensitivity)

Recall = \frac{TP}{TP + FN}

Of all actual positives, the fraction correctly identified.

Data Science & MLIntermediate

Specificity

Specificity = \frac{TN}{TN + FP}

Of all actual negatives, the fraction correctly identified.

PhysicsAdvanced

Snell's Law

n_1\sin\theta_1 = n_2\sin\theta_2

Refraction of light between two media.

Physics Laws & TheoremsIntermediate

Snell's Law

n_1 \sin\theta_1 = n_2 \sin\theta_2

Light bends when passing between media of different refractive index.

Optics & WavesIntermediate

Snell's Law

n_1\sin\theta_1 = n_2\sin\theta_2

Refraction of light between two media.

Optics & WavesIntermediate

Refractive Index

n = \frac{c}{v}

Ratio of light speed in vacuum to that in a medium.

Optics & WavesAdvanced

Diffraction Grating

d\sin\theta = m\lambda

Condition for constructive interference maxima.

Astronomy & SpaceAdvanced

Redshift

z = \frac{\lambda_{obs} - \lambda_{emit}}{\lambda_{emit}}

Fractional wavelength shift of light.

Astronomy & SpaceAdvanced

Gravitational Redshift

z \approx \frac{GM}{rc^2}

Fractional stretching of light climbing out of gravity.

Materials & CivilBasic

Strain

\varepsilon = \frac{\Delta L}{L_0}

Fractional deformation under load.

Aviation & AeronauticsAdvanced

Breguet Range Equation

R = \dfrac{V}{c}\dfrac{L}{D}\ln\dfrac{W_i}{W_f}

Maximum range of a jet aircraft from speed, efficiency, L/D and fuel fraction.

Aviation & AeronauticsAdvanced

Climb Gradient

\gamma = \dfrac{T - D}{W}

Climb angle (as a fraction) equals excess thrust divided by weight.

Business & CommerceIntermediate

Contribution Margin Ratio

CMR = \dfrac{Price - Variable\ Cost}{Price}

Contribution margin expressed as a fraction of the selling price.

EconomicsIntermediate

Marginal Propensity to Consume

MPC = \dfrac{\Delta C}{\Delta Y}

The fraction of an extra dollar of income that is spent rather than saved.

EconomicsBasic

Unemployment Rate

u = \frac{\text{Unemployed}}{\text{Labor Force}}\times 100

Fraction of the labor force without work.

Environmental ScienceAdvanced

Betz Limit

C_{p,max} = 0.593

Maximum fraction of wind energy a turbine can capture.

Environmental ScienceIntermediate

Albedo

\alpha = \frac{\text{reflected}}{\text{incident}}

Fraction of solar radiation reflected by a surface.

Computer ScienceAdvanced

Amdahl Law

S = \frac{1}{(1-p) + p/s}

Maximum speedup from parallelizing a fraction of a task.

Math Tricks (1)

Common Fraction-Decimal Pairs

Memorize common fraction-to-decimal conversions for instant calculation.

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