pAIrmatic Lessons

Ratios, Rates and Variation

Grade 6 Grade 7 Algebra 2

Arithmetic and pre-algebraOrder of Operations and Number Properties Divisibility Rules, Factors and Multiples Fractions and Decimals Integers and Absolute Value Percents and Consumer MathRatios, Rates and VariationDistance, Rate, Time and Work Unit Conversions

Proportional relationships

Direct variation

y = k x

k = y/x, the constant of proportionality

Constant of proportionality

k = \frac{y}{x}

x ≠ 0

Other variation

Inverse variation

y = \frac{k}{x} or x y = k

x ≠ 0

Joint variation

z = k x y

Combined variation

z = \frac{k x}{y}

y ≠ 0

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