Proportional Reasoning and Percentages
Five topics on proportional reasoning, the first half of the SAT's Problem-Solving and Data Analysis domain. Ratios and rates, unit conversion, percentages, proportional relationships, and mixtures and weighted averages. The errors here are setup errors: a part treated as a whole, a rate flipped upside down, a percent taken of the wrong base.
Topics
Reference The exponent and radical rules behind every problem in this unit
Multiply like bases (add)
$x^{a}\cdot x^{b} = x^{a+b}$
Divide like bases (subtract)
$\dfrac{x^{a}}{x^{b}} = x^{a-b}$
Power of a power (multiply)
$(x^{a})^{b} = x^{ab}$
Power over a product, never a sum
$(xy)^{a} = x^{a}y^{a}$
Negative exponent (reciprocal)
$x^{-a} = \dfrac{1}{x^{a}}$
Fractional exponent (root)
$x^{\tfrac{m}{n}} = \sqrt[n]{x^{m}}$
Unit 3 tools