Ratios, percentages and units

Learn to compare quantities and interpret numerical models using ratios, percentages and units. This precalculus foundation set develops part-to-part and part-to-whole reasoning, unit rates, percentage representations, percentage-point changes and conversions of both simple and compound units. It also checks whether a calculation produces the kind of quantity the situation requires.

The early questions establish basic meanings before moving to map scales, density, concentration and unit-price comparisons. Later questions examine reverse percentages and successive changes, where choosing the correct reference amount matters more than memorizing a formula. You will distinguish a discount from the proportion of a price remaining and a percentage-point difference from a relative percentage change.

Use the conversion facts stated in each question, keep units attached to your calculations and estimate whether the result should increase or decrease. Both single-answer and select-all questions are included. Explanations show the numerical steps and the units that justify them. Signed arithmetic and fraction fluency are useful prerequisites; formal equation-solving techniques are not required. These skills support later work on rates of change, scaling and mathematical models.