Ratios, Rates & Proportions Worksheets

Write a ratio comparing two quantities using ratio language and the three notations (a to b, a:b, a/b).

Compute a unit rate (amount per one unit) by dividing the first quantity by the second.

Calculate the price per unit for two options and decide which is the better buy.

Scale a ratio up or down by a whole-number factor to find the missing term in an equivalent ratio.

Fill in missing entries of a ratio table by applying the constant multiplicative relationship between rows or columns.

Convert a measurement by multiplying by a conversion ratio arranged so the old unit cancels — the reasoning behind unit conversion, not a remembered rule.

Plot the pairs from a ratio table on the coordinate plane, see that equivalent ratios fall on a straight line through the origin, and read the unit rate at x = 1.

Find a unit rate when both quantities are fractions — half a mile in a quarter of an hour, three quarters of a liter in a third of a minute. Dividing by a fraction means multiplying by its reciprocal.

Solve for the unknown in a proportion of the form a/b = x/d using cross multiplication.

Set up and solve a proportion from a real-world situation involving scaling, recipes, maps, or similar rates.

Decide whether two quantities are proportional, find the constant of proportionality in a table, graph, equation or description, write y = kx, and say what (0, 0) and (1, r) mean.