A comprehensive course to master the mathematical reasoning skills needed for success on the ISEE Upper Level exam.
Ratios, proportions, and rates help you make sense of how things relate to each other, from recipes to travel.
Show the relationship between two quantities. If there are 2 cats for every 3 dogs, the ratio is 2:3.
A proportion is when two ratios are equal, like \( \frac{2}{3} = \frac{4}{6} \).
A rate compares things with different units, like miles per hour or dollars per pound.
You can solve for unknowns using cross-multiplication: If \( \frac{a}{b} = \frac{c}{d} \), then \( ad = bc \).
\[\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc\]
If 3 pencils cost $1.50, the rate is $0.50 per pencil.
A recipe calls for 2 cups of flour for every 3 eggs. For 6 eggs, you need 4 cups of flour.
Use ratios, proportions, and rates to compare and solve problems involving different quantities.