ISEE Upper Level Quantitative Reasoning
A comprehensive course to master the mathematical reasoning skills needed for success on the ISEE Upper Level exam.
Ratios, Proportions, and Rates
Comparing and Relating Quantities
Ratios, proportions, and rates help you make sense of how things relate to each other, from recipes to travel.
Ratios
Show the relationship between two quantities. If there are 2 cats for every 3 dogs, the ratio is 2:3.
Proportions
A proportion is when two ratios are equal, like \( \frac{2}{3} = \frac{4}{6} \).
Rates
A rate compares things with different units, like miles per hour or dollars per pound.
Solving Proportions
You can solve for unknowns using cross-multiplication: If \( \frac{a}{b} = \frac{c}{d} \), then \( ad = bc \).
Everyday Uses
- Cooking (recipes)
- Comparing prices
- Figuring out speed or cost per minute
Key Formula
\[\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc\]
Examples
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.
In a Nutshell
Use ratios, proportions, and rates to compare and solve problems involving different quantities.