SSAT Upper Level Quantitative (Math)

This subject focuses on the quantitative reasoning and mathematical skills required for the SSAT Upper Level exam.

Arithmetic and Number PropertiesFractions, Decimals, and PercentsRatios, Proportions, and Rates
Algebraic Expressions and EquationsGeometry: Shapes, Area, and PerimeterData Analysis and Probability
Budgeting and Money MathCooking and RecipesTravel Planning and Maps
Smart Guessing and EliminationTime Management and Pacing
Arithmetic and Numbe...Fractions, Decimals,...Ratios, Proportions,...Algebraic Expression...Geometry: Shapes, Ar...Data Analysis and Pr...Budgeting and Money ...Cooking and RecipesTravel Planning and ...Smart Guessing and E...Time Management and ...
Basic Concepts

Ratios, Proportions, and Rates

Comparing Amounts

Ratios compare two quantities, proportions show two equal ratios, and rates describe how one quantity changes compared to another.

How to Use Ratios and Proportions

  • Ratio: Written as \( a:b \) or \( \frac{a}{b} \).
  • Proportion: An equation that shows two ratios are equal (\( \frac{a}{b} = \frac{c}{d} \)).
  • Rate: A special ratio where the units are different (like miles per hour).

Solving Proportion Problems

Cross-multiply to solve for unknowns: If \( \frac{a}{b} = \frac{c}{d} \), then \( a \times d = b \times c \).

Everyday Uses

Recipes use ratios, speed limits use rates, and maps use proportions for scale.

Examples

  • If a recipe calls for 2 cups of flour for every 3 cups of sugar, the ratio is 2:3.

  • If a car travels 60 miles in 2 hours, its rate is 30 miles per hour.

In a Nutshell

Ratios, proportions, and rates help us compare and relate different quantities.

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Algebraic Expressions and Equations