ISEE Middle Level Math

ISEE Middle Level Math covers essential mathematical concepts and problem-solving skills needed for middle school students preparing for the ISEE exam.

Basic Concepts

Ratios, Proportions, and Rates

Comparing Quantities

Ratios, proportions, and rates help compare different quantities, whether it's measuring ingredients or calculating speed.

Ratios

A ratio compares two values. If there are 2 cats for every 3 dogs, the ratio is 2:3.

Proportions

A proportion is an equation that shows two ratios are equal, like \( \frac{a}{b} = \frac{c}{d} \).

Rates

A rate is a special ratio that compares two different units, like miles per hour or price per pound.

Why They Matter

Understanding these concepts helps you solve problems like scaling recipes or figuring out travel time.

Solving Proportions

You can solve for a missing value using cross-multiplication: If \( \frac{a}{b} = \frac{c}{d} \), then \( a \times d = b \times c \).

Examples

  • A recipe calls for 2 cups of flour for every 3 cups of sugar. That's a 2:3 ratio.

  • If a car travels 150 miles in 3 hours, its rate is 50 miles per hour.

In a Nutshell

Ratios, proportions, and rates help you compare and solve real-world problems.