ISEE Middle Level Quantitative Reasoning

A course designed to strengthen middle school students' quantitative reasoning skills, focusing on problem-solving and mathematical thinking for the ISEE exam.

Number Sense and OperationsAlgebraic Thinking and PatternsData Analysis and Probability
Ratios, Proportions, and PercentsGeometry and Spatial ReasoningWord Problems and Logical Reasoning
Using Math in Daily LifeMath in Science and TechnologySmart Shopping and Money Math
Time Management for Test DayMultiple Choice Test Tactics
Number Sense and Ope...Algebraic Thinking a...Data Analysis and Pr...Ratios, Proportions,...Geometry and Spatial...Word Problems and Lo...Using Math in Daily ...Math in Science and ...Smart Shopping and M...Time Management for ...Multiple Choice Test...
Advanced Topics

Ratios, Proportions, and Percents

Comparing Quantities

Ratios help you compare two amounts, like the number of apples to oranges. Proportions show that two ratios are equal. Percents are a special way to show ratios out of 100.

How to Use Them

  • Ratios: If there are 2 cats for every 3 dogs, the ratio is 2:3.
  • Proportions: If 1/2 = 2/4, that's a proportion!
  • Percents: 50% means 50 out of 100.

Solving Ratio Problems

Set up proportions to solve real-life problems, like mixing juice or finding discounts during sales.

Why Are They Important?

These concepts are used in cooking, shopping, and comparing test scores.

Common Formula

  • Percent: \( \text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100 \)

Key Formula

\[\text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100\]

Examples

  • If 3 out of 12 students are left-handed, what percent is that?

  • If a recipe calls for 2 cups of sugar for every 5 cups of flour, how much sugar for 10 cups of flour?

In a Nutshell

Helps compare, scale, and find parts of a whole using ratios, proportions, and percents.

Key Terms

Ratio
A comparison of two numbers by division.
Percent
A ratio that compares a number to 100.
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Geometry and Spatial Reasoning