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Rates & Ratios

Master rates & ratios with interactive lessons and practice problems! Designed for students like you!

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Rates & Ratios

Study Guide

Key Definition

A ratio is a comparison of two numbers, such as $3 : 5$ or $\frac{3}{5}$. A rate is a comparison of two quantities with different units, like $5 \, \text{miles per} \, 3 \, \text{hours}$.

Important Notes

A ratio can be simplified by dividing both terms by their greatest common factor, e.g., $6 : 21$ simplifies to $2 : 7$.
The total of all parts in a ratio is the sum of the individual parts.
Rates often describe speed, cost, or density.
Understanding ratios helps in comparing different quantities.
Simplifying rates and ratios makes them easier to interpret.

Mathematical Notation

$\frac{a}{b}$ represents a fraction

$:$ is used to denote a ratio

$+$ represents addition

$-$ represents subtraction

Remember to use proper notation when solving problems

Why It Works

Ratios and rates provide a way to compare quantities, allowing us to understand relationships and solve problems involving proportions and conversions.

Remember

Ratios can be simplified just like fractions, and rates can help compare quantities with different units.

Quick Reference

Simplified Ratio:$\frac{6}{21} = \frac{2}{7}$

Rate Example:$34 \, \text{dollars per square foot}$

Understanding Rates & Ratios

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Ratios compare two numbers, like $3 : 5$, and can be written as fractions $\frac{3}{5}$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the simplified form of the ratio $6 : 21$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have a part-time job that pays $10$ dollars per hour. How much do you earn if you work $15$ hours?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If the ratio of boys to girls in a class is $3 : 4$ and there are $28$ students, how many are boys?

Challenge Quiz

Single Choice Quiz

Advanced

If the rate of speed is $60 \, \text{miles per hour}$, how far will you travel in $2.5$ hours?

Recap

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Review key concepts and takeaways