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Proportions

Master proportions with interactive lessons and practice problems! Designed for students like you!

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Proportions

Study Guide

Key Definition

Proportions are comparisons of two equal ratios, expressed as $\frac{a}{b} = \frac{x}{y}$

Important Notes

A proportion states that two ratios are equal: $\frac{a}{b} = \frac{x}{y}$
Cross multiplication helps solve proportions: $b \times x = a \times y$
The terms $a$ and $y$ are called extremes.
The terms $b$ and $x$ are called means.
Proportions can be written using colons: $5 : 7 = 10 : 14$

Mathematical Notation

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

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

Remember to use proper notation when solving problems

Why It Works

Cross multiplication works because multiplying both sides of the proportion $\frac{a}{b} = \frac{x}{y}$ by $b \cdot y$ results in a balanced equation.

Remember

Always simplify ratios before comparing them in proportions. Use $\frac{a}{b}$ and $\frac{x}{y}$ for accurate cross multiplication.

Quick Reference

Cross Product:$b \times x = a \times y$

Understanding Proportions

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A proportion states that two ratios are equal. For example, $\frac{1}{2} = \frac{2}{4}$ shows how one half is the same as two quarters.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which of the following equations holds true as a proportion?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

If you have 45 T-shirts in 5 suitcases, how many suitcases will you need for 90 T-shirts?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If the ratio of cats to dogs is $3 : 5$ and there are 15 cats, how many dogs are there?

Challenge Quiz

Single Choice Quiz

Advanced

Solve the proportion $\frac{x}{4} = \frac{6}{8}$ for $x$.

Recap

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Review key concepts and takeaways