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Equivalent Ratios

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Equivalent Ratios

Study Guide

Key Definition

Equivalent ratios are ratios that express the same relationship between numbers. If $\frac{a}{b} = \frac{c}{d}$, then the ratios $a:b$ and $c:d$ are equivalent.

Important Notes

Equivalent ratios have the same value when simplified.
Cross-multiplication can be used to check if two ratios are equivalent: $a \times d = b \times c$
Simplifying a ratio involves dividing both parts by their greatest common factor.
Ratios can be expressed in different forms, such as $\frac{a}{b}$ or $a:b$.
Always check for the simplest form of a ratio for clarity.

Mathematical Notation

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

$:$ represents ratio notation

$=$ represents equality

$×$ represents multiplication

Use ':' to separate terms in a ratio, '=' to show equivalence, and '×' for cross multiplication.

Why It Works

Equivalent ratios work because they maintain the same relationship between quantities by scaling them up or down by the same factor, keeping the proportion constant.

Remember

To find equivalent ratios, multiply or divide both terms of the ratio by the same non-zero number.

Quick Reference

Cross Multiplication:$a \times d = b \times c$

Understanding Equivalent Ratios

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

An equivalent ratio shows the same relationship between numbers even when scaled. For example, the ratio 2:5 can also be written as 4:10 because multiplying both terms by 2 yields 4:10, and as fractions, $\frac{2}{5} = \frac{4}{10}$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Are the ratios $\frac{6}{9}$ and $\frac{2}{3}$ equivalent?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have $15$ apples and $5$ oranges. How can you express their ratio?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Determine if $\frac{24}{36}$ and $\frac{2}{3}$ are equivalent.

Challenge Quiz

Single Choice Quiz

Advanced

Which of the following pairs are equivalent ratios? Pair 1: $\frac{10}{15}$ and $\frac{2}{3}$. Pair 2: $\frac{14}{28}$ and $\frac{1}{2}$

Recap

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Review key concepts and takeaways