Recent Lessons

Show all results for ""

Feature Overview

Ace your exams with our all-in-one platform for creating and sharing quizzes and tests.

Quizzes

Create quizzes and tests automatically from your content using AI.

Flashcards

Automatically turn your notes into digital flashcards.

Share, Export & Embed

Share with classmates or export to Excel and your learning management system.

Stats & Reporting

Auto-grading quizzes and tests with detailed stats and reports.

Mobile Apps

The smarter way to study – wherever you are.

Pricing

Search...

Properties of Equal Ratios in Mathematics

10 Questions

1 Views

Properties of Equal Ratios in Mathematics

Choose a study mode

Play Quiz

Study Flashcards

Spaced Repetition

Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What does the Invertendo property state about ratios?

If $a/b = c/d$, then $a/c = b/d$.

If $a/b = c/d$, then $b/a = d/c$. (correct)

If $a/b = c/d$, then $b/a = c/d$.

If $a/b = c/d$, then $a-b = c-d$.

Which operation is described by the Alternando property?

If $a/b = c/d$, then $a/c = b/d$. (correct)

If $a/b = c/d$, then $a+c = b+d$.

If $a/b = c/d$, then $b/d = a/c$.

If $a/b = c/d$, then $c/d = a+b/b.

What is the result of applying the Dividendo property?

If $a/b = c/d$, then $(a-b)/b = (c-d)/d$. (correct)

If $a/b = c/d$, then $(a-b)/a = (c-d)/c$.

If $a/b = c/d$, then $(a-b)/b = (c+d)/d$.

If $a/b = c/d$, then $(a+b)/b = (c+d)/d$.

Which property provides an equation in the form $(a+b)/b = (c+d)/d$?

Componendo-Dividendo Signup and view all the answers

What utility do these properties of equal ratios provide?

They simplify equations and help in solving problems involving ratios. Signup and view all the answers

What is the result when applying the Componendo property to the ratio $rac{a}{b} = rac{c}{d}$?

$rac{a+b}{b} = rac{c+d}{d}$ Signup and view all the answers

Which equation represents the Dividendo property when applied to the ratio $rac{a}{b} = rac{c}{d}$?

$rac{a-b}{b} = rac{c-d}{d}$ Signup and view all the answers

What is the result of combining the Componendo and Dividendo properties?

$rac{a+b}{a-b} = rac{c+d}{c-d}$ Signup and view all the answers

How is the Componendo property generalized according to the provided information?

$rac{a + mb}{b} = rac{c + md}{d}$ Signup and view all the answers

Which of the following describes the application of the Dividendo property multiple times?

$rac{a-mb}{b} = rac{c-md}{d}$ Signup and view all the answers

Study Notes

Properties of Equal Ratios

Invertendo: If two ratios are equal, then their reciprocals are also equal.
Alternando: If two ratios are equal, then their alternate ratios are also equal.
Dividendo: If two ratios are equal, then the ratio of their differences to their denominators is also equal.
Componendo-Dividendo: If two ratios are equal, then the ratio of their sum to their difference is equal to the ratio of the sum of the corresponding terms of the other ratio to the difference of the corresponding terms.

Componendo

Adding 1 to both sides of the equation $\frac{a}{b} = \frac{c}{d}$ yields $\frac{a+b}{b} = \frac{c+d}{d}$

Dividendo

Subtracting 1 from both sides of the equation $\frac{a}{b} = \frac{c}{d}$ yields $\frac{a-b}{b} = \frac{c-d}{d}$

Componendo-Dividendo

This property is a combination of Componendo and Dividendo.

General Forms

Componendo: If $\frac{a}{b} = \frac{c}{d}$, then $\frac{a + mb}{b} = \frac{c + md}{d}$
Dividendo: If $\frac{a}{b} = \frac{c}{d}$, then $\frac{a-mb}{b} = \frac{c-md}{d}$
These general forms demonstrate the reversibility of Componendo and Dividendo operations.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

This quiz explores the key properties of equal ratios including Invertendo, Alternando, Dividendo, and Componendo-Dividendo. You will test your understanding of these mathematical principles and how they apply in different scenarios. Perfect for students looking to strengthen their grasp of ratio concepts in algebra.