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Direct & inverse proportion

Proportions with Squares and Roots Worksheet and Examples

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Proportions with Squares and Roots Worksheet and Examples
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Poppy

@pgtips23

·

448 Followers

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A comprehensive guide to direct and inverse proportion problems, including squares, roots, and real-world applications. The material covers essential mathematical concepts for solving proportional relationships with practical examples and graphical representations.

• Direct proportion with squares and roots concepts are thoroughly explained with step-by-step solutions
• Detailed coverage of inverse proportion with squares and roots calculations and formulas
• Practical applications through written proportion problems, specifically focusing on man-hours scenarios
• Visual representations of different proportional relationships through graphs
• Step-by-step problem-solving methodology for both simple and complex proportional relationships

28/06/2022

168

<h2 id="directproportion">Direct proportion</h2> <p>Direct proportion occurs when one quantity increases in the same proportion as another

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Written Proportion Applications and Graphical Representations

This page focuses on practical applications of proportion through written problems and visual representations through graphs.

Example: A practical written proportion question involving man-hours demonstrates how 3 mechanics taking 40 minutes to service a car can be calculated for 5 mechanics using inverse proportion.

Highlight: When solving man-hours problems, it's crucial to assume all workers maintain the same work rate.

Definition: In man-hours calculations, more workers result in less time (inverse proportion), following the principle that time × number of workers = constant.

Example: The solution process involves:

  1. Finding total man-minutes (3 × 40 = 120)
  2. Dividing by new number of workers (120 ÷ 5 = 24 minutes)

Highlight: The page includes graphs showing various proportional relationships, including y = k/x² and y = k√x, helping visualize different types of proportional relationships.

<h2 id="directproportion">Direct proportion</h2> <p>Direct proportion occurs when one quantity increases in the same proportion as another

View

Direct and Inverse Proportion Fundamentals

This page introduces fundamental concepts of direct and inverse proportion, with detailed explanations of more complex relationships involving squares and roots.

Definition: Direct proportion occurs when one quantity increases in the same proportion as another quantity.

Example: When A is directly proportional to B, and B = 4 results in A = 0.8, we can find A when B = 3 using the formula A = KB, where K is the constant of proportionality.

Highlight: For direct proportion with squares and roots, problems can involve relationships like w ∝ v³ or p ∝ √m.

Vocabulary: The symbol ∝ means "proportional to" and is used to express relationships between quantities.

Example: In a problem where p is directly proportional to the square root of m, with p = 18 when m = 36, we can find m when p = 100 using the formula p = K√m.

Similar content

Know Direct and Indirect Proportion thumbnail

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434

10/11

Direct and Indirect Proportion

contents: - what is indirect and direct proportion - examples

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Subjects

/

Maths

/

Ratio, proportion & rates of change

/

Direct & inverse proportion

Proportions with Squares and Roots Worksheet and Examples

user profile picture

Poppy

@pgtips23

·

448 Followers

Follow

A comprehensive guide to direct and inverse proportion problems, including squares, roots, and real-world applications. The material covers essential mathematical concepts for solving proportional relationships with practical examples and graphical representations.

• Direct proportion with squares and roots concepts are thoroughly explained with step-by-step solutions
• Detailed coverage of inverse proportion with squares and roots calculations and formulas
• Practical applications through written proportion problems, specifically focusing on man-hours scenarios
• Visual representations of different proportional relationships through graphs
• Step-by-step problem-solving methodology for both simple and complex proportional relationships

28/06/2022

168

 

10/11

 

Maths

7

<h2 id="directproportion">Direct proportion</h2> <p>Direct proportion occurs when one quantity increases in the same proportion as another

Written Proportion Applications and Graphical Representations

This page focuses on practical applications of proportion through written problems and visual representations through graphs.

Example: A practical written proportion question involving man-hours demonstrates how 3 mechanics taking 40 minutes to service a car can be calculated for 5 mechanics using inverse proportion.

Highlight: When solving man-hours problems, it's crucial to assume all workers maintain the same work rate.

Definition: In man-hours calculations, more workers result in less time (inverse proportion), following the principle that time × number of workers = constant.

Example: The solution process involves:

  1. Finding total man-minutes (3 × 40 = 120)
  2. Dividing by new number of workers (120 ÷ 5 = 24 minutes)

Highlight: The page includes graphs showing various proportional relationships, including y = k/x² and y = k√x, helping visualize different types of proportional relationships.

<h2 id="directproportion">Direct proportion</h2> <p>Direct proportion occurs when one quantity increases in the same proportion as another

Direct and Inverse Proportion Fundamentals

This page introduces fundamental concepts of direct and inverse proportion, with detailed explanations of more complex relationships involving squares and roots.

Definition: Direct proportion occurs when one quantity increases in the same proportion as another quantity.

Example: When A is directly proportional to B, and B = 4 results in A = 0.8, we can find A when B = 3 using the formula A = KB, where K is the constant of proportionality.

Highlight: For direct proportion with squares and roots, problems can involve relationships like w ∝ v³ or p ∝ √m.

Vocabulary: The symbol ∝ means "proportional to" and is used to express relationships between quantities.

Example: In a problem where p is directly proportional to the square root of m, with p = 18 when m = 36, we can find m when p = 100 using the formula p = K√m.

Similar content

Maths - Direct and Indirect Proportion

contents: - what is indirect and direct proportion - examples

13

434

0

Know Direct and Indirect Proportion thumbnail

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the #1 education app in five European countries

4.9+

Average app rating

15 M

Pupils love Knowunity

#1

In education app charts in 12 countries

950 K+

Students have uploaded notes

Still not convinced? See what other students are saying...

iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.