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Proportions with Squares and Roots Worksheet and Examples

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Poppy

6/28/2022

Maths

Proportion

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Ratio, proportion & rates of change

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Direct & inverse proportion

Proportions with Squares and Roots Worksheet and Examples

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

...

6/28/2022

261

<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 inverseproportioninverse proportion, following the principle that time × number of workers = constant.

Example: The solution process involves:

  1. Finding total man-minutes 3×40=1203 × 40 = 120
  2. Dividing by new number of workers 120÷5=24minutes120 ÷ 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.

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Subjects

Maths

Ratio, proportion & rates of change

Direct & inverse proportion

 

Maths

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261

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Jul 21, 2025

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2 pages

Proportions with Squares and Roots Worksheet and Examples

user profile picture

Poppy

@pgtips23

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 rootsconcepts are... Show more

<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 inverseproportioninverse proportion, following the principle that time × number of workers = constant.

Example: The solution process involves:

  1. Finding total man-minutes 3×40=1203 × 40 = 120
  2. Dividing by new number of workers 120÷5=24minutes120 ÷ 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

Sign up to see the contentIt's free!

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Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

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.

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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

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This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

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Brad T

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Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

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Greenlight Bonnie

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Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

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This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user