This lesson covers how to simplify complex ratios in math... Show more
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9
1
roseee
7/16/2025
Maths
Maths - ratio and proportion
780
•
Jul 16, 2025
•
Fun with Ratios: Easy Ways to Understand and Simplify Complex Ratios
roseee
@rosee_t
Sharing in Ratios and Fractional Proportions
This page focuses on sharing in ratios and finding fractional proportions.
Sharing in ratios involves dividing a total amount proportionally based on given ratio parts. For example, sharing £24 in a 1:2 ratio would result in £8 and £16.
Example: Sharing £24 in a 7:5 ratio results in £14 and £10
The page also covers finding fractional proportions, which involves calculating parts of a whole based on given ratios.
Vocabulary: Equivalent fractions are fractions that represent the same value, such as 1/2 and 3/6
Combining ratios is introduced, showing how to work with multiple related ratios. An example is given of a car dealership with three types of cars: diesel, petrol, and electric. The ratios between these types are combined to form a single ratio representing all three types.
Highlight: When combining ratios, multiply the terms of one ratio by the other ratio to find the equivalent combined ratio
This concept is crucial in various real-world applications, such as resource allocation, financial planning, and statistical analysis.
Complex Ratios and Advanced Simplification
This page delves into more advanced topics related to combining and expanding complex ratios.
The page starts with an example of expanding and simplifying ratios involving squares and triangles. It demonstrates how to manipulate ratios with different geometric shapes.
Example: A ratio of squares to triangles 3:4 can be expanded to 15:20:4 when considering rectangles as well
Complex ratios involving square roots are introduced. These ratios require more sophisticated simplification techniques.
Vocabulary: LCM is often used in simplifying complex ratios
The page provides step-by-step guidance on simplifying complex ratios involving square roots. It shows how to expand, factorize, and simplify these ratios.
Highlight: When working with square roots in ratios, it's often helpful to simplify the square roots first before combining terms
The final example demonstrates how to combine three complex ratios into a single simplified ratio. This process involves careful manipulation of square roots and fractions.
These advanced ratio techniques are particularly useful in higher-level mathematics, physics, and engineering applications where precise proportions involving complex numbers are required.
Simplifying Ratios and Scale Models
This page covers techniques for simplifying ratios and working with scale models.
Simplifying ratios involves reducing them to their lowest terms by dividing both sides by their greatest common factor. For example, 2:4 simplifies to 1:2, and 3:63 simplifies to 1:21.
Example: The ratio 123:369 simplifies to 1:3
The page also covers currency conversions using ratios. For instance, if £1 is worth 291.84 would be equivalent to £256.
Scale models are introduced, showing how ratios are used to represent real-world measurements:
Highlight: Common scale conversions include:
- 1 cm = 10 mm
- 1 m = 1000 mm
- 1 m = 100 cm
- 1 km = 1000 m
- 1 km = 1,000,000 mm
These scale conversions are essential in fields like architecture, engineering, and cartography where accurate representations of large objects or distances are needed.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
You have the choice, we offer a 100% secure payment via PayPal or an Amazon gift card. There is no limit to how much you can earn.
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
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.
Stefan S
iOS user
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
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
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!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
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
iOS user
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
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.
Stefan S
iOS user
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
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
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!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
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
iOS user
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
Fun with Ratios: Easy Ways to Understand and Simplify Complex Ratios
roseee
@rosee_t
This lesson covers how to simplify complex ratios in math, understanding fractional proportions and ratios, and sharing money using ratios in math problems. It explores ratio simplification, scale models, sharing in ratios, and working with complex ratios... Show more
Sharing in Ratios and Fractional Proportions
This page focuses on sharing in ratios and finding fractional proportions.
Sharing in ratios involves dividing a total amount proportionally based on given ratio parts. For example, sharing £24 in a 1:2 ratio would result in £8 and £16.
Example: Sharing £24 in a 7:5 ratio results in £14 and £10
The page also covers finding fractional proportions, which involves calculating parts of a whole based on given ratios.
Vocabulary: Equivalent fractions are fractions that represent the same value, such as 1/2 and 3/6
Combining ratios is introduced, showing how to work with multiple related ratios. An example is given of a car dealership with three types of cars: diesel, petrol, and electric. The ratios between these types are combined to form a single ratio representing all three types.
Highlight: When combining ratios, multiply the terms of one ratio by the other ratio to find the equivalent combined ratio
This concept is crucial in various real-world applications, such as resource allocation, financial planning, and statistical analysis.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Complex Ratios and Advanced Simplification
This page delves into more advanced topics related to combining and expanding complex ratios.
The page starts with an example of expanding and simplifying ratios involving squares and triangles. It demonstrates how to manipulate ratios with different geometric shapes.
Example: A ratio of squares to triangles 3:4 can be expanded to 15:20:4 when considering rectangles as well
Complex ratios involving square roots are introduced. These ratios require more sophisticated simplification techniques.
Vocabulary: LCM is often used in simplifying complex ratios
The page provides step-by-step guidance on simplifying complex ratios involving square roots. It shows how to expand, factorize, and simplify these ratios.
Highlight: When working with square roots in ratios, it's often helpful to simplify the square roots first before combining terms
The final example demonstrates how to combine three complex ratios into a single simplified ratio. This process involves careful manipulation of square roots and fractions.
These advanced ratio techniques are particularly useful in higher-level mathematics, physics, and engineering applications where precise proportions involving complex numbers are required.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Simplifying Ratios and Scale Models
This page covers techniques for simplifying ratios and working with scale models.
Simplifying ratios involves reducing them to their lowest terms by dividing both sides by their greatest common factor. For example, 2:4 simplifies to 1:2, and 3:63 simplifies to 1:21.
Example: The ratio 123:369 simplifies to 1:3
The page also covers currency conversions using ratios. For instance, if £1 is worth 291.84 would be equivalent to £256.
Scale models are introduced, showing how ratios are used to represent real-world measurements:
Highlight: Common scale conversions include:
- 1 cm = 10 mm
- 1 m = 1000 mm
- 1 m = 100 cm
- 1 km = 1000 m
- 1 km = 1,000,000 mm
These scale conversions are essential in fields like architecture, engineering, and cartography where accurate representations of large objects or distances are needed.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
You have the choice, we offer a 100% secure payment via PayPal or an Amazon gift card. There is no limit to how much you can earn.
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
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.
Stefan S
iOS user
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
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
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!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
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
iOS user
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
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.
Stefan S
iOS user
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
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
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!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
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
iOS user
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