Subjects

Careers

Open the App

Subjects

Fun with Ratios: Easy Ways to Understand and Simplify Complex Ratios

Open

9

1

user profile picture

roseee

3/8/2023

Maths

Maths - ratio and proportion

Fun with Ratios: Easy Ways to Understand and Simplify Complex Ratios

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 involving square roots.

Key points:

  • Simplifying ratios by finding common factors
  • Converting between different units of measurement
  • Sharing money or quantities using given ratios
  • Working with fractional proportions
  • Combining and simplifying complex ratios with square roots
...

3/8/2023

779

Unit 9-ratio and proportion
Working with ratios.
Simplifying:
2:4 = 1:2
3:63=1:21
123:369=1:3
examples:
£-1 is worth $1.-14.
how much is $29

View

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.

Unit 9-ratio and proportion
Working with ratios.
Simplifying:
2:4 = 1:2
3:63=1:21
123:369=1:3
examples:
£-1 is worth $1.-14.
how much is $29

View

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 LeastCommonMultipleLeast Common Multiple 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 a:b,b:c,anda:ca:b, b:c, and a:c 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.

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

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and 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 ranked education app in five European countries

4.9+

Average App Rating

21 M

Students use Knowunity

#1

In Education App Charts in 17 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

 

Maths

779

Mar 8, 2023

3 pages

Fun with Ratios: Easy Ways to Understand and Simplify Complex Ratios

user profile picture

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

Unit 9-ratio and proportion
Working with ratios.
Simplifying:
2:4 = 1:2
3:63=1:21
123:369=1:3
examples:
£-1 is worth $1.-14.
how much is $29

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

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.

Unit 9-ratio and proportion
Working with ratios.
Simplifying:
2:4 = 1:2
3:63=1:21
123:369=1:3
examples:
£-1 is worth $1.-14.
how much is $29

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 LeastCommonMultipleLeast Common Multiple 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 a:b,b:c,anda:ca:b, b:c, and a:c 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.

Unit 9-ratio and proportion
Working with ratios.
Simplifying:
2:4 = 1:2
3:63=1:21
123:369=1:3
examples:
£-1 is worth $1.-14.
how much is $29

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 1.14,then1.14, then 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.

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