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Changing Ratios and Algebraic Solutions
This page focuses on solving changing ratio problems with algebra, providing a comprehensive example and step-by-step solution process.
The example problem involves Jan and Kim's marbles, initially in a ratio of 5:6. After Jan gains 2 marbles, the new ratio becomes 7:8. The goal is to determine how many marbles each owned initially.
Example: Jan and Kim own numbers of marbles that are in the ratio 5:6. Jan gains 2 more marbles and the ratio is now 7:8. How many marbles do each own initially?
The solution process involves:
- Writing the initial ratio in algebraic form (5x : 6x)
- Expressing the new ratio after the change
- Setting up an equation based on the new ratio
- Using cross multiplication to solve for x
- Substituting the value of x to find the original numbers of marbles
Highlight: This problem demonstrates how to apply algebraic techniques to solve complex ratio problems involving changes in quantities.
The solution reveals that initially, Jan owned 40 marbles and Kim owned 48 marbles.
Vocabulary: Changing ratios refer to situations where the ratio between quantities changes due to an increase or decrease in one or more of the quantities involved.
This example illustrates the power of algebra in solving ratio problems, especially when dealing with changing ratios. It combines the concepts of cross multiplication, algebraic manipulation, and ratio analysis to arrive at a precise solution.
Quote: "Initially Jan owned 40, Kim owned 48"
This page provides valuable practice for students preparing for exams like GCSE, where changing ratio questions and algebraic ratio GCSE questions are common.
Solving Ratio Problems with Cross Multiplication
This page introduces the concept of using cross multiplication to solve ratio problems with variables. It provides a step-by-step example of how to apply this method effectively.
The example problem involves two brothers, Rich and Andrew, sharing money in a ratio of 2:7, with Andrew receiving £30 more than Rich. The solution demonstrates how to use blocks to represent the ratio and solve for the total amount shared.
Example: Two brothers, Rich and Andrew, share a sum of money in the ratio 2:7. Andrew gets £30 more than Rich. Calculate how much the brothers share.
The solution process involves:
- Representing the difference between the ratio parts (7 - 2 = 5)
- Assigning a value to the difference
- Calculating the value of one block (£6)
- Determining the total amount shared (6 × (7 + 2) = £54)
Highlight: This method of using blocks to represent ratio parts is particularly useful for visualizing and solving ratio problems.
The page also covers finding the value of n in a ratio, using the example : 2n = 3 : 5. This introduces the concept of cross multiplication for solving proportions with variables.
Vocabulary: Cross multiplication is a technique used to solve proportions by multiplying the numerator of each fraction by the denominator of the other fraction.
The solution process for finding n involves:
- Cross multiplying the ratios
- Simplifying the resulting equation
- Solving for n
Definition: The cross multiplication property of proportion states that if a:b = c:d, then ad = bc.
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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.
Stefan S
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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
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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
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Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
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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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. 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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. 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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
How to Cross Multiply to Solve Ratio Problems with Examples
Cross multiplication is a powerful method for solving proportions with variables. This guide explores its application in ratio problems and changing ratios.
- Learn how to use cross multiplication to solve ratio problems with variables
- Understand the cross multiplication property... Show more
Changing Ratios and Algebraic Solutions
This page focuses on solving changing ratio problems with algebra, providing a comprehensive example and step-by-step solution process.
The example problem involves Jan and Kim's marbles, initially in a ratio of 5:6. After Jan gains 2 marbles, the new ratio becomes 7:8. The goal is to determine how many marbles each owned initially.
Example: Jan and Kim own numbers of marbles that are in the ratio 5:6. Jan gains 2 more marbles and the ratio is now 7:8. How many marbles do each own initially?
The solution process involves:
- Writing the initial ratio in algebraic form (5x : 6x)
- Expressing the new ratio after the change
- Setting up an equation based on the new ratio
- Using cross multiplication to solve for x
- Substituting the value of x to find the original numbers of marbles
Highlight: This problem demonstrates how to apply algebraic techniques to solve complex ratio problems involving changes in quantities.
The solution reveals that initially, Jan owned 40 marbles and Kim owned 48 marbles.
Vocabulary: Changing ratios refer to situations where the ratio between quantities changes due to an increase or decrease in one or more of the quantities involved.
This example illustrates the power of algebra in solving ratio problems, especially when dealing with changing ratios. It combines the concepts of cross multiplication, algebraic manipulation, and ratio analysis to arrive at a precise solution.
Quote: "Initially Jan owned 40, Kim owned 48"
This page provides valuable practice for students preparing for exams like GCSE, where changing ratio questions and algebraic ratio GCSE questions are common.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Solving Ratio Problems with Cross Multiplication
This page introduces the concept of using cross multiplication to solve ratio problems with variables. It provides a step-by-step example of how to apply this method effectively.
The example problem involves two brothers, Rich and Andrew, sharing money in a ratio of 2:7, with Andrew receiving £30 more than Rich. The solution demonstrates how to use blocks to represent the ratio and solve for the total amount shared.
Example: Two brothers, Rich and Andrew, share a sum of money in the ratio 2:7. Andrew gets £30 more than Rich. Calculate how much the brothers share.
The solution process involves:
- Representing the difference between the ratio parts (7 - 2 = 5)
- Assigning a value to the difference
- Calculating the value of one block (£6)
- Determining the total amount shared (6 × (7 + 2) = £54)
Highlight: This method of using blocks to represent ratio parts is particularly useful for visualizing and solving ratio problems.
The page also covers finding the value of n in a ratio, using the example : 2n = 3 : 5. This introduces the concept of cross multiplication for solving proportions with variables.
Vocabulary: Cross multiplication is a technique used to solve proportions by multiplying the numerator of each fraction by the denominator of the other fraction.
The solution process for finding n involves:
- Cross multiplying the ratios
- Simplifying the resulting equation
- Solving for n
Definition: The cross multiplication property of proportion states that if a:b = c:d, then ad = bc.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
App Store
4.7/5
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. 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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. 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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user