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Arithmetic
7 Dec 2025
212
4 pages
Poppy @poppy_helpingyoustudy
Working with ratios can seem tricky at first, but once you understand the patterns, these problems become much... Show more
When two people share money in a ratio, you're essentially dividing a total amount into parts based on the given ratio. If Kallan and Adam share £240 in the ratio 53, think of it as Kallan getting 5 parts and Adam getting 3 parts out of 8 total parts.
The key is identifying what information you have and what you need to find. Sometimes you'll know the total amount and need to find individual shares. Other times, you'll know one person's amount and need to work backwards.
Quick Tip Always add up the ratio numbers first (5+3=8) to find the total number of parts, then work from there.
Each problem type requires a slightly different approach, but they all follow the same basic principles of proportional sharing.
These problems get more interesting when you know one person's share and need to find the other amounts. If Kallan has £240 and the ratio is still 53, you can work out Adam's share by setting up a proportion.
Difference problems add another layer of complexity. When you're told "Kallan has £240 more than Adam," you're dealing with the difference between the ratio parts, not the actual amounts themselves.
Remember In a 53 ratio, the difference between the parts is 2 (5-3=2), which represents the actual difference in money.
The trick is figuring out what each "part" of the ratio is worth, then multiplying to get your final answers.
School trip problems are brilliant examples of how ratios work with groups of people. When the ratio of boys to girls is 14, this means for every 1 boy, there are 4 girls on the trip.
These problems test whether you can identify what the "60 students" represents. Is it the total? Just the boys? Just the girls? Each scenario requires a different calculation method.
Pro Tip Draw a simple diagram showing the ratio parts - it helps you visualise which part the given number represents.
The beauty of ratio problems is that once you identify what you know, the maths becomes straightforward division and multiplication.
The trickiest ratio problems involve finding totals when you know individual parts, or working with differences between groups. When 60 students are boys and the ratio is 14, you know that 1 part equals 60 students.
Difference scenarios require extra thinking. If there are "60 more girls than boys" with a 14 ratio, you need to work out what that difference of 3 parts (4-1=3) represents in real numbers.
These problems often appear on tests because they check whether you truly understand ratios or just memorise formulas. Take your time to identify what each number represents before jumping into calculations.
Success Strategy Always check your answer makes sense - if the ratio is 14, girls should outnumber boys significantly in your final answer.
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.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
3
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the fundamentals of ratios and proportions with this comprehensive revision sheet. Learn how to express ratios, solve problems involving sharing amounts, and apply ratios in real-life scenarios. Key concepts include equivalent ratios and practical examples for better understanding.
ArithmeticExplore a comprehensive set of practice questions and solutions on ratios, including simplification, division, and real-world applications. This resource covers key concepts such as equivalent ratios, proportional relationships, and angle calculations, making it ideal for exam preparation. Perfect for students looking to enhance their understanding of ratios and proportions.
MathsExplore the fundamentals of ratios, including how to calculate and manipulate them. This study note covers solving ratio problems, finding unknowns using cross multiplication, and handling changing ratios with practical examples. Ideal for students looking to master ratios and proportions.
MathsApp Store
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 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 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 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 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
Poppy
@poppy_helpingyoustudy
Working with ratios can seem tricky at first, but once you understand the patterns, these problems become much easier to solve. This guide shows you different types of ratio problems you'll encounter in your maths lessons, from basic sharing to... Show more
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
When two people share money in a ratio, you're essentially dividing a total amount into parts based on the given ratio. If Kallan and Adam share £240 in the ratio 5:3, think of it as Kallan getting 5 parts and Adam getting 3 parts out of 8 total parts.
The key is identifying what information you have and what you need to find. Sometimes you'll know the total amount and need to find individual shares. Other times, you'll know one person's amount and need to work backwards.
Quick Tip: Always add up the ratio numbers first (5+3=8) to find the total number of parts, then work from there.
Each problem type requires a slightly different approach, but they all follow the same basic principles of proportional sharing.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
These problems get more interesting when you know one person's share and need to find the other amounts. If Kallan has £240 and the ratio is still 5:3, you can work out Adam's share by setting up a proportion.
Difference problems add another layer of complexity. When you're told "Kallan has £240 more than Adam," you're dealing with the difference between the ratio parts, not the actual amounts themselves.
Remember: In a 5:3 ratio, the difference between the parts is 2 (5-3=2), which represents the actual difference in money.
The trick is figuring out what each "part" of the ratio is worth, then multiplying to get your final answers.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
School trip problems are brilliant examples of how ratios work with groups of people. When the ratio of boys to girls is 1:4, this means for every 1 boy, there are 4 girls on the trip.
These problems test whether you can identify what the "60 students" represents. Is it the total? Just the boys? Just the girls? Each scenario requires a different calculation method.
Pro Tip: Draw a simple diagram showing the ratio parts - it helps you visualise which part the given number represents.
The beauty of ratio problems is that once you identify what you know, the maths becomes straightforward division and multiplication.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The trickiest ratio problems involve finding totals when you know individual parts, or working with differences between groups. When 60 students are boys and the ratio is 1:4, you know that 1 part equals 60 students.
Difference scenarios require extra thinking. If there are "60 more girls than boys" with a 1:4 ratio, you need to work out what that difference of 3 parts (4-1=3) represents in real numbers.
These problems often appear on tests because they check whether you truly understand ratios or just memorise formulas. Take your time to identify what each number represents before jumping into calculations.
Success Strategy: Always check your answer makes sense - if the ratio is 1:4, girls should outnumber boys significantly in your final answer.
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.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
3
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the fundamentals of ratios and proportions with this comprehensive revision sheet. Learn how to express ratios, solve problems involving sharing amounts, and apply ratios in real-life scenarios. Key concepts include equivalent ratios and practical examples for better understanding.
ArithmeticExplore a comprehensive set of practice questions and solutions on ratios, including simplification, division, and real-world applications. This resource covers key concepts such as equivalent ratios, proportional relationships, and angle calculations, making it ideal for exam preparation. Perfect for students looking to enhance their understanding of ratios and proportions.
MathsExplore the fundamentals of ratios, including how to calculate and manipulate them. This study note covers solving ratio problems, finding unknowns using cross multiplication, and handling changing ratios with practical examples. Ideal for students looking to master ratios and proportions.
MathsApp Store
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 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 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 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 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
Sociology