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Britain & the wider world: 1745 -1901
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Maths
10 Dec 2025
1,994
46 pages
katana @canelakaare
Right, let's tackle proportional reasoning- one of the most useful maths topics you'll actually use in real... Show more
Ratios compare two quantities and show their relationship - like "for every 5 boys there are 3 girls" written as 53. The order matters massively, so always write ratios in the same order as the information given.
To simplify ratios, find the biggest common factor that divides into both numbers. For example, 64 becomes 32 when you divide both sides by 2. When sharing amounts, add up all the ratio parts first, then divide the total by this number to find one part.
Scale factors help you work with similar shapes and maps. If one side of a rectangle is 3m and the corresponding side is 4.5m, the scale factor is 1.5. Always ensure your units match when working with ratios and scales.
Remember Ratios are like recipes - if you double one ingredient, you must double them all to keep the same taste!
This block covers the essential skills you'll need for ratio and scale, multiplicative change, and multiplying and dividing fractions. These aren't just random maths topics - they're incredibly practical skills you'll use constantly.
Whether you're splitting pizza costs with mates, converting currencies for holidays, or following recipes, proportional reasoning is everywhere. The key is understanding that when one thing changes, another changes in a predictable way.
Quick Tip Always look for the relationship between numbers - that's what makes proportional reasoning click!
Direct proportion means when one variable changes, the other changes at the same rate. Think currency conversion - if £1 = 90 rupees, then £10 = 900 rupees (multiply both sides by 10).
Conversion graphs always create straight lines because the relationship stays constant. To use them, find your starting point on one axis, draw a line to the graph, then across to the other axis. A ruler helps with accuracy.
Scale diagrams work similarly - if a car model has a 130 scale and the model is 10cm long, the real car is 300cm long. Maps use the same principle, though you'll often need to convert units first.
Pro Tip When stuck with proportions, work out what one unit is worth first - it makes everything easier!
Multiplying fractions is straightforward - multiply the numerators together, then multiply the denominators together. For example ½ × ¾ = 3/8. You can often cancel down first to make calculations easier.
Dividing by fractions uses reciprocals - flip the second fraction and multiply instead. So ⅔ ÷ ¼ becomes ⅔ × 4/1 = 8/3. Think of it as "how many quarters fit into two-thirds?"
When multiplying fractions by whole numbers, remember it's repeated addition. 4 × ⅖ means adding ⅖ four times, giving you 8/5. Visual models really help here - draw rectangles and shade the relevant parts.
Memory Trick "Dividing fractions? Don't ask why - just flip and multiply!"
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.
132
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Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the fundamentals of ratios, including part-to-part comparisons, simplification techniques, and the relationship between ratios and fractions. This summary covers key concepts such as the Highest Common Factor (HCF) and provides examples to illustrate how to express ratios in simplest form. Ideal for students looking to grasp the basics of ratios and their applications in mathematics.
MathsThis comprehensive revision sheet covers essential concepts of ratios, including comparison, simplification, and application in word problems. Learn how to express ratios as fractions, share quantities in given ratios, and combine multiple ratios effectively. Ideal for students preparing for exams in mathematics.
MathsExplore the essential concepts of ratios and proportions in mathematics. This comprehensive guide covers definitions, formulas, properties, and practical examples to help Year 7 students master these foundational topics. Ideal for enhancing problem-solving skills and understanding real-world applications.
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
katana
@canelakaare
Right, let's tackle proportional reasoning- one of the most useful maths topics you'll actually use in real life! This covers three brilliant areas: ratios and scale (perfect for cooking and maps), multiplicative change (great for currency conversion), and multiplying/dividing... Show more
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Improve your grades
Join milions of students
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Ratios compare two quantities and show their relationship - like "for every 5 boys there are 3 girls" written as 5:3. The order matters massively, so always write ratios in the same order as the information given.
To simplify ratios, find the biggest common factor that divides into both numbers. For example, 6:4 becomes 3:2 when you divide both sides by 2. When sharing amounts, add up all the ratio parts first, then divide the total by this number to find one part.
Scale factors help you work with similar shapes and maps. If one side of a rectangle is 3m and the corresponding side is 4.5m, the scale factor is 1.5. Always ensure your units match when working with ratios and scales.
Remember: Ratios are like recipes - if you double one ingredient, you must double them all to keep the same taste!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This block covers the essential skills you'll need for ratio and scale, multiplicative change, and multiplying and dividing fractions. These aren't just random maths topics - they're incredibly practical skills you'll use constantly.
Whether you're splitting pizza costs with mates, converting currencies for holidays, or following recipes, proportional reasoning is everywhere. The key is understanding that when one thing changes, another changes in a predictable way.
Quick Tip: Always look for the relationship between numbers - that's what makes proportional reasoning click!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Direct proportion means when one variable changes, the other changes at the same rate. Think currency conversion - if £1 = 90 rupees, then £10 = 900 rupees (multiply both sides by 10).
Conversion graphs always create straight lines because the relationship stays constant. To use them, find your starting point on one axis, draw a line to the graph, then across to the other axis. A ruler helps with accuracy.
Scale diagrams work similarly - if a car model has a 1:30 scale and the model is 10cm long, the real car is 300cm long. Maps use the same principle, though you'll often need to convert units first.
Pro Tip: When stuck with proportions, work out what one unit is worth first - it makes everything easier!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Multiplying fractions is straightforward - multiply the numerators together, then multiply the denominators together. For example: ½ × ¾ = 3/8. You can often cancel down first to make calculations easier.
Dividing by fractions uses reciprocals - flip the second fraction and multiply instead. So ⅔ ÷ ¼ becomes ⅔ × 4/1 = 8/3. Think of it as "how many quarters fit into two-thirds?"
When multiplying fractions by whole numbers, remember it's repeated addition. 4 × ⅖ means adding ⅖ four times, giving you 8/5. Visual models really help here - draw rectangles and shade the relevant parts.
Memory Trick: "Dividing fractions? Don't ask why - just flip and multiply!"
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
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.
132
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the fundamentals of ratios, including part-to-part comparisons, simplification techniques, and the relationship between ratios and fractions. This summary covers key concepts such as the Highest Common Factor (HCF) and provides examples to illustrate how to express ratios in simplest form. Ideal for students looking to grasp the basics of ratios and their applications in mathematics.
MathsThis comprehensive revision sheet covers essential concepts of ratios, including comparison, simplification, and application in word problems. Learn how to express ratios as fractions, share quantities in given ratios, and combine multiple ratios effectively. Ideal for students preparing for exams in mathematics.
MathsExplore the essential concepts of ratios and proportions in mathematics. This comprehensive guide covers definitions, formulas, properties, and practical examples to help Year 7 students master these foundational topics. Ideal for enhancing problem-solving skills and understanding real-world applications.
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