Place value might sound boring, but it's actually the secret... Show more
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peachy
08/12/2025
Maths
Numbers
307
•
8 Dec 2025
•
Understanding Numbers: Key Concepts and Operations
peachy
@indi_014
1 / 5
Place Value Basics
Inequality symbols are your best mates for comparing numbers. Remember: < means "less than", > means "greater than", and you can add the line underneath (≤ or ≥) when things are equal too.
Rounding decimals is dead simple once you know the trick. Count to your decimal place, then look at the next digit. If it's 0-4, round down; if it's 5-9, round up. So 0.317 rounded to 1 decimal place becomes 0.3.
Negative numbers follow predictable patterns when you add or subtract them. Same signs always give positive answers , whilst different signs give negative answers .
Top Tip: When multiplying or dividing with negative numbers, use the same rule - same signs = positive answer, different signs = negative answer!
Working with Decimals and Fractions
Multiplying decimals looks scary but it's actually quite straightforward. Multiply the numbers normally (ignoring decimal points), then count up all the decimal places in your original numbers and put the point back in the right spot.
Dividing decimals works similarly - take out the decimals, do the division, then pop the decimal point back where it belongs. This method is brilliant for non-calculator questions!
Simplifying fractions follows one golden rule: do the same thing to the top and bottom. Divide both numbers by their biggest common factor until you can't go any further. For example, 6/30 ÷ 6/6 = 1/5.
Remember: Always check if your fraction can be simplified further - examiners love seeing fractions in their simplest form!
Fraction Operations and Prime Numbers
Multiplying fractions is easier than adding them! Just multiply the tops together and the bottoms together: 2/3 × 4/5 = 8/15. Don't forget to simplify your answer if possible.
Dividing fractions uses a clever trick - flip the second fraction upside down and multiply instead. So 2/5 ÷ 3/7 becomes 2/5 × 7/3 = 14/15.
Prime numbers are the building blocks of maths - they can only be divided by 1 and themselves. The key ones to memorise are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Remember, 1 isn't prime, and 2 is the only even prime number.
Quick Check: Can you spot why 1 isn't considered prime? It only has one factor (itself), but prime numbers need exactly two factors!
Factors, Multiples, and Powers
Prime factorisation breaks numbers down into their prime building blocks. Start by splitting your number into two factors, then keep going until you only have primes left. Write 36 as 2² × 3².
HCF (Highest Common Factor) is the biggest number that divides into your given numbers. LCM (Lowest Common Multiple) is the smallest number that both your numbers divide into evenly.
Powers are just repeated multiplication written in shorthand. 7⁶ means 7 × 7 × 7 × 7 × 7 × 7. Powers of 10 are particularly useful: 10² = 100, 10³ = 1000, and so on.
Power Tip: Learning your powers of 10 off by heart will make decimal calculations much faster!
Order of Operations (BIDMAS)
BIDMAS tells you the correct order to tackle calculations: Brackets, Indices (powers), Division, Multiplication, Addition, Subtraction.
When operations have the same priority (like addition and subtraction), work from left to right. So 4 - 3 + 5 = 6, not 4 - 8 = -4!
Brackets always come first - sort out anything in brackets before touching the rest of the calculation. Indices (squared or cubed numbers) come next, then you can tackle the rest following BIDMAS order.
Memory Hook: "Big Insects Destroy Many Apple Sandwiches" - create your own silly sentence to remember BIDMAS!
We thought you’d never ask...
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Most popular content in Maths
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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
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
Understanding Numbers: Key Concepts and Operations
peachy
@indi_014
Place value might sound boring, but it's actually the secret code that makes all of maths work! This chapter covers everything from rounding decimals to working with negative numbers, plus the essential skills you'll need for fractions and basic calculations.
Place Value Basics
Inequality symbols are your best mates for comparing numbers. Remember: < means "less than", > means "greater than", and you can add the line underneath (≤ or ≥) when things are equal too.
Rounding decimals is dead simple once you know the trick. Count to your decimal place, then look at the next digit. If it's 0-4, round down; if it's 5-9, round up. So 0.317 rounded to 1 decimal place becomes 0.3.
Negative numbers follow predictable patterns when you add or subtract them. Same signs always give positive answers , whilst different signs give negative answers .
Top Tip: When multiplying or dividing with negative numbers, use the same rule - same signs = positive answer, different signs = negative answer!
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
Working with Decimals and Fractions
Multiplying decimals looks scary but it's actually quite straightforward. Multiply the numbers normally (ignoring decimal points), then count up all the decimal places in your original numbers and put the point back in the right spot.
Dividing decimals works similarly - take out the decimals, do the division, then pop the decimal point back where it belongs. This method is brilliant for non-calculator questions!
Simplifying fractions follows one golden rule: do the same thing to the top and bottom. Divide both numbers by their biggest common factor until you can't go any further. For example, 6/30 ÷ 6/6 = 1/5.
Remember: Always check if your fraction can be simplified further - examiners love seeing fractions in their simplest form!
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
Fraction Operations and Prime Numbers
Multiplying fractions is easier than adding them! Just multiply the tops together and the bottoms together: 2/3 × 4/5 = 8/15. Don't forget to simplify your answer if possible.
Dividing fractions uses a clever trick - flip the second fraction upside down and multiply instead. So 2/5 ÷ 3/7 becomes 2/5 × 7/3 = 14/15.
Prime numbers are the building blocks of maths - they can only be divided by 1 and themselves. The key ones to memorise are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Remember, 1 isn't prime, and 2 is the only even prime number.
Quick Check: Can you spot why 1 isn't considered prime? It only has one factor (itself), but prime numbers need exactly two factors!
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
Factors, Multiples, and Powers
Prime factorisation breaks numbers down into their prime building blocks. Start by splitting your number into two factors, then keep going until you only have primes left. Write 36 as 2² × 3².
HCF (Highest Common Factor) is the biggest number that divides into your given numbers. LCM (Lowest Common Multiple) is the smallest number that both your numbers divide into evenly.
Powers are just repeated multiplication written in shorthand. 7⁶ means 7 × 7 × 7 × 7 × 7 × 7. Powers of 10 are particularly useful: 10² = 100, 10³ = 1000, and so on.
Power Tip: Learning your powers of 10 off by heart will make decimal calculations much faster!
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
Order of Operations (BIDMAS)
BIDMAS tells you the correct order to tackle calculations: Brackets, Indices (powers), Division, Multiplication, Addition, Subtraction.
When operations have the same priority (like addition and subtraction), work from left to right. So 4 - 3 + 5 = 6, not 4 - 8 = -4!
Brackets always come first - sort out anything in brackets before touching the rest of the calculation. Indices (squared or cubed numbers) come next, then you can tackle the rest following BIDMAS order.
Memory Hook: "Big Insects Destroy Many Apple Sandwiches" - create your own silly sentence to remember BIDMAS!
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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Most popular content: Basic Operations
Most popular content in Maths
Most popular content
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
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