Place value might sound boring, but it's actually the secret...
Maths319 views·Updated 28 Jul 2026·5 pagesUnderstanding Numbers: Key Concepts and Operations
peachy@indi_014
1 / 5
1
of 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 (+ and + = +, or - and - = +), whilst different signs give negative answers (+ and - = -, or - and + = -).
Top Tip: When multiplying or dividing with negative numbers, use the same rule - same signs = positive answer, different signs = negative answer!
2
of 5
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!
3
of 5
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!
4
of 5
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!
5
of 5
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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Maths319 views·Updated 28 Jul 2026·5 pagesUnderstanding 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.
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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 (+ and + = +, or - and - = +), whilst different signs give negative answers (+ and - = -, or - and + = -).
Top Tip: When multiplying or dividing with negative numbers, use the same rule - same signs = positive answer, different signs = negative answer!
2
of 5Sign up to see the content. It's free!
- Access to all documents
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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!
3
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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!
4
of 5Sign up to see the content. It'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!
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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...
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.
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Students love us — and so will you.
4.6/5App Store
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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.
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Samantha KlichAndroid 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.
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