Maths319 views·Updated Jun 19, 2026·5 pages

Understanding Numbers: Key Concepts and Operations

peachy@indi_014

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Place value might sound boring, but it's actually the secret...

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of 5

$! Π Σ # Maths Chapter 1: Place Valul < less than > greater than $\\\$ less/equal to $\\\$ more/equal to #Not equal to To round to a given$

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!

of 5

$! Π Σ # Maths Chapter 1: Place Valul < less than > greater than $\\\$ less/equal to $\\\$ more/equal to #Not equal to To round to a given$

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!

of 5

$! Π Σ # Maths Chapter 1: Place Valul < less than > greater than $\\\$ less/equal to $\\\$ more/equal to #Not equal to To round to a given$

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!

of 5

$! Π Σ # Maths Chapter 1: Place Valul < less than > greater than $\\\$ less/equal to $\\\$ more/equal to #Not equal to To round to a given$

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!

of 5

$! Π Σ # Maths Chapter 1: Place Valul < less than > greater than $\\\$ less/equal to $\\\$ more/equal to #Not equal to To round to a given$

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!

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Maths319 views·Updated Jun 19, 2026·5 pages

Understanding Numbers: Key Concepts and Operations

peachy@indi_014

Add to Google sources

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.

of 5

$! Π Σ # Maths Chapter 1: Place Valul < less than > greater than $\\\$ less/equal to $\\\$ more/equal to #Not equal to To round to a given$

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.

Top Tip: When multiplying or dividing with negative numbers, use the same rule - same signs = positive answer, different signs = negative answer!

of 5

$! Π Σ # Maths Chapter 1: Place Valul < less than > greater than $\\\$ less/equal to $\\\$ more/equal to #Not equal to To round to a given$

Working with Decimals and Fractions

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!

Remember: Always check if your fraction can be simplified further - examiners love seeing fractions in their simplest form!

of 5

$! Π Σ # Maths Chapter 1: Place Valul < less than > greater than $\\\$ less/equal to $\\\$ more/equal to #Not equal to To round to a given$

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.

Quick Check: Can you spot why 1 isn't considered prime? It only has one factor (itself), but prime numbers need exactly two factors!

of 5

$! Π Σ # Maths Chapter 1: Place Valul < less than > greater than $\\\$ less/equal to $\\\$ more/equal to #Not equal to To round to a given$

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!

of 5

$! Π Σ # Maths Chapter 1: Place Valul < less than > greater than $\\\$ less/equal to $\\\$ more/equal to #Not equal to To round to a given$

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!

Memory Hook: "Big Insects Destroy Many Apple Sandwiches" - create your own silly sentence to remember BIDMAS!