M2 - Builder

Negative numbers

-a + b = b - a

Numbers below zero are negative. Adding a negative moves left, subtracting a negative moves right.

Order of operations (BIDMAS)

Brackets, Indices, Division/Multiplication, Addition/Subtraction

Work through brackets first, then powers, then multiplication and division left to right, then addition and subtraction.

Rounding

Look at the digit after the place you round to: 5 or more rounds up, less than 5 rounds down.

Prime factorization

n = 2^a x 3^b x 5^c x ...

Every whole number over 1 is a product of primes.

HCF and LCM

The HCF is the largest shared factor. The LCM is the smallest shared multiple.

Decimals

Decimals show parts of a whole using tenths, hundredths and thousandths. Line up the decimal points to add.

Simplifying fractions

Divide the numerator and denominator by their HCF.

Adding and subtracting fractions

a/b + c/d = (ad + bc) / bd

Find a common denominator, then add the numerators. Never add denominators.

Multiplying fractions

a/b x c/d = ac / bd

Multiply numerators together and denominators together.

Dividing fractions

a/b / c/d = a/b x d/c

Keep, flip, multiply: keep the first fraction, flip the second and multiply.

Mixed numbers and improper fractions

a b/c = (a x c + b) / c

A mixed number has a whole part and a fraction. Convert to an improper fraction to calculate.

Fraction, decimal and percentage

1/2 = 0.5 = 50%

Divide the numerator by the denominator for a decimal; multiply by 100 for a percentage.

Percentage of a number

p% of n = (p / 100) x n

A percentage is a fraction out of 100.