BIDMAS gives the order: Brackets, Indices, Division and Multiplication (equal priority, left to right), Addition and Subtraction (equal priority, left to right). The Edexcel specification itself just calls this the "hierarchy of operations," but BIDMAS is the standard way to remember it.

Example: $20 - 4 \times 3$.

1. No brackets, no indices.
2. Multiplication before subtraction: $4 \times 3 = 12$.
3. Now subtract: $20 - 12 = 8$.

Example (the left-to-right trap): $10 \div 2 \times 5$.

1. Division and multiplication are equal priority, so work left to right: $10 \div 2 = 5$ first.
2. Then $5 \times 5 = 25$.
3. (Doing the multiplication first, $2\times5=10$, then $10\div10=1$, gives the wrong answer — order matters here.)

Treat the entire numerator of a fraction as if it's in its own set of brackets, and the entire denominator as if it's in its own set of brackets — resolve each separately before dividing.

Example: $\dfrac{10-2}{4+1}$.

1. Numerator: $10-2=8$.
2. Denominator: $4+1=5$.
3. Result: $\dfrac{8}{5}=1.6$.

The exact same priority order applies when simplifying algebraic expressions — expand any brackets first, then combine like terms by addition/subtraction.

Example: Simplify $3(2x+1)+4x$.

1. Expand the bracket first: $3(2x+1) = 6x+3$.
2. The expression becomes $6x+3+4x$.
3. Combine like terms: $6x+4x+3 = 10x+3$.

Brackets always come first, overriding every other rule — including overriding the left-to-right tie-break for equal-priority operations. If a calculation would normally be done in a different order, putting brackets around part of it forces that part to be evaluated first instead.

Example: Compare $8 - 3 \times 2$ and $(8-3)\times2$.

1. Without brackets: multiplication first, $3\times2=6$, then $8-6=2$.
2. With brackets: the bracket is evaluated first, $8-3=5$, then $5\times2=10$.
3. Two very different answers from the same digits — the brackets entirely change which operation happens first.

The area of a composite shape is given by the formula $A = 5 \times 4^2 - 10$. Work out the value of $A$.

1. Indices first: $4^2 = 16$.
2. Multiplication next: $5 \times 16 = 80$.
3. Subtraction last: $80 - 10 = 70$.
4. So $A = 70$.