L1 · Order of operations: parentheses first

Learning goal

“I can evaluate an expression by following the agreed order: parentheses first, then multiplication and division, then addition and subtraction - and I can explain why the order changes the answer.”

Expression — a mathematical phrase of numbers and operations, like 5 + 3 x 4, with no equals sign.

Evaluate — work out the value of an expression.

Parentheses — the brackets ( ) that mark the part of an expression to do FIRST.

Worked example

Evaluate (5 + 3) x 4. Step 1: Parentheses first: 5 + 3 = 8. Step 2: Then multiply: 8 x 4 = 32. In the expression tree, the lowest branch joins 5 and 3 with + (because the parentheses group them); that branch's value, 8, then joins 4 with x at the top. Contrast: WITHOUT parentheses, 5 + 3 x 4 means multiply first: 3 x 4 = 12, then 5 + 12 = 17. Same numbers, same operations - different order, different answer (32 vs 17). The parentheses are instructions, not decoration.

Check yourself — explain it

Parentheses in an expression tell us...

Paired problem — example still visible

Evaluate 2 x (6 - 3) -> 6 (parentheses: 6 - 3 = 3; then 2 x 3 = 6)

Faded completion — last step is yours

"(10 - 4) x 3: parentheses give ___, then x 3 gives ___" -> 6; 18

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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