L2 · Order of operations: parentheses first

Learning goal

“I can evaluate numerical expressions using the conventional order of operations - parentheses first, then multiplication and division, then addition and subtraction, working left to right - and I can explain how parentheses change the value.”

Numerical expression — a phrase made only of numbers and operations, like 4 x (10 - 6). Its value is one number.

Parentheses — the brackets ( ) that group numbers and operations: the grouped part is calculated first.

Order of operations — the agreed order everyone uses: parentheses, then x and /, then + and -, left to right within each level.

Evaluate — to work out the value of an expression, step by step.

Worked example

Compare two expressions with the same numbers. Expression 1: 2 + 3 x 4. No parentheses, so multiply first: 3 x 4 = 12, then 2 + 12 = 14. Expression 2: (2 + 3) x 4. Parentheses first: 2 + 3 = 5, then 5 x 4 = 20. Say it plainly: parentheses are instructions. They promote the grouped operation to the front of the line, and that can change the final value - 14 versus 20 from identical numbers. Balance view, in words: without parentheses the multiplication pan is served first; parentheses move the addition pan to the front.

Check yourself — explain it

Why do (2 + 3) x 4 and 2 + 3 x 4 have different values?

Paired problem — example still visible

Evaluate (5 + 2) x 3 -> 21 (5 + 2 = 7; 7 x 3 = 21)

Faded completion — last step is yours

"6 x (4 + 1): parentheses first: 4 + 1 = 5, so 6 x 5 = ___" -> 30

Ready to practise?

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

Start practice →Take the unit quiz