Brackets in Maths for Beginners: Simple Rules

In short: how do you calculate expressions with brackets?

• Brackets come first. Calculate what is inside the brackets before anything outside them.
• After the brackets do multiplication and division before addition and subtraction.
• Write each step. On a new line, replace the brackets with their result and copy everything else unchanged.
• Brackets can change the answer: (8 + 2) × 3 = 30, while 8 + 2 × 3 = 14.
• In a word problem brackets show what must be calculated together before you do the rest.

What do brackets mean in a calculation?

Brackets mean: “do this part first”. Without brackets, use the usual order of operations: multiplication and division before addition and subtraction. Brackets let you change that order.

Compare two expressions with the same numbers:

• (8 + 2) × 3 = 10 × 3 = 30,
• 8 + 2 × 3 = 8 + 6 = 14.

By Grade 4 / Year 5, pupils are expected to apply the order of operations to calculations. Brackets are an important first step in making that order explicit.

How do you calculate expressions with brackets step by step?

Use the same five steps for every example.

1. Find the brackets and underline them in pencil.
2. Calculate what is inside. If there are two operations inside the brackets, use the normal order there too, for example multiplication before subtraction.
3. Copy the whole expression onto a new line. Replace the brackets with their result and copy the rest unchanged.
4. Continue calculating using the normal order of operations.
5. Check the first step, because that is where many mistakes begin.

Example: 3 × (12 – 2 × 4). Inside the brackets, multiply first: 2 × 4 = 8. Then subtract: 12 – 8 = 4. That leaves 3 × 4 = 12. In a notebook, each new step can begin with an equals sign:

• 3 × (12 – 2 × 4) =
• = 3 × (12 – 8) =
• = 3 × 4 = 12.

Working confidently inside brackets is easier when multiplication facts are secure. If your child still has to count out many products, see how to learn multiplication facts without rote memorisation.

When do brackets change the answer, and when do they not?

Brackets around a multiplication or division do not change the result if that operation would already be done first. Brackets around addition alone also leave the sum unchanged. The result most often changes when addition or subtraction sits inside brackets next to multiplication, division or a minus sign outside.

How do you write a word problem as an expression with brackets?

Brackets are useful when one part must be worked out together before the rest. As you read, ask: what do I need to calculate first? That part goes inside the brackets.

Problem 1. Emma had 50 coins. She bought a book for 18 coins and paints for 12 coins. How many coins did she have left? Expression: 50 – (18 + 12) = 50 – 30 = 20 coins. You could also write 50 – 18 – 12 = 20 coins. Both are correct.

Problem 2. Oliver bought 4 notebooks at 3 coins each and 4 pens at 2 coins each. How much did he pay? Expression: 4 × (3 + 2) = 4 × 5 = 20 coins, because each notebook-and-pen pair costs 5 coins. The equivalent form 4 × 3 + 4 × 2 = 12 + 8 = 20 coins gives the same answer.

Problem 3. Sophia shared 36 stickers equally between herself and three friends. How many stickers did each person get? Expression: 36 ÷ (1 + 3) = 36 ÷ 4 = 9. Without the brackets, 36 ÷ 1 + 3 = 39, which does not fit the situation.

You can find more multiplication and division word problems in multiplication and division word problems for Grade 3 / Year 4.

Practice: calculate and add brackets

Part A. Calculate.

1. (9 + 6) ÷ 3
2. 9 + 6 ÷ 3
3. 40 – (12 + 8)
4. 40 – 12 + 8
5. (7 – 2) × 6
6. 7 – 2 × 3
7. 48 ÷ (2 × 4)
8. 100 – (45 – 15)
9. (18 + 12) ÷ (8 – 3)
10. 5 × (20 – 4 × 3)

Part B. Add brackets so that each equation is true.

11. 2 + 3 × 4 = 20
12. 12 – 4 – 2 = 10
13. 24 ÷ 4 + 2 = 4
14. 10 – 4 × 3 + 2 = 30

Answers: 1) 5; 2) 11; 3) 20; 4) 36; 5) 30; 6) 1; 7) 6; 8) 70; 9) 6; 10) 40; 11) (2 + 3) × 4; 12) 12 – (4 – 2); 13) 24 ÷ (4 + 2); 14) (10 – 4) × (3 + 2).

For a warm-up before these examples, use the math worksheet generator. You can set multiplication or division within 100 and print a sheet with an answer key. Other topics from this stage are available in Grade 4 / Year 5 maths.

What mistakes should you avoid?

• Calculating from left to right “as it comes” and ignoring the brackets.
• Losing numbers when copying the expression. Every new line must include everything that has not yet been calculated.
• Adding after the brackets before multiplying. 2 + (3 + 1) × 5 becomes 2 + 4 × 5 = 22, not 6 × 5 = 30.
• An incorrect chain of equals signs. Writing 8 + 2 = 10 × 3 = 30 is wrong because 8 + 2 is not equal to 30. The equals sign must connect equal values.
• Trying to hold too much in your head. At first, write every step on a new line, even when it seems obvious.

When should you talk to the teacher?

If, despite writing every step, your child keeps confusing the order of operations for several weeks or gets lost in every longer expression, talk to the maths teacher. Gaps in earlier skills, such as multiplication facts, may be contributing. The teacher can help decide what to review first.

Sources

• Podstawa programowa kształcenia ogólnego, matematyka, klasy IV–VIII — podstawaprogramowa.pl (requirement: the pupil applies the rules on the order of operations; version in force from the school year 2024/2025).
• Khan Academy po polsku — Myślenie algebraiczne, 5. klasa (exercises: working out expressions with brackets and writing sentences as expressions with brackets).
• Education Endowment Foundation — Improving Mathematics in Key Stages 2 and 3 (2017, updated 2022; pupils often treat the equals sign as an instruction to “work it out” rather than as a sign of equal values).