Working with brackets

Brackets are the most powerful tool in an expression. They override the usual order — whatever is inside the brackets gets computed first. Once you're comfortable with brackets, you can write almost any calculation you want.

What brackets really do

A bracket says: treat the inside like a single number. It doesn't matter how messy what's inside is — the rest of the expression has to wait.

4 × (7 − 3) = 4 × 4 = 16

The "7 − 3" is a temporary little problem inside the bigger one. Solve it, write down the answer (4), and continue.

Brackets that change the answer

Same numbers, different brackets, different answer:

Reading the brackets carefully is half the work.

Nested brackets

When one set of brackets sits inside another, start from the innermost.

20 − (3 × (4 + 2))

Innermost first: 4 + 2 = 6. Rewrite: `20 − (3 × 6)`.

Next bracket: 3 × 6 = 18. Rewrite: `20 − 18`.

Finally: 20 − 18 = 2.

((10 − 2) × 3) + 5

Innermost: 10 − 2 = 8. Rewrite: `(8 × 3) + 5`.

Next: 8 × 3 = 24. Rewrite: `24 + 5`.

Finally: 29.

To keep them straight, some books use different shapes: `( … )`, `[ … ]`, `{ … }`. In Year 5 you'll mostly meet plain round brackets.

Where to place brackets

Sometimes you're given an expression and asked to insert brackets so it equals a target value.

Place brackets in `8 + 2 × 5 − 1` to make the answer 49.

Try `(8 + 2) × 5 − 1` = 10 × 5 − 1 = 50 − 1 = 49. ✓

Place brackets in `8 + 2 × 5 − 1` to make the answer 8.

Try `8 + 2 × (5 − 1)` = 8 + 2 × 4 = 8 + 8 = 16. No.

Try `(8 + 2 × 5) − 1` = (8 + 10) − 1 = 17. No.

Try `8 + 2 × 5 − 1 × ?` — no, we can't add operations.

The puzzle is: which placement turns this into the target?

When brackets are *not* needed

Brackets that don't change anything are clutter. These are equivalent:

`2 + (3 × 4)` is the same as `2 + 3 × 4` — × goes first anyway, brackets just confirm it.

But these are different:

`(2 + 3) × 4` is not the same as `2 + 3 × 4`.

Use brackets when they change the order, not for decoration.

Brackets and negative or implicit signs

In Year 5 you'll occasionally see expressions like:

3 × (2 + 5) − (1 + 2)

Two separate bracket sets. Do each independently:

• 2 + 5 = 7
• 1 + 2 = 3

Rewrite: `3 × 7 − 3 = 21 − 3 = 18`.

What's next

• Order of operations — back to the rule
• PEMDAS tricks and shortcuts
• Writing expressions from words
• For parents

Try it out

• 🔢 Evaluate expression with PEMDAS
• 🧩 Insert parentheses to make an equation true