Removing brackets not after a minus sign

The idea

When brackets not preceded by a minus sign are removed, the terms inside them keep their signs, since the terms can be added in any order.

Hira’s coins

Hira has 28 coins in one bag and 35 in another. She gives her friend 10 coins from the second bag. Coins left: 28 + (35 − 10).

Last time every sign changed when the brackets went. What happens to the signs here?

• All the signs inside change
• The signs inside stay the same
• Only the first sign changes

Fix the signs

Here the brackets were removed with last lesson’s trick, flipping every sign. Does the value still match? Fix the signs until it does.

Plus keeps the signs

28 + (35 − 10) means 28 + (35 + (−10)). Terms can be added in any order, so this is 28 + 35 + (−10), or 28 + 35 − 10. Nothing changed.

When brackets not preceded by a minus sign are removed, the terms inside keep their signs, since the terms can be added in any order.

You do not have to memorise two rules. Think about what the expression means: a plus lets the terms join in as they are, and a minus takes the whole bracket away.

• With brackets | Without brackets
• 28 + (35 − 10) | 28 + 35 − 10 = 53
• 50 + (20 + 5) | 50 + 20 + 5 = 75
• 40 + (15 − 6 + 8) | 40 + 15 − 6 + 8 = 57

Notes

When brackets not preceded by a minus sign are removed, the terms inside keep their signs, since the terms can be added in any order.

Check yourself

Which is the same as 60 + (25 − 8)?

In which expression can you remove the brackets without changing any sign?

Remove the brackets and work out 100 + (35 − 20 + 5).

Answer: 120

100 + (35 − 20 + 5) = 100 + 35 − 20 + 5 = 120.

Remove the brackets and work out 75 − (25 + 15).

Answer: 35

75 − (25 + 15) = 75 − 25 − 15 = 35.

• 60 − 25 + 8. That is 43. A plus in front does not flip the signs.
• 60 + 25 − 8 — correct. Yes! No minus sign in front, so no sign changes. Both are 77.
• 60 − 25 − 8. That is 27. A plus in front does not flip the signs.
• 15 − (9 − 4). There is a minus in front, so every sign inside changes: 15 − 9 + 4.
• Both of them. Only the one with a plus in front keeps its signs.
• 15 + (9 − 4) — correct. Yes! A plus in front keeps the signs: 15 + 9 − 4.