Removing brackets after a minus sign

The idea

When brackets preceded by a minus sign are removed, the sign of every term inside the brackets changes.

Irfan’s change

Irfan pays ₹100 for biscuits (₹15) and toor dal (₹56). His change is 100 − (15 + 56). Instead of adding the two prices first, he takes the biscuits away from 100, and then the dal.

Which expression, with no brackets, does that?

• 100 − 15 − 56
• 100 − 15 + 56
• 100 + 15 + 56

Take the brackets away

Each expression has a bracket after a minus sign. Write it again without brackets. Tap the signs to flip them until the value matches the original.

Every sign changes

200 − (40 + 3): take away 40, then take away 3. That is 200 − 40 − 3, not 200 − 40 + 3.

In 500 − (250 − 100), taking away 250 would take away 100 too much. So that 100 is put back: + 100. Check: 500 − 250 − 100 is only 150.

When brackets preceded by a minus sign are removed, the sign of every term inside the brackets changes.

• With brackets | Without brackets
• 200 − (40 + 3) | 200 − 40 − 3 = 157
• 100 − (15 + 56) | 100 − 15 − 56 = 29
• 500 − (250 − 100) | 500 − 250 + 100 = 350

Notes

When brackets preceded by a minus sign are removed, the sign of every term inside the brackets changes.

Check yourself

Which is the same as 80 − (25 + 15)?

Which is the same as 70 − (20 − 5)?

Remove the brackets, then work out 100 − (40 − 10 + 5).

Answer: 65

100 − (40 − 10 + 5) = 100 − 40 + 10 − 5 = 65.

• 80 − 25 − 15 — correct. Yes! Both signs inside change. Both are 40.
• 80 − 25 + 15. That is 70, but 80 − 40 = 40. The 15 must change sign too: every term inside changes.
• 80 + 25 + 15. That is 120. The minus in front means the terms are taken away.
• 70 − 20 − 5. That is 45. The −5 inside must change to +5.
• 70 + 20 − 5. That is 85. The 20 must change sign too.
• 70 − 20 + 5 — correct. Yes! The 20 becomes −20, and the −5 becomes +5. Both are 55.