Taking the brackets away
You pay with a ₹600 note. The bill is a ₹230 bag and a ₹70 belt. Count the change two ways.
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Step 1 of 7
- The bill: 600 − (230 + 70).
- The bracket is 300. So 600 − 300 = 300.
- Or take the two away one by one: 600 − 230 − 70 = 300.
- Each sign inside flipped: + 230 became − 230, + 70 became − 70.
- Now ₹60 comes off the bill: 600 − (300 − 60) = 360.
- The bill is 300 − 60 = 240. So 600 − 240 = 360.
- Without the bracket: 600 − 300 + 60 = 360. The − 60 became + 60.
The rule
The change is ₹300 both ways.
Taking the brackets away means writing the same value without them.
A minus before a bracket flips every sign inside. The minus takes away everything in the bracket. So each + becomes − and each − becomes +.
600 − (230 + 70) is 600 − 230 − 70. Both give ₹300.
With ₹60 off, 600 − (300 − 60) is 600 − 300 + 60. Both give ₹360: 600 − 240 = 360, and 300 + 60 = 360. A minus takes away the whole bracket. The −60 inside means you take away 60 less.
A plus before a bracket changes no sign. So 150 + (70 − 20) is 150 + 70 − 20.
| With brackets | Brackets away | Value |
|---|---|---|
| 90 + (30 − 12) | 90 + 30 − 12 | 108 |
| 90 − (30 + 12) | 90 − 30 − 12 | 48 |
| 90 − (30 − 12) | 90 − 30 + 12 | 72 |
| 20 − (−6 − 4) | 20 + 6 + 4 | 30 |