A bracket with a minus sign
Take away a bracket: take away every term inside it.
One bill for two things
Rani has ₹68. She buys a notebook for ₹18 and a pen for ₹13, and pays one bill for both: 18 + 13. What is left is 68 − (18 + 13).
Which is the same as 68 − (18 + 13)?
What this lesson covers
The idea
A bracket preceded by a minus sign is opened as in arithmetic: each term inside the bracket is subtracted.
One bill for two things
Rani has ₹68. She buys a notebook for ₹18 and a pen for ₹13, and pays one bill for both: 18 + 13. What is left is 68 − (18 + 13).
Which is the same as 68 − (18 + 13)?
- 68 − 18 + 13
- 68 − 18 − 13
- 68 + 18 + 13
Open the bracket
The minus sign is in front of the bracket. For each term inside, choose its sign in the opened expression. The table tests your choice.
The minus sign reaches every term
Taking away a bill of 18 + 13 is the same as taking away 18 and then taking away 13. The minus sign in front of the bracket applies to each term inside it.
Look at the last row. Inside the bracket, −9q is a term of its own. Taking it away puts 9q back, so its sign changes to +.
Then simplify each one: 68 − 18 − 13 = 37, 40x + 75y − 6x − 10y = 34x + 65y, and 23p − 7q − 21p + 9q = 2p + 2q.
A bracket preceded by a minus sign is opened as in arithmetic: each term inside the bracket is subtracted.
- With the bracket | Bracket opened
- 68 − (18 + 13) | 68 − 18 − 13
- 40x + 75y − (6x + 10y) | 40x + 75y − 6x − 10y
- 23p − 7q − (21p − 9q) | 23p − 7q − 21p + 9q
Notes
A bracket preceded by a minus sign is opened as in arithmetic: each term inside the bracket is subtracted.
Check yourself
Open the bracket and find 100 − (35 + 15).
Answer: 50
100 − (35 + 15) = 100 − 35 − 15 = 50.
Open the bracket: 50 − (m + 7).
Open the bracket: 9x − (3x − 2y).
Simplify 8a + 9b − (3a + 4b) to ?a + ?b. How many *b* are there?
Answer: 5
8a + 9b − 3a − 4b = (8 − 3)a + (9 − 4)b = 5a + 5b.
- 50 − m + 7. The minus sign reaches every term in the bracket, so 7 is taken away too.
- 50 + m + 7. A minus sign in front of the bracket takes terms away. It does not add them.
- 50 − m − 7 — correct. Yes! Both terms in the bracket are taken away.
- 9x − 3x + 2y — correct. Yes! The term −2y is taken away, which puts 2y back.
- 9x − 3x − 2y. The term inside is −2y. Taking it away gives +2y, so its sign must change.
- 9x + 3x − 2y. The minus sign in front of the bracket applies to 3x too.