Removing brackets

Can we write an expression with brackets without them? Yes, but sometimes the signs inside must change. Let's see why, so you don't have to memorise it.

500 − (250 − 100). Inside first: 250 − 100 = 150, so the value is 500 − 150 = 350.

Now suppose we just take away 250 from 500. We have taken away 100 too many (the bracket only asked for 150). So we must add the 100 back: 500 − 250 + 100 = 350. ✓

The trap: 500 − 250 − 100 = 150. That is not 350. One wrong sign changes everything.

So: when you remove brackets that have a minus in front, every sign inside flips. Here 250 and −100 became −250 and +100.

With a plus in front, nothing changes. Hira has 28 coins in one bag and 35 in another, and gives a friend 10 from the second bag. Coins left: 28 + (35 − 10) = 28 + 35 − 10 = 53. Instead of memorising which case is which, think about what the expression means, like the 100 that had to be added back.