The expression 10 − (3 + 2) asks you to subtract one grouped amount. That amount is five, so the result is five. Removing the brackets as 10 − 3 + 2 changes the instruction and produces nine instead.
Imagine ten counters on a table. You need to remove a group containing three red counters and two blue counters. Both colours leave the table. You do not remove three and then return two simply because a plus sign appeared inside the original group.
Follow the operation through the group
Subtracting the sum can be written as 10 − 3 − 2. Both terms are being removed. A minus sign outside brackets applies to the entire expression within them, so each term’s contribution must be handled accordingly.
Now compare 10 − (3 − 2). Work inside first: three minus two is one, and ten minus one is nine. If you expand the expression, it becomes 10 − 3 + 2. The second sign changes because subtracting a difference is not the same as subtracting both quantities.
Check with two routes
For practice, solve the bracket first, then solve the expanded version. The answers should agree. If they do not, trace the signs rather than immediately repeating the same calculation faster.
- 12 − (4 + 3) becomes 12 − 4 − 3, giving 5.
- 12 − (4 − 3) becomes 12 − 4 + 3, giving 11.
- 8 − (2 + 1 + 3) becomes 8 − 2 − 1 − 3, giving 2.
On a number line, subtracting the grouped total gives another way to check. Keep the original brackets visible until you have decided what they contain. Crossing them out too early can make the line look simpler while hiding the operation that mattered most.
Once the numerical examples feel clear, the same reasoning applies to letters. The rule describes the relationship between operations; it is not a trick reserved for one worksheet.