Missing Parentheses in Arithmetic

1) Read the expression carefully

In these problems, some parentheses are missing. Your job is to place them so the arithmetic matches the intended grouping, then simplify the result.

2) Use order of operations as your guide

Parentheses tell you what to do first. Without them, multiplication and division happen before addition and subtraction. So when you are deciding where the parentheses belong, ask: Which parts must be calculated together?

3) Test the grouping step by step

• Identify the numbers and operations.
• Look at the part that seems meant to stay together.
• Add parentheses around that part.
• Recompute the expression in the correct order.

If more than one placement seems possible, check which one gives a valid and sensible result for the problem.

4) Simplify completely

After the parentheses are placed correctly, carry out the arithmetic from the inside out and write the final simplified answer.

5) Check your work

Re-read the expression with your parentheses included and evaluate again. Make sure the final answer matches the intended grouping and that no operation was skipped.

Quick tip

If you are unsure, compute the expression two ways: once with your chosen parentheses and once using the usual order of operations. The correct version should match the meaning of the exercise and simplify cleanly.