Short Answer

To solve expressions with parentheses, we always start by solving the values inside the parentheses first. Parentheses group numbers and operations, so they must be handled before any other operation like multiplication or addition.

After solving the parentheses, we follow the remaining steps of BODMAS. This method makes the expression simple and helps us get the correct answer without confusion.

Detailed Explanation:

Solving expressions with parentheses first

In mathematics, parentheses play a very important role in solving expressions. Parentheses are used to group numbers and operations together. When an expression has parentheses, we must always solve them first before doing any other operation. This rule is part of the BODMAS system and helps in getting the correct answer.

When we look at an expression, the first step is to identify if there are any parentheses. If they are present, we focus only on the part inside the parentheses and solve it completely. This means we perform all operations inside the parentheses first, following the BODMAS rule within them if needed.

Sometimes, parentheses may contain more than one operation. In such cases, we again follow the order of operations inside the parentheses. For example, if there is multiplication and addition inside the parentheses, we solve multiplication first and then addition.

Solving inner expressions

If there are multiple parentheses in an expression, we solve the innermost parentheses first. This means we start with the smallest group and then move outward step by step.

For example, in an expression like:
(8 + (6 × 2))

We first solve the inner parentheses (6 × 2) and then solve the outer parentheses.

This step-by-step approach helps in simplifying the expression gradually and makes it easier to solve.

Example explanation

Let us understand with an example:

Expression:
10 + (4 × 3)

Step 1: Solve inside parentheses
4 × 3 = 12

Step 2: Add
10 + 12 = 22

So, the correct answer is 22.

Another example with more steps:

Expression:
20 − (6 + 2 × 3)

Step 1: Solve multiplication inside parentheses
2 × 3 = 6

Step 2: Add inside parentheses
6 + 6 = 12

Step 3: Subtract
20 − 12 = 8

This shows how we solve everything inside the parentheses first.

Role of parentheses in calculations

Parentheses are very useful in organizing expressions. They tell us which part of the expression should be solved first. Without parentheses, it would be difficult to know the correct order of operations.

Simplifying complex expressions

Parentheses help in breaking down complex expressions into smaller parts. Instead of solving everything at once, we solve one group at a time. This makes calculations simple and easy to manage.

Avoiding mistakes

Many mistakes happen when students ignore parentheses and start solving other operations first. This leads to incorrect answers. By always solving parentheses first, we can avoid such errors.

Use in BODMAS

In the BODMAS rule, brackets (including parentheses) are always solved first. This makes them the most important part of any expression. After solving parentheses, we move to orders, division, multiplication, addition, and subtraction.

Use in real life

Parentheses are used in many real-life calculations. For example, while calculating total cost with grouped items, we may need to solve certain parts first. Parentheses help in organizing such calculations properly.

Improving problem solving

Practicing expressions with parentheses improves logical thinking. It helps students follow a clear step-by-step method. Over time, this becomes a habit and makes solving problems faster and more accurate.

Conclusion

Solving expressions with parentheses first is an important rule in mathematics. By focusing on the grouped part first, we simplify the problem and avoid mistakes. This method ensures correct and clear calculations and is a key part of the BODMAS rule.