What is a Parenthesis?

S3-SA1-0082

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

A parenthesis (plural: parentheses) is a pair of round brackets, like these: ( ). In Maths, they are used to group parts of an expression together, telling us which operations to do first. Think of them as a special instruction to solve whatever is inside them before anything else.

Simple Example

Quick Example

Imagine you go to a shop and buy 2 packets of biscuits, and each packet costs ₹10. You also buy a cold drink for ₹20. If you write it as 2 x 10 + 20, you might get confused. But if you write (2 x 10) + 20, the brackets clearly show you need to calculate the cost of biscuits first, then add the cold drink price.

Worked Example

Step-by-Step

Let's solve: 5 + (3 x 4) - 2

Step 1: Look for the parentheses. Here, we have (3 x 4).
---Step 2: Solve the operation inside the parentheses first. 3 x 4 = 12.
---Step 3: Replace the parentheses and their content with the result. Our expression now becomes 5 + 12 - 2.
---Step 4: Now, solve the remaining operations from left to right. First, 5 + 12 = 17.
---Step 5: Next, 17 - 2 = 15.
---Answer: The final answer is 15.

Why It Matters

Parentheses are super important in many fields! In Computer Science and Engineering, they help write clear code and design circuits. Data Scientists use them to organize complex calculations. Understanding parentheses is the first step to solving bigger, more complex problems in the real world, from designing rockets at ISRO to predicting stock market trends.

Common Mistakes

MISTAKE: Ignoring parentheses and solving operations from left to right directly. For example, solving 2 + (3 x 4) as (2 + 3) x 4 = 5 x 4 = 20. | CORRECTION: Always solve the operations inside the parentheses first, no matter where they are in the expression.

MISTAKE: Only solving the first part inside parentheses if there are multiple operations. For example, in (5 + 2 - 1), only doing 5 + 2 and then stopping. | CORRECTION: Solve ALL operations within the parentheses completely until only one number remains inside, following the correct order of operations (like BODMAS/PEMDAS).

MISTAKE: Confusing parentheses with multiplication. For example, thinking 2(3+4) means 2 AND (3+4). | CORRECTION: When a number is directly next to a parenthesis with no sign in between, it means multiplication. So, 2(3+4) means 2 x (3+4).

Practice Questions

Try It Yourself

QUESTION: Solve 10 - (2 + 3) | ANSWER: 5

QUESTION: Calculate 7 x (8 - 4) + 5 | ANSWER: 33

QUESTION: A family orders 3 plates of samosas, each costing ₹20, and 2 plates of jalebi, each costing ₹30. How much do they spend in total? Write an expression with parentheses and solve it. | ANSWER: (3 x 20) + (2 x 30) = 60 + 60 = ₹120

MCQ

Quick Quiz

Which of the following expressions correctly uses parentheses to show that addition should be done before multiplication?

5 + 2 x 3

(5 + 2) x 3

5 x (2 + 3)

5 x 2 + 3

The Correct Answer Is:

Option B, (5 + 2) x 3, correctly uses parentheses to indicate that the addition (5 + 2) must be performed first, before multiplying by 3. Options A, C, and D would prioritize multiplication or result in a different order of operations.

Real World Connection

In the Real World

When cricket statisticians calculate a player's strike rate or economy rate, they often use formulas with parentheses to ensure the calculations are done in the correct order. For example, to calculate runs per over, they might use (runs given / overs bowled) to group the division, before multiplying by a factor or adding other stats.

Key Vocabulary

Key Terms

PARENTHESIS: A pair of round brackets ( ) used to group operations | EXPRESSION: A mathematical phrase that can contain numbers, variables, and operations | OPERATION: A mathematical action like addition, subtraction, multiplication, or division | ORDER OF OPERATIONS: The specific sequence in which mathematical operations should be performed (e.g., BODMAS/PEMDAS)

What's Next

What to Learn Next

Great job understanding parentheses! The next important concept is the 'Order of Operations', often called BODMAS or PEMDAS. This will teach you the full set of rules for solving any mathematical expression, building on what you've learned about parentheses.