What is Brackets in Expressions?

S3-SA1-0779

Grade Level:

Class 6

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

Definition

What is it?

Brackets are special symbols like ( ), [ ], or { } used in mathematical expressions to group numbers and operations together. They tell us which part of the calculation should be done first, even if it goes against the usual order of operations.

Simple Example

Quick Example

Imagine you buy 2 packets of biscuits, each costing ₹10, and also 1 packet of chips for ₹20. If you write 2 x 10 + 20, it means you first multiply 2 by 10, then add 20. But if you wanted to add the biscuit cost and chip cost first, then multiply by the number of packets, that wouldn't make sense. Brackets help us show the correct order for calculations.

Worked Example

Step-by-Step

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

Step 1: Identify the operation inside the brackets. Here, it's (3 x 4).
---Step 2: Perform the operation inside the brackets first. 3 x 4 = 12.
---Step 3: Replace the bracketed part with its result. The expression becomes 5 + 12 - 2.
---Step 4: Now, solve the rest of the expression from left to right. 5 + 12 = 17.
---Step 5: Continue solving. 17 - 2 = 15.

Answer: 15

Why It Matters

Understanding brackets is super important for solving complex problems in fields like Computer Science and Engineering, where steps must be followed in a strict order. It's also crucial in Data Science to correctly interpret formulas, helping you build amazing apps or analyze cricket statistics accurately.

Common Mistakes

MISTAKE: Ignoring brackets and solving from left to right | CORRECTION: Always solve the operations inside the brackets first, before anything else.

MISTAKE: Confusing different types of brackets (e.g., treating [ ] like ( )) | CORRECTION: While different bracket types indicate grouping, the rule to solve inside them first remains the same. Often, they are used to show nested groups, like [ ( ) ].

MISTAKE: Forgetting that a number directly next to a bracket means multiplication (e.g., 2(3+1)) | CORRECTION: If there's no sign between a number and a bracket, it means 'multiply'. So, 2(3+1) means 2 x (3+1).

Practice Questions

Try It Yourself

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

QUESTION: What is the value of 4 x (5 - 2) + 1? | ANSWER: 13

QUESTION: A family of 4 goes to a fair. Each ticket costs ₹50. They also buy 2 ice creams for ₹30 each. How much do they spend in total? Write an expression with brackets and solve it. | ANSWER: Expression: (4 x 50) + (2 x 30) = 200 + 60 = 260. They spend ₹260.

MCQ

Quick Quiz

Which operation should be performed first in the expression 7 + (8 - 3) x 2?

7 + 8

8 - 3

3 x 2

7 + 2

The Correct Answer Is:

According to the rule of brackets, operations inside the brackets must be performed first. So, 8 - 3 is the first step.

Real World Connection

In the Real World

When you use a calculator app on your mobile phone to figure out your monthly budget, if you type something like '5000 - (1200 + 800)', the calculator uses brackets to correctly subtract the total of your rent and electricity bill from your salary. This ensures your calculations are always accurate for managing your finances, just like shopkeepers use them for billing.

Key Vocabulary

Key Terms

EXPRESSION: A combination of numbers, variables, and operation symbols | OPERATION: A mathematical action like addition, subtraction, multiplication, or division | GROUPING: Putting numbers and operations together to be treated as a single unit | ORDER OF OPERATIONS: The specific sequence in which mathematical operations should be performed (e.g., BODMAS/PEMDAS)

What's Next

What to Learn Next

Now that you understand brackets, you're ready to learn about the 'Order of Operations' (BODMAS/PEMDAS). This concept builds on brackets and teaches you the complete sequence for solving any mathematical expression, making you a math problem-solving champ!