What is Calculating Brackets First?

S1-SA1-0178

Grade Level:

Class 5

Maths, Computing, Programming, AI

Definition

What is it?

Calculating brackets first means solving the math operations inside the parentheses (brackets) before any other operations in a mathematical expression. It's a fundamental rule to ensure you get the correct answer in multi-operation problems.

Simple Example

Quick Example

Imagine you are buying 2 packets of biscuits, and each packet costs ₹10. You also buy a cold drink for ₹15. If you write it as 2 x 10 + 15, you might think 2 x (10 + 15) = 2 x 25 = ₹50. But the correct way is (2 x 10) + 15 = 20 + 15 = ₹35. The brackets tell you to calculate the cost of biscuits first.

Worked Example

Step-by-Step

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

Step 1: Identify the brackets. Here, it's (3 x 4).
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Step 2: Solve the operation inside the brackets. 3 x 4 = 12.
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Step 3: Replace the bracket with its calculated value. The expression becomes 5 + 12 - 2.
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Step 4: Now, solve the remaining operations from left to right. 5 + 12 = 17.
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Step 5: Continue from left to right. 17 - 2 = 15.
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Answer: 15

Why It Matters

Understanding 'brackets first' is crucial for solving complex math problems correctly, just like a computer needs a clear sequence of steps. It's used by engineers designing bridges, programmers writing code for apps, and even data scientists analysing cricket match statistics to ensure calculations are always accurate.

Common Mistakes

MISTAKE: Solving operations from left to right without paying attention to brackets. For example, in 10 + (2 x 3), doing 10 + 2 = 12, then 12 x 3 = 36. | CORRECTION: Always look for brackets first and solve whatever is inside them before anything else. So, 10 + (2 x 3) becomes 10 + 6 = 16.

MISTAKE: Distributing a number outside the bracket incorrectly. For example, in 5(2 + 3), doing 5 + 2 + 3 = 10. | CORRECTION: If there's a number directly next to a bracket with no sign, it means multiplication. So, 5(2 + 3) means 5 x (2 + 3), which is 5 x 5 = 25.

MISTAKE: Ignoring nested brackets (brackets inside other brackets). For example, in 10 + [2 x (3 + 1)], solving 2 x 3 first. | CORRECTION: When you have brackets inside brackets, always solve the innermost bracket first. So, (3 + 1) = 4, then [2 x 4] = 8, then 10 + 8 = 18.

Practice Questions

Try It Yourself

QUESTION: Solve: 7 + (8 - 3) | ANSWER: 12

QUESTION: Solve: 20 - (4 x 2) + 5 | ANSWER: 17

QUESTION: Your school trip costs ₹300 per student. If you pay for 3 students and also buy a souvenir for ₹50, how much do you spend? Write an expression and solve. | ANSWER: (3 x 300) + 50 = 900 + 50 = ₹950

MCQ

Quick Quiz

What is the first step to solve the expression: 15 - (6 + 2) x 3?

Subtract 6 from 15

Add 6 and 2

Multiply 2 by 3

Subtract 2 from 15

The Correct Answer Is:

According to the rule of 'brackets first', you must always solve the operation inside the parentheses before any other calculations. In this case, it's 6 + 2.

Real World Connection

In the Real World

When you use a calculator app on your mobile phone or a computer spreadsheet program like Microsoft Excel to calculate your monthly expenses, it automatically follows the 'brackets first' rule. If you enter '200 + (50 * 3)', it knows to multiply 50 by 3 first, just like calculating the cost of 3 chai teas at ₹50 each before adding it to your ₹200 bus fare.

Key Vocabulary

Key Terms

Brackets: Symbols like ( ) or [ ] that group parts of a mathematical expression | Operation: A mathematical action like addition, subtraction, multiplication, or division | Expression: A combination of numbers, variables, and operations | Parentheses: Another name for round brackets ( )

What's Next

What to Learn Next

Great job learning about brackets! Next, you should explore the full 'Order of Operations', often called BODMAS or PEMDAS. This will teach you the correct sequence for all operations (like powers, multiplication, division, addition, and subtraction) along with brackets, so you can solve even more complex problems!