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Chapter 1: Problem 18

Simplify. $$20+(9-4) \cdot 2$$

Short Answer

Expert verified
The result of simplifying the expression \(20+(9-4) \cdot 2\) is \(30\).

Step by step solution

01

Simplify the expression inside the brackets

Our first operation is to simplify inside the bracket. This leaves us with the expression: \(20 + (5) \cdot 2\).
02

Perform the multiplication

The next step in the BIDMAS order of operations is to perform the multiplication. Hence, our operation becomes: \(20 + 10\).
03

Perform the addition

Finally, we only have one operation left, which is the addition of 20 and 10. Therefore, the result is \(30\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

BIDMAS
When tackling mathematical expressions, it's crucial to follow the BIDMAS rule, which stands for Brackets, Indices, Division, Multiplication, Addition, and Subtraction. This sequence ensures that calculations are performed correctly and consistently.

  • Brackets: Always solve expressions inside brackets first.
  • Indices: Solve powers and roots next.
  • Division and Multiplication: Execute these operations from left to right.
  • Addition and Subtraction: Perform these operations last, also from left to right.
In the exercise given, the calculation inside the brackets (9 - 4) is completed first. Then, multiplication is performed before addition. Following BIDMAS ensures accurate results.
Simplifying Expressions
Simplifying expressions involves breaking them down into simpler forms while maintaining their original value. It requires a systematic approach to reduce complexity, making calculations easier.

The process often involves:
  • Removing parentheses by solving expressions inside them.
  • Combining like terms, if applicable.
  • Executing operations in the correct order, as guided by BIDMAS.
In the exercise, we first simplify inside the brackets: 9 minus 4 becomes 5. This gives us a cleaner expression to work with: \(20 + 5 \cdot 2\). By reducing each part step by step, we make the overall problem more manageable.
Mathematical Operations
Understanding mathematical operations is key to solving expressions correctly. These operations include addition, subtraction, multiplication, and division. Each operation plays a specific role and needs to be performed accurately.

Here's a brief overview:
  • Addition: Combining numbers to increase value.
  • Subtraction: Deducting one number from another to decrease value.
  • Multiplication: Calculating the total of one number added repeatedly.
  • Division: Splitting a number into equal parts.
In our example, after simplifying the expression \(20 + (5) \cdot 2\), we first multiply 5 by 2 to get 10.
We then add 20 to 10 to arrive at the final result: 30. Each of these steps reflects the essential operations that build up more complex calculations.

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