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Chapter 5: Problem 170

In the following exercises, simplify. $$\$ 63+0.18(\$ 63)$$

Short Answer

Expert verified
74.34

Step by step solution

01

- Understand the Problem

The expression to be simplified is \(63 + 0.18(63)\). This involves adding 18% of 63 to the original 63.
02

- Calculate 18% of 63

Calculate 18% of 63 by multiplying 63 by 0.18: \[ 0.18 \times 63 = 11.34 \]
03

- Adding the Results

Add the result from Step 2 to the original 63: \[ 63 + 11.34 = 74.34 \]

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Key Concepts

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

Percentage Calculations
In the given exercise, you are asked to simplify the expression by calculating a percentage of a given number. Percentage calculations often appear in various real-life scenarios, such as calculating sales tax, discounts, or interest rates. To find 18% of a number, you convert the percentage to a decimal by dividing by 100. For example, 18% becomes 0.18. Then, multiply this by the given number to determine the value. In this case, multiplying 0.18 by 63.
Arithmetic Operations
Simplifying algebraic expressions often involves arithmetic operations such as addition, subtraction, multiplication, and division. In this exercise, you see that first, multiplication is used to find 18% of 63. Then, the result is added to the original number. Arithmetic operations follow the order of operations (PEMDAS/BODMAS), ensuring calculations are performed correctly, often simplifying the expression step by step.
Step-by-Step Solutions
A step-by-step approach ensures clarity and helps avoid mistakes. Let's look closer at each step of our example:
Step 1: Recognize the components of the expression and understand that you need to find a percentage of a number.
Step 2: Convert the percentage to a decimal and multiply it by the number 63. This gives you \(0.18 \times 63 = 11.34\).
Step 3: Add the product to the original number. The final simplified result is \(63 + 11.34 = 74.34\). This methodical approach helps ensure you do not miss or miscalculate any part of the problem.

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