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Chapter 5: Problem 169

In the following exercises, simplify. $$\$ 45+0.08(\$ 45)$$

Short Answer

Expert verified
48.6

Step by step solution

01

Identify the Expression

The given expression is \(45 + 0.08(45)\). Our goal is to simplify this expression.
02

Multiply Inside the Parentheses

Calculate \(0.08 \times 45\).
03

Perform the Calculation

\(0.08 \times 45 = 3.6\). This simplifies the expression to \(45 + 3.6\).
04

Add the Numbers

Now add \(45\) and \(3.6\) together: \(45 + 3.6 = 48.6\).

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Key Concepts

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

Order of Operations
Understanding the order of operations is crucial when simplifying expressions. The order of operations is a set of rules that tells us the sequence in which we need to perform mathematical operations. These rules can be remembered using the acronym PEMDAS, which stands for:
  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)
In the given exercise, we need to follow these rules to simplify the expression correctly. We start by addressing the multiplication inside the parentheses before moving on to addition.
Multiplication
In our expression, we encounter multiplication within the parentheses: \(45 + 0.08(45)\). According to the order of operations, we must first handle this multiplication.
\[0.08 \times 45\] When we multiply 0.08 by 45, we get 3.6. This step simplifies our expression to:\[45 + 3.6\] Multiplication allows us to deal with portions or parts of numbers, especially useful when dealing with percentages or fractions. Remember to always handle multiplication before moving on to addition or subtraction, as per the PEMDAS rules.
Addition
After completing the multiplication, we now proceed to the addition step: \(45 + 3.6\) Adding these two numbers is straightforward:
\[45 + 3.6 = 48.6\] Addition involves combining values to get a total sum. It鈥檚 important to align the decimal points when dealing with decimals to avoid mistakes. In this exercise, you can clearly see that by incrementing 45 by 3.6, we arrive at the final simplified expression of 48.6.
Understanding and practicing these core concepts can greatly help in simplifying various mathematical expressions accurately and efficiently.

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