Problem 41 - Prealgebra

Question

Simplify. $$3,000+0.07(3,000)$$

Step-by-Step Solution

Answer

The simplified expression is 3,210.

Step 1: Understand the Expression

The given expression is \(3,000 + 0.07(3,000)\). This expression consists of a base amount \(3,000\) and 7% of this base amount, which means we have to calculate 7% of \(3,000\) and then add it to the base amount.

Step 2: Calculate 7% of 3,000

To find 7% of \(3,000\), we multiply \(3,000\) by 0.07. This calculation is done as follows: \[0.07 \times 3,000 = 210\] Thus, 7% of \(3,000\) is \(210\).

Step 3: Add the Percent Amount to the Base

Now add the calculated 7% of \(3,000\), which is \(210\), to the base amount \(3,000\): \[3,000 + 210 = 3,210\]

Step 4: Simplify the Expression

The simplified expression is \(3,210\).

Key Concepts

Understanding Percent Calculation

Percent calculation is a basic yet powerful concept in mathematics that deals with the idea of parts per hundred. When we talk about percentages, we're essentially referring to how many parts of 100 we have. For instance, saying 7% means we're discussing 7 parts out of 100.

To calculate the percentage of a number, you convert the percentage into its decimal form by dividing it by 100, and then multiply by the number you're interested in. For example, calculating 7% of 3,000 involves the following steps:

• Convert 7% into a decimal: 7% becomes 0.07.
• Multiply by the given amount: 0.07 × 3,000.
• This results in 210, which is 7% of 3,000.

Percentages are commonly used in everyday scenarios like calculating discounts, interest rates, and more. Understanding how to work with percentages is crucial for financial literacy and other real-world applications.

Basic Arithmetic Operations

Basic arithmetic operations form the foundation of mathematics and include addition, subtraction, multiplication, and division. They are the building blocks that we use to manipulate numbers and solve problems, from simple calculations to complex equations.

Let's break down the operations as they apply to the given exercise:

• Addition: The process of combining numbers to get a sum. In the expression 3,000 + 210, we add to find the total amount.
• Multiplication: This involves repeated addition and is used to calculate percentages, as seen in 0.07 × 3,000 to find 7% of 3,000.

Addition and multiplication were the focal operations in this expression, helping us to increase the base amount by its percentage. Mastery of these operations is essential for tackling a wide range of mathematical tasks, including understanding algebraic expressions.

Mathematical Expression Simplification

Simplifying mathematical expressions is about reducing them to their most concise form while retaining their original value. This usually involves applying arithmetic operations to combine or eliminate terms.

In the original exercise, the expression 3,000 + 0.07(3,000) was simplified through a few steps:

• First, calculate 7% of 3,000: 0.07 × 3,000 = 210.
• Next, add this value to the base amount: 3,000 + 210.
• The result is the simplified expression: 3,210.

Simplification helps make expressions easier to understand and work with, especially in more complicated equations. Learning to identify parts of an expression that can be combined or broken down is a valuable skill in mathematics.