Problem 39 - Prealgebra

Question

Simplify. $$2,000+0.07(2,000)$$

Step-by-Step Solution

Answer

The simplified expression is $2,140$.

Step 1: Identify the Expression Components

The given expression is made up of two parts: the base amount is \(2,000\) and the additional amount is \(0.07 \times 2,000\). Our task is to simplify this entire expression.

Step 2: Calculate the Additional Amount

Calculate the additional amount, which is a percentage of the base amount. Multiply \(2,000\) by \(0.07\): \[ 0.07 \times 2,000 = 140 \]

Step 3: Add the Additional Amount to the Base Amount

Now add the additional amount you calculated in Step 2 to the base amount of \(2,000\):\[ 2,000 + 140 = 2,140 \]

Step 4: Solution Presentation

The simplified result of the expression \(2,000 + 0.07(2,000)\) is \(2,140\). This represents the total amount after adding \(7\%\) of \(2,000\) to the base amount itself.

Key Concepts

Basic Arithmetic Operations

Understanding basic arithmetic operations is crucial in simplifying expressions. These operations include addition, subtraction, multiplication, and division. In the given exercise, we primarily used addition and multiplication.

- **Addition** is simply combining two numbers to get a total. It's indicated by the plus symbol (+). For example, in the expression provided, we added the base amount to the additional amount calculated. - **Multiplication** involves repeated addition. It's represented by the multiplication symbol (×). In the exercise, we used this operation to calculate the percentage of the base number, specifically multiplying 0.07 by 2,000.

Mastering these operations can greatly aid in simplifying and solving math problems efficiently.

Percentage Calculation

Percentage calculation is a practical mathematical concept used frequently in various fields. It involves expressing a number as a fraction of 100. For instance, calculating percentages helps in understanding discounts, interest rates, and in our case, increase amounts.

The given problem involved calculating 7% of 2,000. To express a percentage as a decimal for easier calculation, simply divide by 100. Thus, 7% becomes 0.07.

The next step is to apply this in a multiplication operation. In our example, multiplying 2,000 by 0.07 simplifies to finding how much 7% of 2,000 is, resulting in 140.

When calculating percentages:

• Convert the percentage to a decimal.
• Multiply the decimal by the number for which you are finding a percentage.

This straightforward method will help anyone become adept at handling percentages in various scenarios.

Mathematical Expressions

Mathematical expressions represent problems using numbers, symbols, and operations. They can range from simple operations, like addition and multiplication, to more complex algebraic expressions. These expressions must be simplified to understand the final value clearly.

The exercise presented the expression \(2,000 + 0.07(2,000)\). Simplifying such expressions involves accurately following several steps:- Identify each part of the expression. - Perform calculations sequentially, adhering to the order of operations. In this exercise, identifying the expression components was crucial before calculations. Recognizing that 0.07(2,000) part represented 7% of 2,000, simplified the task.

Finally, combining all parts as seen in the simplified expression where basic arithmetic operations led us to the final result of 2,140. Understanding how to handle each component contributes to simplifying and solving any type of mathematical expression efficiently.