Problem 75 - Algebra 1

Question

Evaluate the expression. $$16.9-1.5(1.8+0.2)$$

Step-by-Step Solution

Answer

The evaluated expression is \(13.9\).

Step 1: Solve the expression inside the brackets

Add the values \(1.8 + 0.2\) together, which makes \(2.0\). Now, the expression becomes \(16.9 -1.5(2.0)\).

Step 2: Perform the multiplication

Next, multiply \(1.5\) with \(2.0\) to get \(3.0\). Substitute this into the equation so it becomes \(16.9 - 3.0\).

Step 3: Perform the subtraction

Finally, subtract \(3.0\) from \(16.9\) to get \(13.9\).

Key Concepts

Order of Operations

Understanding the order of operations is essential when evaluating algebraic expressions. The order of operations provides a set of rules that dictate the sequence in which arithmetic operations should be performed to ensure consistent and correct results. These rules are often memorized using the acronym PEMDAS:

• Parentheses: Solve expressions inside parentheses or brackets first.
• Exponents: Next, calculate any exponents in the expression.
• Multiplication and Division: Performed from left to right.
• Addition and Subtraction: Finally, perform all addition and subtraction from left to right.

Each Rule is important to solve a problem accurately. In the given expression, start by evaluating the expression within the parentheses. This sets the stage for correctly applying the remaining operations.

Arithmetic Operations

Arithmetic operations are the basic building blocks of mathematics, consisting mainly of addition, subtraction, multiplication, and division. Understanding each operation fully helps one to evaluate expressions and solve complex equations with ease.
In the exercise, you encountered all but division. Here's a brief look:

• Addition brings two numbers together to create a sum, like the numbers inside the parentheses where the result was 2.0.
• Subtraction involves taking one number away from another, visible in the final step of the example, reducing 16.9 by 3.0.
• Multiplication is all about increasing a number by repeatedly adding it, which you applied to get 3.0 by calculating 1.5 times 2.0.

Learning these operations well allows for accurate and efficient problem solving. Remember to always follow the correct order as described in the previous section.

Expression Evaluation

Expression evaluation is the process of computing a value based on arithmetic operations and the order of operations. It's how we find numerical answers in equations like our original exercise. This process involves:

• Understanding and identifying each component of the expression.
• Applying arithmetic operations correctly while respecting the order of operations.
• Substituting intermediate results back into the expression for further calculation.

In our example,

1. First, you add within the parentheses, turning the expression into a simpler form.
2. Then, by multiplying, it reduces further for easier subtraction.
3. Lastly, calculating a neat subtraction provides the final result, 13.9.

Mastering expression evaluation enables you to tackle even more complicated algebraic problems with confidence.