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Chapter 5: Problem 244

Simplify. 30\((18.1-32.5)\)

Short Answer

Expert verified
-432

Step by step solution

01

Evaluate the expression inside the parenthesis

Calculate the value inside the parenthesis: \(18.1 - 32.5\). Subtract 32.5 from 18.1 to get the result. \(18.1 - 32.5 = -14.4\)
02

Multiply the result by 30

Now, take the result from step 1 and multiply it by 30. \(30 \times -14.4\). Perform the multiplication: \(30 \times -14.4 = -432\).

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Key Concepts

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

Basic Arithmetic Operations
Basic arithmetic operations are the foundation of math. These operations include addition, subtraction, multiplication, and division. Understanding how to perform these correctly is essential for solving more complex problems.
  • Addition: Combining two numbers to find their total. For example, 3 + 5 = 8.
  • Subtraction: Finding the difference between two numbers. For example, 8 - 5 = 3.
  • Multiplication: Repeated addition of a number. For example, 3 脳 4 means adding 3 four times, so 3 + 3 + 3 + 3 = 12.
  • Division: Splitting a number into equal parts. For example, 12 梅 4 means dividing 12 into 4 equal parts, each being 3.
Performing these operations correctly is crucial when simplifying arithmetic expressions. In our exercise, we used subtraction first and then multiplication, emphasizing the importance of following the correct order of operations.
Parentheses in Math
Parentheses are used in mathematics to group parts of an expression that need to be evaluated first. This is due to the rules of the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Why Use Parentheses?
  • They clarify which operations to perform first, overriding the usual order.
  • They help avoid ambiguity in mathematical expressions.
In the given problem, \(30(18.1 - 32.5)\), the expression inside the parentheses \(18.1 - 32.5\) must be solved before multiplying by 30. This ensures that the calculation follows the proper sequence and yields the correct result. Without parentheses, the expression might be misinterpreted, leading to errors.
Multiplication with Negative Numbers
Multiplying numbers can get tricky when negative numbers are involved. It is important to understand the rules of multiplication with negatives:
  • A positive number times a positive number equals a positive number. For example, \(3 \times 4 = 12\).
  • A positive number times a negative number equals a negative number. For example, \(3 \times -4 = -12\).
  • A negative number times a negative number equals a positive number. For example, \(-3 \times -4 = 12\).
In our exercise, after evaluating \(18.1 - 32.5 = -14.4\), we multiplied 30 by -14.4. Since multiplying a positive number (30) by a negative number (-14.4) gives a negative result, the final answer was -432. Understanding this principle helps avoid mistakes and ensures accurate results when dealing with negative numbers in arithmetic operations.

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