Problem 53 Find the opposite, or additive i... [FREE SOLUTION]

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Intermediate Algebra : Concepts and Applications

Marvin L. Bittinger, David J. Ellenbogen, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

10 Edition

Chapter 1: Problem 53

Find the opposite, or additive inverse. $$ 2.37 $$

Short Answer

Expert verified

-2.37

Step by step solution

Understand the concept of additive inverse

The additive inverse of a number is what you add to that number to get zero. For any number given, its additive inverse is simply its negative.

Identify the given number

In this exercise, the given number is 2.37.

Determine the additive inverse

To find the additive inverse of 2.37, change its sign. So, the additive inverse of 2.37 is -2.37.

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Key Concepts

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

Opposite Numbers

In mathematics, opposite numbers are two numbers that, when added together, result in zero. Every number has an opposite. For example, the opposite of 5 is -5. This concept is directly linked to the idea of additive inverse. Essentially, finding the opposite number helps in numerous calculations, like solving equations and understanding the number line. Opposite numbers can be visualized on the number line as being equidistant from zero but on opposite sides. Therefore, if you start at zero and move 2.37 units to the right, you get 2.37. If you move 2.37 units to the left of zero, you get -2.37.

Negative Numbers

Negative numbers are numbers less than zero and are usually denoted with a minus sign (-). They are essential in various real-world contexts, like temperatures below freezing, depths below sea level, and financial debts. Negative numbers are used hand in hand with positive numbers to describe values. For example, having 2.37 dollars in debt is expressed as -2.37 dollars. Understanding negative numbers involves recognizing their position on the number line. Always remember, the more negative the number, the further it is from zero.

Zero Property

The zero property is a fundamental concept in arithmetic and algebra. It states that the sum of any number and its additive inverse (opposite) is zero. Mathematically, this is written as: \[a + (-a) = 0\] For instance, 2.37 + (-2.37) = 0. This property is very useful in solving various types of equations and simplifying expressions, as it helps us eliminate terms and isolate variables. It also forms the basis for many other mathematical rules and operations. Knowing this property can significantly ease the understanding of more complex mathematical concepts.

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91影视

Find the opposite, or additive inverse. $$ 2.37 $$

Short Answer

Step by step solution

Understand the concept of additive inverse

Identify the given number

Determine the additive inverse

Key Concepts

Opposite Numbers

Negative Numbers

Zero Property

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