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Chapter 7: Problem 351

In the following exercises, find the additive inverse. $$ 19.4 $$

Short Answer

Expert verified
-19.4

Step by step solution

01

Understand the Concept of Additive Inverse

The additive inverse of a number is a number that, when added to the original number, results in zero. In mathematical terms, the additive inverse of a number 'a' is '-a' because 'a + (-a) = 0'.
02

Identify the Given Number

The given number in this exercise is 19.4.
03

Apply the Concept

To find the additive inverse of 19.4, change the sign of the number. Since 19.4 is positive, its additive inverse will be negative.
04

Determine the Additive Inverse

The additive inverse of 19.4 is -19.4.

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Key Concepts

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

Additive Inverse Explained
The concept of the additive inverse is key in understanding how numbers interact. An additive inverse of a number is simply a number that, when added to the original, results in zero. For any number 'a', its additive inverse is '-a'. This is because when you add 'a' and '-a', the result is zero ( a + (-a) = 0 ). The idea is straightforward: it's all about finding the number that 'cancels out' the original one.
Understanding Prealgebra
Prealgebra is the foundation of all other mathematics. It's where we start learning about numbers, their properties, and basic operations. In prealgebra, we learn essential concepts such as:
  • Addition and subtraction
  • Multiplication and division
  • Basic equations
Understanding the additive inverse is part of this journey. It helps us to comprehend how numbers can nullify each other and prepares us for more complex algebraic concepts later on.
Working with Negative Numbers
Negative numbers can initially seem confusing, but they're just as integral as positive numbers. A negative number is simply a number that is less than zero. When visualizing numbers on a number line, negatives are to the left of zero, while positives are to the right. Negative numbers come into play in the real world more often than we might think, for instance:
  • Temperatures below freezing
  • Depths below sea level
  • Financial debts
Learning about additive inverses involves understanding that each positive number has a 'partner' negative number that sums to zero with it. In this exercise, the number 19.4 has the additive inverse of -19.4, demonstrating that both 19.4 and -19.4 sum up to zero.

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Most popular questions from this chapter

In the following exercises, simplify using the commutative and associative properties. $$ \frac{14}{11} \cdot \frac{35}{9} \cdot \frac{14}{11} $$

In the following exercises, simplify the given expression. $$ \left(\frac{8}{15}+\frac{2}{9}\right)+\frac{7}{9} $$

In the following exercises, convert between U.S. units. Round to the nearest tenth. Kelly is 5 feet 4 inches tall. Convert her height to inches.

In the following exercises, convert between metric units. One cup of yogurt contains 13 grams of protein. Convert this to milligrams.

In the following exercises, simplity using the distributive property. $$ (a-4)-(6 a+9) $$
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