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Chapter 13: Problem 40

Rewrite expression as an addition expression by using the additive inverse. \(15 c-26\)

Short Answer

Expert verified
The expression as an addition is \(15c + (-26)\).

Step by step solution

01

Understanding the Problem

The given expression is \(15c - 26\). We need to express this as an addition expression using the additive inverse property.
02

Identify the Subtraction Operation

In the expression \(15c - 26\), the term \(-26\) involves a subtraction. To rewrite this as an addition expression, we need to express this subtraction using the additive inverse.
03

Write the Additive Inverse

The additive inverse of a number is the number that, when added to the original number, results in zero. Thus, the additive inverse of \(-26\) is \(+26\).
04

Rewrite as an Addition Expression

Replace the subtraction with the additive inverse written as an addition: \(15c - 26\) can be rewritten as \(15c + (-26)\). This uses the additive inverse \(-26\) within an addition expression.

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Key Concepts

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

Additive Inverse
The additive inverse is a fascinating concept in prealgebra as it lays the foundation for understanding how numbers relate and interact. Imagine you have a number, let's say -26. The additive inverse of this number is the value that, when added to it, results in zero. So, in this case, the additive inverse of -26 is 26.
  • If you add -26 and 26, you get zero: \(-26 + 26 = 0\).
  • It's like having a negative and a positive weight in balance, canceling each other out.
This principle helps in transforming expressions to different forms, often simplifying equations or making them easier to work with.
Subtraction
Subtraction might seem straightforward, but there's a deeper way it connects to addition through the concept of the additive inverse.
  • Subtraction is simply adding the opposite of a number. For example, instead of subtracting 26, we add -26.
  • In the expression \(15c - 26\), we are essentially doing the same thing as \(15c + (-26)\).
This approach is helpful because it provides consistency in algebraic operations, allowing us to handle complex algebraic expressions more effectively.
Addition Expression
An addition expression is just a way of writing a mathematical equation where all operations are addition operations. For example, instead of having subtraction, we use the additive inverse to write everything in terms of addition.
  • Changing subtraction to addition can simplify solving equations by keeping the method uniform.
  • For instance, rewriting \(15c - 26\) as \(15c + (-26)\) fits this structure.
This alternate way of looking at subtraction encourages more straightforward problem-solving skills in algebra.
Algebraic Expressions
Understanding algebraic expressions is crucial in prealgebra. They are combinations of numbers, variables, and operations.
  • Expressions like \(15c + (-26)\) combine coefficients, variables, and numerical constants, bound by operations.
  • Variables, such as \(c\), act as placeholders that can represent numbers and are essential for solving equations.
Mastering the manipulation of these expressions helps develop deep algebraic skills, crucial for future math studies.

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Most popular questions from this chapter

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A number cube is rolled. Determine whether each event is mutually exclusive or inclusive. Then find the probability. \(P(\text { odd or greater than } 3)\)

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