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Chapter 3: Problem 70

Write each subtraction expression as an addition expression. $$-8-4$$

Short Answer

Expert verified
-8 - 4 can be rewritten as -8 + (-4).

Step by step solution

01

Understand the Expression

The given expression is \[-8 - 4\].Here, we are asked to convert a subtraction expression into an addition expression.
02

Rewrite Subtraction as Addition

When converting subtraction into addition, remember that subtracting a number is the same as adding its opposite. Hence, we rewrite \[-8 - 4\] as \[-8 + (-4)\].
03

Verify the Conversion

Check the logic of the conversion. In the subtraction \[-8 - 4\], subtracting 4 is equivalent to adding \(-4\). Thus, \(-8 - 4\) is correctly expressed as \[-8 + (-4)\].

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Key Concepts

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

Negative Numbers
Negative numbers appear below zero on the number line. They are used to represent quantities less than zero and are an essential component of arithmetic.
For instance, when discussing temperature, negative numbers indicate values below freezing. Similarly, in a financial context, they often represent debts or money owed.
When dealing with negative numbers in mathematics, it鈥檚 crucial to remember:
  • A negative number is simply the opposite of a positive number.
  • In mathematical expressions, negative numbers are typically denoted by a minus sign (-) preceding the number.
  • Negative numbers are used in various mathematical operations, such as addition and subtraction.
Being comfortable with negative numbers allows you to easily navigate through more complex mathematical concepts.
Arithmetic Operations
Arithmetic operations are basic mathematical operations that include addition, subtraction, multiplication, and division.
Each operation has its own rules, but they all work together to help us express and solve different mathematical problems.
When approaching subtraction, for example:
  • Subtraction can often be converted to addition by changing the sign of the number being subtracted. This means subtracting a number is the same as adding its opposite.
  • This principle simplifies the process of operating with negative numbers and helps prevent errors. For instance, \(-8 - 4\) becomes \(-8 + (-4)\).
Understanding how to apply arithmetic operations is foundational for solving equations and manipulating mathematical expressions.
Mathematical Expressions
Mathematical expressions are combinations of numbers, variables, operations, and sometimes symbols, which represent a specific value or relationship.
They are the language of mathematics, allowing us to model real-world situations and solve problems.
Key elements of mathematical expressions include:
  • Numbers and/or variables: These are the basic building blocks of an expression.
  • Operations: These dictate the calculations to be performed, such as addition or subtraction.
  • Parentheses: These can alter the order in which operations are performed.
Translating a subtraction expression into an addition expression is a common manipulation in algebra that simplifies calculations. This manipulation often makes it easier to combine like terms and make more complex expressions manageable.

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