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Chapter 3: Problem 4

Write each expression in words. $$ -16-(+8) $$

Short Answer

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Question: Write the following mathematical expression in words: -16 - (+8) Answer: Negative sixteen minus positive eight.

Step by step solution

01

Identify the problem type and clarify terms

The given expression is a subtraction problem (-16 - (+8)). The first term is -16 (a negative integer), and the second term is +8 (a positive integer). Before writing this expression in words, let's make sure we state the operation being performed clearly.
02

Write the expression in words

To write the expression in words, describe each term and the operation being performed. The expression -16 - (+8) written in words is: "Negative sixteen minus positive eight."

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Key Concepts

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

Integer Operations
In algebra, understanding how to perform operations with integers is crucial. Integers are whole numbers and can be either positive, negative, or zero. Dealing with them requires familiarity with a few basic rules.
  • **Addition:** When adding integers of the same sign, combine their absolute values and keep the common sign.
  • **Subtraction:** Subtraction can be turned into addition by changing the subtractand to its opposite and then following the rules of addition.
  • **Multiplication & Division:** Same signs result in a positive outcome, while different signs lead to a negative outcome.
For example, in the expression \(-16 - (+8)\), we are facing a subtraction operation where both integers have different signs.
Negative Numbers
Negative numbers represent values less than zero and are typically found on the left side of the number line. They are crucial in representing deficits, decreases, or temperatures below zero, all of which are common in real-life scenarios.
  • **Understanding:** Negative numbers are written with a minus sign (e.g., \(-5\)).
  • **Addition:** Adding a negative number is like subtracting its positive counterpart.
  • **Positioning:** They are always less than any positive number and smaller numbers in absolute value are greater (e.g., \(-3 > -7\)).
In the expression \(-16\), the number is negative, indicating a value below zero. Understanding negative numbers helps in interpreting expressions like \(-16 - (+8)\) accurately.
Subtraction in Algebra
In algebra, subtraction reflects the action of removing or taking away. It can be expressed as finding the difference between numbers or expressions. Understanding how to handle subtraction, especially with positive and negative numbers, helps prevent calculation errors.
  • **Changing to Addition:** Subtraction of a positive number (\(- a - b\)) is similar to adding a negative (\(- a + (-b)\)).
  • **Real-life Examples:** Think of temperature drops or money spent to grasp subtraction better.
In the example \(-16 - (+8)\), we turn it into \(-16 + (-8)\) to simplify understanding. This transformation helps to apply familiar rules of integer addition.

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