Problem 23 In Exercises $1-66,$ compute t... [FREE SOLUTION]

91影视

Understanding Elementary Algebra with Geometry

Lewis Hirsch, Arthur Goodman

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 23

In Exercises $1-66,$ compute the value of each expression. $$8+(-15)$$

Short Answer

Expert verified

-7

Step by step solution

Understand the Problem

Identify the operation and the numbers involved. The problem asks to compute the value of the expression: $$8 + (-15).$$

Recognize Addition of a Negative Number

Adding a negative number is the same as subtracting its absolute value. Here, it means: $$8 - 15.$$

Perform the Subtraction

Subtract from 8 to find the result: $$8 - 15 = -7.$$

Write the Final Answer

Therefore, the value of the expression $$8 + (-15)$$ is $$-7.$$

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Key Concepts

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

Addition of Negative Numbers

When adding negative numbers, it's essential to remember that it is akin to subtracting their absolute value from the other number.
For instance, let's look at our example: $$8 + (-15).$$
Here, you are essentially subtracting 15 from 8.

Think of the negative number as 'taking away' instead of 'adding.'
This leads us to compute: $$8 - 15.$$

So, whenever you see an addition sign followed by a negative number, just think subtraction!

Absolute Value

The absolute value of a number is simply how far that number is from zero, regardless of its direction on the number line.
Absolute value is always positive.
For example:

The absolute value of 15 is written as \|15\| and is 15.
Similarly, the absolute value of -15 is written as \|-15\| and is also 15.

In our example, converting $-15$ then means using the absolute value of 15 in the subtraction operation:
$$(8 - 15)$$.
This isn't an 'addition' problem anymore, but a straightforward subtraction.

Subtraction of Integers

Subtraction is about finding the difference between numbers. When subtracting integers, it's useful to think of the number line:
For our given exercise: $$8 - 15 = -7.$$

Starting from 8, you move 15 units to the left, past zero, ending at -7.
This movement represents the negative space after surpassing zero.

Remember, moving 'left' on the number line means getting closer to more negative values.
This is why our final result here is \-7\.
So, whenever you encounter subtraction of integers, visualize a number line for better understanding.

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91影视

In Exercises \(1-66,\) compute the value of each expression. $$8+(-15)$$

Short Answer

Step by step solution

Understand the Problem

Recognize Addition of a Negative Number

Perform the Subtraction

Write the Final Answer

Key Concepts

Addition of Negative Numbers

Absolute Value

Subtraction of Integers

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