Problem 15 $-7+(-8)$... [FREE SOLUTION]

91影视

Elementary Algebra

Jerome E. Kaufmann, Karen L. Schwitters

$Math Studyset 91影视 Explanations$ Math

9 Edition

Chapter 1: Problem 15

$-7+(-8)$

Short Answer

Expert verified

The result is -15.

Step by step solution

Understanding Negative Numbers

Both -7 and -8 are negative numbers. When adding negative numbers, we are essentially moving further down the number line in the negative direction.

Combining the Numbers

When you add two negative numbers, you add their absolute values (ignore the negative signs for now). So, calculate 7 + 8, which equals 15.

Applying the Negative Sign

Since both numbers were negative, the sum of 7 and 8 (which is 15) will also be negative. Therefore, the result of adding -7 and -8 is -15.

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Key Concepts

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

Adding Negative Numbers

Adding negative numbers can seem tricky at first, but it's like adding any other numbers. Imagine having two debts 鈥� each a negative value. When you add these debts together, your overall debt increases.

Think of it like this:

Both numbers are below zero.
The operation involves adding their absolute values.
Finally, the answer will also be negative, as we are working within the negative range.

For example, with $-7 + (-8)$, you calculate by adding 7 and 8 to get 15. Because both numbers are negative, the result is $-15$.

Whenever you add negative numbers, imagine taking steps further away from zero into the negative territory. Each step you take makes the number more negative.

Number Line

A number line is a visual tool that helps us understand numbers. It's a straight line where you can see positive numbers positioned right of zero and negative numbers to the left.

When adding negative numbers, the number line can be quite helpful:

Starting point: Identify your first number. For $-7$, you'd start seven steps left of zero.
Direction: Since you鈥檙e adding another negative number ($-8$), you continue moving left.
Result: You end up at $-15$, 15 steps left of zero.

By visualizing this movement on the number line, it becomes easier to see how negative numbers add up, reinforcing your understanding.

Absolute Values

Absolute values represent the distance a number is from zero on the number line. It's always non-negative and makes calculations simpler by ignoring the direction.

To handle negative numbers:

Convert each to its absolute value. So $-7$ becomes 7, and $-8$ becomes 8.
Add them together. Here, 7 + 8 = 15.
As both original numbers were negative, append a minus sign to the sum, yielding $-15$.

Using absolute values, especially when adding negatives, allows you to focus solely on how far each number is from zero, ignoring the direction they face on the number line. This strategy simplifies the process and helps to avoid confusion.

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91影视

\(-7+(-8)\)

Short Answer

Step by step solution

Understanding Negative Numbers

Combining the Numbers

Applying the Negative Sign

Key Concepts

Adding Negative Numbers

Number Line

Absolute Values

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