Problem 108 In the following exercises, add ... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 5: Problem 108

In the following exercises, add or subtract. $$-8.6+(-8.6)$$

Short Answer

Expert verified

-17.2

Step by step solution

Understand the Problem

We need to add two negative numbers: -8.6 and -8.6.

Combine the Numbers

When adding two negative numbers, think of moving left on the number line. Adding -8.6 to -8.6 means you are moving 8.6 units to the left from an initial position of -8.6 units.

Perform the Addition

Combine -8.6 and -8.6. Mathematically, this is represented as: -8.6 + (-8.6) = -17.2

Write the Final Answer

The sum of -8.6 + (-8.6) is -17.2.

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Key Concepts

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

negative number addition

Adding negative numbers might seem tricky at first, but it's actually simple once you understand it. When you add two negative numbers, you are essentially combining their absolute values and then applying the negative sign to the total.
For example, adding -8.6 and -8.6 means you are combining the two 8.6s together and then keeping the result negative.
Here鈥檚 a step-by-step way to think about it:

First, ignore the negative signs and just add the numbers as if they were positive: 8.6 + 8.6.
This gives you 17.2.
Finally, since both original numbers were negative, the result is also negative: -17.2.

So the equation -8.6 + (-8.6) = -17.2 makes perfect sense!

number line

Visualizing negative number addition on a number line can help make the concept clearer.
Think of the number line as a horizontal line that includes positive numbers, zero, and negative numbers. Positive numbers are to the right of zero and negative numbers are to the left.

When you add a negative number, you move to the left on the number line, because going left means you are decreasing the value.
For instance, starting at -8.6 and then adding another -8.6 means you take 8.6 steps to the left twice.
After the first addition, you are at -8.6.
After the second addition, you move another 8.6 steps to the left, which lands you at -17.2.

Using the number line is a handy visual tool to understand how adding negative numbers decreases value.

basic arithmetic operations

Basic arithmetic operations like addition and subtraction apply to both positive and negative numbers, but their rules need to be clearly understood.

Adding Numbers: Like above, adding two negative numbers intensifies their negativity.
Subtracting Numbers: Subtraction, especially with negative numbers, can be thought of as adding the opposite. For example, subtracting -8.6 is the same as adding +8.6.

To recap, when you add negative numbers, combine their absolute values and then apply the negative sign. When you encounter subtraction, switch to adding the opposite, and use the number line for a visual representation. Mastering these basic arithmetic operations with negative numbers will help build a solid foundation for more complex mathematical problems.

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91影视

In the following exercises, add or subtract. $$-8.6+(-8.6)$$

Short Answer

Step by step solution

Understand the Problem

Combine the Numbers

Perform the Addition

Write the Final Answer

Key Concepts

negative number addition

number line

basic arithmetic operations

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