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Chapter 1: Problem 3

Add. See Examples I through 7. $$ -6+(-8) $$

Short Answer

Expert verified
The sum is \(-14\).

Step by step solution

01

Identify the Operation

The exercise asks us to add two numbers: \(-6\) and \(-8\). These numbers are both negative integers.
02

Understand the Rule

When adding two negative numbers, we combine their absolute values and attach a negative sign to the sum. The absolute value of \(-6\) is 6, and the absolute value of \(-8\) is 8.
03

Add the Absolute Values

Now add the absolute values: \[6 + 8 = 14\]
04

Apply the Negative Sign

Since both numbers were negative, the result of their addition will also be negative. So, we apply a negative sign to 14, giving us:\[-14\]

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Key Concepts

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

Understanding Absolute Value
The absolute value of a number is simply how far that number is from zero on the number line, without considering its direction. It measures the "size" of the number, ignoring its positive or negative sign. For instance, the absolute value of
  • -6 is 6 because -6 is 6 units away from zero.
  • Similarly, the absolute value of -8 is 8.

Whenever you're asked to find the absolute value, you just take the number and drop the negative sign, if there is one. Think of the absolute value as a tool to focus purely on numbers' magnitudes without any distractions from signs.
Addition Rules Simplified
Adding numbers can feel easy when they're all positive, but becomes trickier with negatives. Some important rules make it easier:
  • **Adding Positive Numbers:** Just add the values as they are. For example, 3 + 5 equals 8.
  • **Adding Negative Numbers:** Combine their absolute values and then put a negative sign in front of the result. For instance, adding -6 and -8, we combine the values of 6 and 8 to get 14, and then make it negative, so it becomes -14.
  • **Mixed Sign Addition (one positive, one negative):** Subtract the smaller absolute value from the larger one, and give the result the sign of the number with the larger absolute value.

When you master these rules, tackling addition becomes straightforward, even when negative numbers are involved.
Negative Integers Explained
Negative integers can initially seem confusing, but they're just as simple as positive numbers, just in the opposite direction. Imagine a number line:
  • All numbers to the left of zero are negative.
  • Their absolute values increase the further left you go.

Negative integers are useful in many real-world situations, like measuring temperatures below zero or indicating loss in finance. When computing with them, especially in addition or subtraction, understanding the role of negative signs is crucial. They tell you the direction (left or right on a number line) that an operation is moving. Viewing negative integers in this way not only simplifies math problems but also uncovers their practical significance.

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Perform the following operations. Write answers in lowest terms. $$ \frac{57}{132}-\frac{13}{132} $$

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Perform the following operations. Write answers in lowest terms. $$ \frac{8}{11}-\frac{1}{4}+\frac{1}{2} $$
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