Problem 147
Question
perform the indicated operation. \(-6+(-3)\) (Section 1.5 , Example 3)
Step-by-Step Solution
Verified Answer
The result of \(-6 + (-3)\) is \(-9\).
1Step 1: Identify the numbers and operation
Looking at the problem, the numbers involved are -6 and -3, and the operation is addition.
2Step 2: Perform the addition
When we add the absolute values of the numbers, we have \(6 + 3 = 9\).
3Step 3: Apply the negative sign
As both numbers were negative, the result will also be negative. So, the final answer is \(-9\).
Key Concepts
Negative Number AdditionInteger OperationsAbsolute Value
Negative Number Addition
Understanding how to add negative numbers is essential for mastering the basics of algebra and arithmetic. When we think about negative number addition, it's crucial to consider the direction each number represents on a number line. Negative numbers are to the left of zero, while positive numbers are to the right.
To add negative numbers, like (-6) and (-3), envision each negative number as a step to the left on the number line. So, if you start at zero and move 6 steps to the left, you reach -6. From there, adding -3 means taking 3 more steps to the left, landing you at -9. The key here is that adding two negative numbers involves moving further left on the number line, which effectively means the value is becoming more negative. Therefore, (-6) + (-3) equals -9.
A mistake often made is to overlook that when adding negatives, the values compound rather than cancel each other out. Remember, the more negative numbers you add, the further left you go!
To add negative numbers, like (-6) and (-3), envision each negative number as a step to the left on the number line. So, if you start at zero and move 6 steps to the left, you reach -6. From there, adding -3 means taking 3 more steps to the left, landing you at -9. The key here is that adding two negative numbers involves moving further left on the number line, which effectively means the value is becoming more negative. Therefore, (-6) + (-3) equals -9.
A mistake often made is to overlook that when adding negatives, the values compound rather than cancel each other out. Remember, the more negative numbers you add, the further left you go!
Integer Operations
Integer operations include addition, subtraction, multiplication, and division involving whole numbers and their opposites. In this context, it's important to understand how addition works with negatives, as integers can be positive, negative, or zero.
When performing integer operations, the rules change slightly depending on whether you're working with positives or negatives. For example, when adding two positive integers, the value increases, but when adding two negative integers, as shown in the example with (-6) + (-3), the value becomes a larger negative number.
Remember the simple rules:
When performing integer operations, the rules change slightly depending on whether you're working with positives or negatives. For example, when adding two positive integers, the value increases, but when adding two negative integers, as shown in the example with (-6) + (-3), the value becomes a larger negative number.
Remember the simple rules:
- Addition of two positive numbers or two negative numbers results in a sum that follows the sign of the numbers.
- Subtracting a larger number from a smaller one results in a negative number.
- Multiplying or dividing two numbers with different signs results in a negative number, while the same signs yield a positive number.
Absolute Value
The absolute value of a number refers to its distance from zero on a number line, ignoring whether it's positive or negative. It's like asking how far a number is from zero without considering direction. For example, the absolute value of both 6 and -6 is 6 since both are six units away from zero.
Why is this important? When adding negative numbers, or during any integer operations, sometimes you'll work with absolute values to understand the problem. In the shared exercise, the operation (-6) + (-3) required looking at the absolute values of the numbers during the calculation process.
The sum of their absolute values was 6 + 3, which is 9, but because the original numbers were negative, the final answer retained a negative sign, resulting in -9. The concept of absolute value is central to understanding the magnitude of numbers in addition, regardless of their sign, and plays a pivotal role in various mathematical operations.
Why is this important? When adding negative numbers, or during any integer operations, sometimes you'll work with absolute values to understand the problem. In the shared exercise, the operation (-6) + (-3) required looking at the absolute values of the numbers during the calculation process.
The sum of their absolute values was 6 + 3, which is 9, but because the original numbers were negative, the final answer retained a negative sign, resulting in -9. The concept of absolute value is central to understanding the magnitude of numbers in addition, regardless of their sign, and plays a pivotal role in various mathematical operations.
Other exercises in this chapter
Problem 145
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{1}{2}+\frac{1}{5
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Use your calculator to attempt to find the quotient of \(-3\) and \(0 .\) Describe what happens. Does the same thing occur when finding the quotient of 0 and \(
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Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Every fraction has infin
View solution Problem 148
perform the indicated operation. \(-6-(-3) \text { (Section } 1.6, \text { Example } 1)\)
View solution