Problem 28
Question
Find the sums. \((-16)+(-8)\)
Step-by-Step Solution
Verified Answer
Answer: The sum of -16 and -8 is -24.
1Step 1: Identify the numbers being added and their signs.
The two numbers being added are \(-16\) and \(-8\). They both have a minus (-) sign in front of them which shows that they are negative.
2Step 2: Add the absolute values of the numbers.
Ignoring the negative signs, add the absolute values of the numbers. The absolute values are \(16\) and \(8\). Adding these numbers gives: \(16 + 8 = 24\).
3Step 3: Add the negative sign to the result from Step 2.
Since both original numbers were negative, the sum will also be negative. To find the sum, add the negative sign to the result from Step 2: \(-24\).
4Step 4: Final Answer:
The sum of \((-16)+(-8)\) is \(-24\).
Key Concepts
Understanding Negative NumbersExploring Absolute ValuesArithmetic Operations with Negative Numbers
Understanding Negative Numbers
Negative numbers represent values that are less than zero. They are often found in various real-life scenarios, like temperatures below zero or financial debts.
In mathematics, negative numbers have a minus (-) sign in front. This sign is essential because it indicates that the number is a certain distance below zero. For example, -16 is 16 units below zero on the number line.
Adding and subtracting negative numbers may seem tricky at first, but it's simply a matter of understanding that negative numbers deal with values below zero. With practice, negative numbers can become as familiar as positive ones."},{
In mathematics, negative numbers have a minus (-) sign in front. This sign is essential because it indicates that the number is a certain distance below zero. For example, -16 is 16 units below zero on the number line.
Adding and subtracting negative numbers may seem tricky at first, but it's simply a matter of understanding that negative numbers deal with values below zero. With practice, negative numbers can become as familiar as positive ones."},{
Exploring Absolute Values
Absolute value is a fundamental concept in arithmetic that represents the magnitude of a number, regardless of its sign. It is denoted by two vertical bars surrounding the number, such as \(|-8|\) or \(|16|\).
The absolute value indicates how far a number is from zero on the number line, without considering direction.
For instance:
Utilizing absolute values is especially useful when performing arithmetic operations with negative numbers, as it helps simplify calculations by focusing only on size, not sign."},{
The absolute value indicates how far a number is from zero on the number line, without considering direction.
For instance:
- The absolute value of -8 is 8, because it is 8 units away from zero.
- The absolute value of 16 is simply 16, as it is already positive.
Utilizing absolute values is especially useful when performing arithmetic operations with negative numbers, as it helps simplify calculations by focusing only on size, not sign."},{
Arithmetic Operations with Negative Numbers
Arithmetic operations like addition and subtraction become more interesting when negative numbers are involved. They follow specific rules which can help simplify calculations.
Consider the problem \((-16) + (-8)\):
Here are some general rules for arithmetic operations with negative numbers:
Consider the problem \((-16) + (-8)\):
- First, observe that both numbers are negative.
- Next, add their absolute values: \(16 + 8 = 24\).
- Since you are adding two negative numbers, keep the result negative: \(-24)\).
Here are some general rules for arithmetic operations with negative numbers:
- Adding two negative numbers results in a negative number.
- Subtracting negative numbers is the same as adding their positive counterparts.
- Multiplying or dividing like-signed numbers (both positive or both negative) yields a positive result.
- Multiplying or dividing opposite-signed numbers yields a negative result.
Other exercises in this chapter
Problem 28
Write the following expressions using only positive exponents. Assume all variables are nonzero. $$ (x-5)^{-3} $$
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For the following exercises, perform the indicated operations. $$ -6-8 $$
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Determine each of the values, \(-|-31|\)
View solution Problem 28
Write the expressions in words. $$ 6-(-8) $$
View solution