Absolute value: Identifying Number opposites

To solve this problem, we shall first evaluate the absolute value of each given number.

• Step 1: Calculate $\left|56\right|$. Since the absolute value of a number is its distance from zero on the number line without regard to sign, $\left|56\right| = 56$.

• Step 2: Calculate $\left|-5.6\right|$. Similarly, $\left|-5.6\right|$ is the magnitude of $-5.6$, hence $\left|-5.6\right| = 5.6$.

Now that we have evaluated the absolute values:

• $\left|56\right| = 56$
• $\left|-5.6\right| = 5.6$

We compare the obtained results to check if they are opposites. By definition, opposites are numbers that are equal in magnitude but different in sign. However, since absolute values are always non-negative, the idea of "opposites" does not apply directly to absolute values. In this context, we check if their magnitudes are the same.

Clearly, $56$ is not equal to $5.6$. Therefore, the numbers $\left|56\right|$ and $\left|-5.6\right|$ are not opposites.

The correct answer is No.

To solve this problem, we'll follow these steps:

• Step 1: Compute the absolute value of each given number.
• Step 2: Determine if the numbers are opposites based on their absolute values.

Now, let's proceed step-by-step:

Step 1: Calculate the absolute values.
The absolute value of a number gives its distance from zero on the number line, disregarding its sign.

$\left|-\frac{1}{3}\right|$
The negative sign is removed by the absolute value, so:
$\left|-\frac{1}{3}\right| = \frac{1}{3}$ $\left|\frac{3}{1}\right|$
The absolute value remains the same as there is no negative sign:
$\left|\frac{3}{1}\right| = 3$

Step 2: Determine if the numbers are opposites.

Two numbers are considered opposites if their sum equals zero. In this case, we compare the results:

The absolute values we found were $\frac{1}{3}$ and $3$. These numbers do not meet the condition for being opposites since their sum $\frac{1}{3} + 3 = \frac{10}{3}$ is not equal to zero.

Therefore, the numbers are not opposites.

Therefore, the correct answer is No.

To determine if the numbers are opposites, consider the following:

• Step 1: Calculate the absolute values:
  • $\left|-3\right| = 3$
  • $\left|3\right| = 3$
• Step 2: Evaluate whether these numbers are opposites.

For two numbers to be opposites in a mathematical context, they must be equidistant from zero on the number line but in opposite directions. Since both calculations give us $3$ and $3$, they are the same numbers, not opposites.

Therefore, the answer to the question is No.

To solve this problem, we will evaluate each expression involving absolute value separately and then determine if they are opposites.

• Step 1: Evaluate the absolute value of -801:
  $\left|-801\right| = 801$ because the absolute value is the positive value or magnitude of the number.
• Step 2: Evaluate the absolute value of +801:
  $\left|+801\right| = 801$ since the absolute value of a positive number is the number itself.
• Step 3: Negate the result of the first step:
  $-\left|-801\right| = -801$.
• Step 4: Compare $-801$ and $801$:
  These numbers have the same magnitude (801) but opposite signs.

Therefore, the numbers $-\left|-801\right|$ and $\left|+801\right|$ are indeed opposites.

The correct choice is Yes.

To solve this problem, let's proceed with the required steps:

• Step 1: Calculate the absolute value $\left|-81\right|$.
  $\left|-81\right| = 81$.
• Step 2: Apply a negative sign to $\left|-81\right|$:
  $-\left|-81\right| = -81$.
• Step 3: Calculate the absolute value $\left|9^2\right|$.
  First, evaluate $9^2 = 81$, so $\left|81\right| = 81$.
• Step 4: Compare $-81$ and $81$.
  The numbers $-81$ and $81$ are indeed opposites since one is the negative of the other.

Therefore, the solution to the problem is Yes, the numbers are opposites.

The opposite of a number is the number with the same magnitude but different sign. The absolute value of a number is always positive or zero. Let's examine the given numbers:

$\left|-7\right|$ represents the absolute value of -7, which is 7.

$\left|7\right|$ represents the absolute value of 7, which is also 7.

Since both absolute values are equal and positive, they represent the same number, not opposites. Therefore, they are not opposite numbers.

The opposite of a number is defined as the number with the same absolute value but different signs.

We have:

$\left|-5\right| = 5$ and $\left|5\right| = 5$.

Both these absolute values are equal and positive, meaning they are the same number, not opposites. Therefore, the numbers are not opposite.

The opposite of a number is what you add to a number to get zero. The opposite of a positive number is a negative number. And the opposite of a negative number is a positive number.

For instance, the opposite of the number $123$ is $-123$.

In this question, we are asked about $-\left|-123\right|$ and $\left|+123\right|$.

The absolute value of any number, whether positive or negative, is its distance from zero on the number line, without considering the direction. Thus, $\left|+123\right| = 123$ and $\left|-123\right| = 123$.

Therefore, $-\left|-123\right| = -123$ and $+\left|123\right| = 123$.

Since $-123$ is indeed the opposite of $+123$, the correct answer is Yes.

The opposite of a number is what you add to a number to get zero. The opposite of a positive number is a negative number. And the opposite of a negative number is a positive number.

For instance, the opposite of the number $56$ is $-56$.

In this question, we are dealing with $-\left|-56\right|$ and $\left|+56\right|$.

The absolute value of a number is the distance from zero, which is always positive. Hence, $\left|+56\right| = 56$ and $\left|-56\right| = 56$.

Therefore, $-\left|-56\right| = -56$ and $+\left|56\right| = 56$.

Thus, $-56$ and $56$ are opposites, and the answer is Yes.

To solve this problem, we'll follow these steps:

• Step 1: Calculate the absolute value of $-64$.
• Step 2: Apply the negative sign to the absolute value calculated.
• Step 3: Calculate the absolute value of $8^2$.
• Step 4: Compare the two numbers to determine if they are opposites.

Now, let's work through each step:

Step 1: Calculate $\left|-64\right|$.
The absolute value of $-64$ is $|-64| = 64$.

Step 2: Apply the negative sign to this absolute value.
$-\left|-64\right| = -64$

Step 3: Calculate $\left|8^2\right|$.
First, compute $8^2 = 64$. Then, calculate $|64| = 64$.

Step 4: Compare the numbers.
We have $-64$ from Step 2 and $64$ from Step 3. These two numbers are opposites because the opposite of $64$ is $-64$.

Therefore, the two numbers are indeed opposites.

Let's solve the problem by evaluating the given expressions and checking if they are opposites:

• First, evaluate $-\left|3 + 5\right|$:
• Calculate $3 + 5$: $3 + 5 = 8$.
• Find $\left|8\right|$: $\left|8\right| = 8$.
• Evaluate $-\left|8\right|$: $-\left|8\right| = -8$.
• Next, evaluate $\left|-8\right|$:
• Since $-8$ is negative, $\left|-8\right| = 8$.
• Compare the results: $-8$ and $8$ are indeed opposites as $-8 = -1 \times 8$.

Therefore, the expressions $-\left|3 + 5\right|$ and $\left|-8\right|$ are not opposites according to standard mathematical convention.

No

First, let's evaluate both expressions separately.

Calculate $\left|-25 + 5\right|$:

• First, simplify inside the absolute value: $-25 + 5 = -20$.
• Now take the absolute value of $-20$: $\left|-20\right| = 20$ because the absolute value of a negative number is its positive equivalent.

Now, calculate $\left|20\right|$:

• The number $20$ is already positive, so $\left|20\right| = 20$.

Both expressions evaluate to $20$, which means they are equal.

So, the correct answer to the problem is $\text{Yes}$.