Absolute value - Examples, Exercises and Solutions

These signs in the exercises refer to the concept of "absolute value",

In absolute value we don't have "negative" or "positive", instead we measure the distance from point 0,

In other words, we always "cancel out" the negative signs.

In this exercise, we'll change the minus to a plus sign, and simply remain with 19 and a quarter.

And that's the solution!

The "absolute value" can be viewed as the distance of a number from 0.
Therefore, the absolute value will not change the sign from negative to positive, it will always be positive.

To find the absolute value of $0.8$, we will use the definition of absolute value, which states:

• If a number $x$ is positive or zero, then its absolute value is the same number: $|x| = x$.
• If a number $x$ is negative, then its absolute value is the positive version of that number: $|x| = -x$.

Let's apply this to our problem:

Since $0.8$ is a positive number, its absolute value is simply itself:

$|0.8| = 0.8$

Therefore, the absolute value of $0.8$ is $0.8$.

Looking at the given answer choices:

• Choice 1: "There is no absolute value" is incorrect, as every real number has an absolute value.
• Choice 2: $-0.8$ is incorrect, because absolute values are never negative.
• Choice 3: $0$ is incorrect, as the number is not zero.
• Choice 4: $0.8$ is correct, as it matches the calculated absolute value.

Thus, the correct choice is $0.8$.

Therefore, the solution to the problem is $0.8$.

To solve this problem, we will determine the absolute value of the number 3:

• Step 1: Recognize that the number given is 3, which is a positive number.
• Step 2: According to the rules of absolute values, the absolute value of a positive number is the number itself.
• Step 3: Therefore, $|3| = 3$.

In conclusion, the absolute value of 3 is $\mathbf{3}$.

When we have an exercise with these symbols || we understand that it refers to absolute value.

Absolute value does not relate to whether a number is positive or negative, but rather checks how far it is from zero.

In other words, 2 is 2 units away from zero, and -2 is also 2 units away from zero,

Therefore, absolute value essentially "zeroes out" the negativity of the number.

|-2| = 2

The absolute value of a number is the distance of the number from zero on a number line, without considering its direction. For the number $-25$, the absolute value is $25$ because it is 25 units away from zero without considering the negative sign.

The absolute value of a number is always non-negative because it represents the distance from zero. Therefore, the absolute value of $34$ is $34$.

The absolute value of a number is its distance from zero on the number line, without considering its direction. To find the absolute value of $5$, consider the distance of $5$ from zero, which is just $5$. Therefore, $\left|5\right| = 5$.

The absolute value of $0$ is the distance from zero to zero on the number line. Since zero is not negative or positive, $\left|0\right| = 0$.

The absolute value of a number is its distance from zero on the number line, regardless of the direction. To find the absolute value of $-7$, we need to look at the distance of $-7$ from zero, which is $7$. Therefore, $\left|-7\right| = 7$.

The absolute value of a number is the distance of the number from 0 on a number line, regardless of direction. Therefore, the absolute value of $-3.5$ is the same as moving 3.5 units away from 0, which results in $3.5$. Hence, $\left| -3.5 \right| = 3.5$.

The absolute value of a number is always its positive value. It represents the distance of the number from zero on the number line, regardless of direction. The absolute value of any negative number is its opposite positive number.

Step 1: Identify the number to find the absolute value of: $-7\frac{1}{2}$

Step 2: Change the negative sign to positive: $7\frac{1}{2}$

Hence, the absolute value of $-7\frac{1}{2}$ is $7\frac{1}{2}$.

The absolute value of a number is the positive form of that number, representing its distance from zero on the number line.

Step 1: Identify the number whose absolute value is needed: $-4\frac{3}{4}$

Step 2: Remove the negative sign from the number: $4\frac{3}{4}$

Thus, the absolute value of $-4\frac{3}{4}$ is $4\frac{3}{4}$.

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

• Step 1: Calculate the square of 3.
• Step 2: Determine the absolute value of the result.

Now, let's work through each step:
Step 1: Calculate $3^2$.
The square of 3 is calculated as follows: $3 \times 3 = 9$.

Step 2: Apply the concept of absolute value.
Since $9$ is already positive, the absolute value of $9$ is simply $9$, as $|9| = 9$.

Therefore, the solution to the problem is $9$, which corresponds to choice 3 in the provided options.

To solve the expression $|4^2|$, first calculate $4^2$, which equals $16$. The absolute value of $16$ is $16$ since it is already positive.