What is the absolute value of 2 1/2?
Understand the Problem
The question is asking to find the absolute value of the mixed number 2 1/2. Absolute value refers to the non-negative value of a number regardless of its sign.
Answer
The absolute value of the mixed number $2 \frac{1}{2}$ is $2 \frac{1}{2}$.
Answer for screen readers
The absolute value of the mixed number $2 \frac{1}{2}$ is $2 \frac{1}{2}$.
Steps to Solve
- Convert the mixed number to an improper fraction
To find the absolute value of the mixed number $2 \frac{1}{2}$, we begin by converting it into an improper fraction.
The formula to convert a mixed number to an improper fraction is:
$$ \text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator}\right) + \text{Numerator} \text{ over Denominator} $$
For $2 \frac{1}{2}$, this becomes:
$$ \frac{(2 \times 2) + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} $$
- Determine the absolute value
Next, we find the absolute value of the improper fraction.
Since $\frac{5}{2}$ is already positive, the absolute value is the same as the original value:
$$ \left|\frac{5}{2}\right| = \frac{5}{2} $$
- Final Result as a Mixed Number
If you want to express the result back as a mixed number, you can convert $\frac{5}{2}$ back:
Divide 5 by 2:
$$ 5 \div 2 = 2 \quad \text{(whole number)} $$
The remainder is 1:
$$ 1 \quad \text{(remainder)} $$
So, $\frac{5}{2}$ as a mixed number is:
$$ 2 \frac{1}{2} $$
Thus, the absolute value remains:
$$ \left| 2 \frac{1}{2} \right| = 2 \frac{1}{2} $$
The absolute value of the mixed number $2 \frac{1}{2}$ is $2 \frac{1}{2}$.
More Information
The absolute value pertains to the magnitude of a number without considering its direction on the number line. In this case, since $2 \frac{1}{2}$ is positive, its absolute value is the same as the number itself.
Tips
- Confusing absolute value with just finding a fraction's value. Remember, for positive numbers, the absolute value is the same as the number.
- Forgetting to convert the mixed number into an improper fraction before performing operations.
