What is the absolute value of 2 1/2?

Steps to Solve

1. 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:

$$ \frac{(2 \times 2) + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} $$

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:

$$ \left|\frac{5}{2}\right| = \frac{5}{2} $$

3. 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:

$$ \left| 2 \frac{1}{2} \right| = 2 \frac{1}{2} $$