3 4/8 simplified

Steps to Solve

1. Convert the mixed number to an improper fraction

To simplify the mixed number $3 \frac{4}{8}$, first convert it to an improper fraction. This is done using the formula:

$$ \text{Improper Fraction} = \text{Whole Number} \times \text{Denominator} + \text{Numerator} $$

For our mixed number:

$$ \text{Improper Fraction} = 3 \times 8 + 4 = 24 + 4 = 28 $$

So, we have:

$$ 3 \frac{4}{8} = \frac{28}{8} $$

2. Reduce the fraction to its simplest form

Next, simplify the improper fraction $\frac{28}{8}$. We can do this by finding the greatest common divisor (GCD) of the numerator and the denominator.

The GCD of 28 and 8 is 4. Now, divide both the numerator and denominator by 4:

$$ \frac{28 \div 4}{8 \div 4} = \frac{7}{2} $$

So, the fraction $\frac{28}{8}$ simplifies to $\frac{7}{2}$.

3. Convert back to a mixed number if needed

Since $\frac{7}{2}$ is an improper fraction, we can convert it back to a mixed number if required. To do this, divide the numerator by the denominator:

$$ 7 \div 2 = 3 \text{ R } 1 $$

This means we have 3 as the whole number and a remainder of 1, giving us:

$$ 3 \frac{1}{2} $$

So, we can express $3 \frac{4}{8}$ as $3 \frac{1}{2}$.