3 4/8 simplified
Understand the Problem
The question is asking how to simplify the mixed number 3 4/8. We will express it in its simplest form by reducing the fraction and possibly converting the mixed number if necessary.
Answer
$3 \frac{1}{2}$
Answer for screen readers
The simplified form of the mixed number $3 \frac{4}{8}$ is $3 \frac{1}{2}$.
Steps to Solve
- 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:
$$ 3 \frac{4}{8} = \frac{28}{8} $$
- 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 $\frac{7}{2}$.
- 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 $3 \frac{1}{2}$.
The simplified form of the mixed number $3 \frac{4}{8}$ is $3 \frac{1}{2}$.
More Information
When simplifying fractions, it’s important to reduce them as much as possible to find their simplest form. Also note that mixed numbers can often be expressed both as improper fractions and back to mixed forms, depending on the context. The fraction $\frac{4}{8}$ simplifies to $\frac{1}{2}$, which is an additional reduction.
Tips
- Forgetting to convert the mixed number to an improper fraction before simplifying.
- Failing to reduce the remaining fraction completely.