Question

How do I rename mixed numbers in simplest form and what are the steps to simplify the fraction 3/4?

Answer 1

To rename a mixed number in simplest form, you need to convert it into an improper fraction. Here's a step-by-step guide on how to do that:

### Steps to Convert a Mixed Number to an Improper Fraction:

1. **Identify the Mixed Number**: A mixed number consists of a whole number part and a fraction part (e.g., \(2 \frac{1}{3}\)).

2. **Convert the Whole Number to a Fraction**: Multiply the whole number by the denominator of the fraction. For example, in \(2 \frac{1}{3}\), the whole number is 2, and the denominator is 3:
\[
2 \times 3 = 6
\]

3. **Add the Numerator**: Add the result from the previous step to the numerator of the fraction:
\[
6 + 1 = 7
\]

4. **Create the Improper Fraction**: Place the sum (numerator) over the original denominator:
\[
\frac{7}{3}
\]

So, \(2 \frac{1}{3}\) can be renamed as \(\frac{7}{3}\) in its improper fraction form.

### Simplifying the Fraction \( \frac{3}{4} \):

Now, to simplify the fraction \( \frac{3}{4} \), follow these steps:

1. **Check for Common Factors**: Identify the greatest common divisor (GCD) of the numerator (3) and the denominator (4). The only factors of 3 are 1 and 3, while the factors of 4 are 1, 2, and 4. The GCD is 1.

2. **Divide Both Numerator and Denominator by GCD**: Since the GCD is 1, you divide each by 1:
\[
\frac{3 \div 1}{4 \div 1} = \frac{3}{4}
\]

3. **Final Result**: Since \( \frac{3}{4} \) already has no common factors other than 1, it is already in simplest form.

### Conclusion:
- Mixed numbers can be converted to improper fractions using multiplication and addition of the whole number part and fraction part.
- The fraction \( \frac{3}{4} \) is already in simplest form, as it has no common factors other than 1.