To write [tex]\(3 \frac{2}{4}\)[/tex] as an improper fraction and then simplify it to its lowest terms, follow these steps:
1. Identify the components of the mixed number:
- The whole number part is [tex]\(3\)[/tex].
- The fractional part is [tex]\(\frac{2}{4}\)[/tex].
2. Convert the mixed number to an improper fraction:
- Multiply the whole number part by the denominator of the fractional part. That would be [tex]\(3 \times 4 = 12\)[/tex].
- Add the result to the numerator of the fractional part. So, you get [tex]\(12 + 2 = 14\)[/tex].
- The denominator remains the same as that of the fractional part, which is [tex]\(4\)[/tex].
- Hence, the improper fraction is [tex]\(\frac{14}{4}\)[/tex].
3. Simplify the improper fraction:
- Find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of [tex]\(14\)[/tex] and [tex]\(4\)[/tex] is [tex]\(2\)[/tex].
- Divide both the numerator and the denominator by the GCD to simplify the fraction.
- [tex]\(\frac{14}{4} \div 2 = \frac{7}{2}\)[/tex].
Therefore, the mixed number [tex]\(3 \frac{2}{4}\)[/tex] written as an improper fraction in its lowest terms is [tex]\(\frac{7}{2}\)[/tex].
