To convert the mixed number [tex]\(1 \frac{2}{3}\)[/tex] to an improper fraction, we follow these steps:
1. Identify the components of the mixed number:
- Whole number part: [tex]\(1\)[/tex]
- Numerator of the fractional part: [tex]\(2\)[/tex]
- Denominator of the fractional part: [tex]\(3\)[/tex]
2. Convert the whole number to an equivalent fraction with the same denominator as the fractional part:
- Whole number [tex]\(1\)[/tex] can be expressed as [tex]\(\frac{3}{3}\)[/tex], since any number divided by itself equals [tex]\(1\)[/tex].
3. Combine the whole number fraction and the fractional part:
- Transform the whole number part and add it to the fractional part:
[tex]\[
1 \frac{2}{3} = \frac{3}{3} + \frac{2}{3}
\][/tex]
4. Add the fractions:
- Since the denominators are the same, we can add the numerators:
[tex]\[
\frac{3}{3} + \frac{2}{3} = \frac{3 + 2}{3} = \frac{5}{3}
\][/tex]
Therefore, the improper fraction equivalent to the mixed number [tex]\(1 \frac{2}{3}\)[/tex] is [tex]\(\frac{5}{3}\)[/tex].
Given the choices:
- A. [tex]\(\frac{4}{3}\)[/tex]
- B. [tex]\(\frac{6}{3}\)[/tex]
- C. [tex]\(\frac{5}{3}\)[/tex]
- D. [tex]\(\frac{3}{3}\)[/tex]
The correct answer is:
C. [tex]\(\frac{5}{3}\)[/tex]
