To convert the mixed number [tex]\(3 \frac{6}{7}\)[/tex] into an improper fraction, follow these steps:
1. Identify the whole number and the fractional part of the mixed number.
- Whole number: [tex]\(3\)[/tex]
- Fractional part: [tex]\(\frac{6}{7}\)[/tex]
2. Multiply the whole number by the denominator of the fractional part. This converts the whole number into a fraction with the same denominator.
[tex]\[
3 \times 7 = 21
\][/tex]
3. Add the numerator of the fractional part to the result from step 2. This gives the numerator of the improper fraction.
[tex]\[
21 + 6 = 27
\][/tex]
4. The denominator of the improper fraction remains the same as the denominator of the fractional part, which is [tex]\(7\)[/tex].
As a result, the mixed number [tex]\(3 \frac{6}{7}\)[/tex] is converted into the improper fraction:
[tex]\[
\frac{27}{7}
\][/tex]
Therefore, [tex]\(3 \frac{6}{7}\)[/tex] expressed as an improper fraction is [tex]\(\frac{27}{7}\)[/tex].
