To convert the mixed number [tex]\( 6 \frac{4}{7} \)[/tex] to an improper fraction, follow these steps:
1. Identify the whole number and the fractional part:
- The whole number part is [tex]\( 6 \)[/tex].
- The fractional part is [tex]\( \frac{4}{7} \)[/tex].
2. Convert the whole number to a fraction with the same denominator as the fractional part:
- To do this, multiply the whole number by the denominator of the fractional part. Here, the denominator is [tex]\( 7 \)[/tex].
- Thus, [tex]\( 6 \)[/tex] can be expressed as [tex]\( \frac{6 \times 7}{7} = \frac{42}{7} \)[/tex].
3. Add the converted whole number fraction to the original fractional part:
- Now, add [tex]\( \frac{42}{7} \)[/tex] (the converted whole number) to [tex]\( \frac{4}{7} \)[/tex] (the fractional part):
[tex]\[
\frac{42}{7} + \frac{4}{7} = \frac{42 + 4}{7} = \frac{46}{7}
\][/tex]
Therefore, the mixed number [tex]\( 6 \frac{4}{7} \)[/tex] converted to an improper fraction is [tex]\( \frac{46}{7} \)[/tex].
