To convert the mixed number [tex]\( 4 \frac{3}{7} \)[/tex] into an improper fraction, follow these steps:
1. Separate the given mixed number into its integer part and fractional part. Here, the integer part is [tex]\( 4 \)[/tex] and the fractional part is [tex]\( \frac{3}{7} \)[/tex].
2. To form the improper fraction, multiply the integer part by the denominator of the fractional part. In this case:
[tex]\[
4 \times 7 = 28
\][/tex]
3. Add the result from step 2 to the numerator of the fractional part. Here:
[tex]\[
28 + 3 = 31
\][/tex]
4. The numerator of the improper fraction is the result from step 3, and the denominator remains the same as the denominator of the fractional part. Therefore, the improper fraction is:
[tex]\[
\frac{31}{7}
\][/tex]
So, the improper fraction equivalent to [tex]\( 4 \frac{3}{7} \)[/tex] is [tex]\( \frac{31}{7} \)[/tex].
