Answer :
Jessica sold a greater length of ribbon compared to Ramon.
To determine who sold the greater length of ribbon, we need to compare the lengths of the pieces they sold.
First, let's find out the length of each piece Jessica and Ramon sold.
Jessica cut her ribbon into eighths, and she sold 6 pieces. Since the ribbon was cut into eighths, each piece represents [tex]\( \frac{1}{8} \)[/tex] of the total length.
Thus, the total length of ribbon Jessica sold is [tex]\( 6 \times \frac{1}{8}[/tex] = [tex]\frac{6}{8} \)[/tex] of the total length.
Ramon cut his ribbon into twelfths, and he sold 8 pieces. Each piece represents [tex]\( \frac{1}{12} \)[/tex] of the total length.
Therefore, the total length of ribbon Ramon sold is [tex]\( 8 \times \frac{1}{12}[/tex] = [tex]\frac{8}{12} \)[/tex] of the total length.
To compare the lengths, we need to make sure they are in the same unit. We can convert both fractions to a common denominator. The least common multiple (LCM) of 8 and 12 is 24.
Jessica's fraction [tex]\( \frac{6}{8} \)[/tex] is equivalent to [tex]\( \frac{18}{24} \)[/tex] when multiplied by [tex]\( \frac{3}{3} \)[/tex].
Ramon's fraction [tex]\( \frac{8}{12} \)[/tex] is equivalent to [tex]\( \frac{16}{24} \)[/tex] when multiplied by [tex]\( \frac{2}{2} \).[/tex]
Now, we can see that [tex]\( \frac{18}{24}[/tex] > [tex]\frac{16}{24} \)[/tex] , which means Jessica sold a greater length of ribbon than Ramon.
Therefore, Jessica sold more ribbon, as determined by comparing the total lengths of the pieces they sold.