Hernando ate StartFraction 2 Over 8 EndFraction of a pizza for a dinner. He gave his 6 friends the rest of the pizza and told them to share it equally. To determine the fraction of the whole pizza that each of his friends received, Hernando performed the calculations below.

StartFraction 6 Over 8 EndFraction divided by 6 = StartFraction (6 divided by 6) Over 8 EndFraction = one-eighth

He concluded that each person received One-eighth of the whole pizza. Are Hernando’s calculations correct? Explain why or why not.
Yes, they are correct. Hernando divided 6 by 6.
Yes, they are correct. Hernando divided Two-eighths by 6.
No, they are not correct. Hernando should have multiplied by 6, not divided by 6.
No, they are not correct. Hernando should have divided 8 by 6, not 6 by 6.

1 answer

Hernando's calculations are not correct.

He initially ate \( \frac{2}{8} \) of the pizza, which means the remaining pizza was:

\[ 1 - \frac{2}{8} = \frac{8}{8} - \frac{2}{8} = \frac{6}{8} \]

This is the amount of pizza he had left to share with his friends. Now, he has 6 friends, so he should divide \( \frac{6}{8} \) by 6 to find out how much each friend gets:

\[ \frac{6}{8} \div 6 = \frac{6}{8} \times \frac{1}{6} = \frac{6 \times 1}{8 \times 6} = \frac{6}{48} = \frac{1}{8} \]

The calculations Hernando performed seem confusing because he stated "6" but didn't use the remaining pizza correctly. He should have correctly calculated:

\[ \frac{6}{8} \div 6 \]

This simplifies to \( \frac{1}{8} \). So, while Hernando did reach the right conclusion in the end about each friend getting \( \frac{1}{8} \) of the pizza, his explanation of the division process was incorrect.

Thus, the correct statement is:

No, they are not correct. Hernando should have divided \( \frac{6}{8} \) by 6, not just stated "6 divided by 6."