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. Let's go through the reasoning step by step.

  1. Hernando ate \( \frac{2}{8} \) of the pizza, which means the remaining pizza is: \[ 1 - \frac{2}{8} = \frac{8}{8} - \frac{2}{8} = \frac{6}{8} \]

  2. He has \( \frac{6}{8} \) of the pizza left to share among his 6 friends.

  3. To find out how much each friend gets, he needs to divide the remaining pizza by the number of friends: \[ \frac{6}{8} \div 6 \]

  4. Dividing by 6 can be expressed as multiplying by the reciprocal of 6: \[ \frac{6}{8} \div 6 = \frac{6}{8} \times \frac{1}{6} = \frac{6 \times 1}{8 \times 6} = \frac{6}{48} \]

  5. Simplifying \( \frac{6}{48} \): \[ \frac{6 \div 6}{48 \div 6} = \frac{1}{8} \]

Thus, while Hernando ultimately arrived at the correct answer that each friend receives \( \frac{1}{8} \) of the pizza, his reasoning was flawed because he stated \( \frac{6}{8} \div 6 \) as \( \frac{6}{8} \) divided by 6 incorrectly by attempting to use \( \frac{6}{6} \) instead of considering the whole fraction \( \frac{6}{8} \).

The correct conclusion is: Although the final answer was correct, Hernando's method was incorrect. Therefore, the best response from the options given is:

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