Question

Half of a large pizza is cut into 4 equal-sized pieces, and the other half is cut into 6 equal-sized pieces. If a person were to eat 1 of the larger pieces and 2 of the smaller pieces, what fraction of the pizza would remain uneaten?

• A. frac{5}{12
• B. frac{13}{24
• C. frac{7}{12
• D. frac{17}{24

Answer 1

The Correct Option is D

The pizza is divided into two halves. 
The first half is cut into 4 pieces, so each piece is \( \frac{1}{8} \) of the pizza. 
The second half is cut into 6 pieces, so each piece is \( \frac{1}{12} \) of the pizza. 
The person eats 1 of the larger pieces (\( \frac{1}{8} \)) and 2 of the smaller pieces (\( 2 \times \frac{1}{12} = \frac{2}{12} = \frac{1}{6} \)). 
The total amount of pizza eaten is:
\[ \frac{1}{8} + \frac{1}{6} \]
To add these fractions, find a common denominator:
\[ \frac{1}{8} + \frac{1}{6} = \frac{3}{24} + \frac{4}{24} = \frac{7}{24} \]
The fraction of the pizza remaining uneaten is:
\[ 1 - \frac{7}{24} = \frac{17}{24} \]

To find the fraction of pizza remaining, subtract the eaten portions from the total (which is 1 or the whole pizza).