Question

solve using a strategy that you have used before. 1. one third of a pizza was set aside for later. the rest was cut into eight equal slices. five of these slices were then eaten. all together, how much of the original pizza remains?

Explanation:

Step1: Find the fraction of the pizza not set aside

The whole pizza is 1. One third is set aside, so the remaining fraction is $1 - \frac{1}{3} = \frac{2}{3}$.

Step2: Find the fraction of the original pizza in each of the eight slices

The remaining $\frac{2}{3}$ is cut into 8 equal slices, so each slice is $\frac{2}{3} \div 8 = \frac{2}{3} \times \frac{1}{8} = \frac{1}{12}$ of the original pizza.

Step3: Find the fraction of the pizza eaten

Five slices are eaten, so the fraction eaten is $5 \times \frac{1}{12} = \frac{5}{12}$.

Step4: Find the remaining fraction of the original pizza

First, the fraction set aside is $\frac{1}{3} = \frac{4}{12}$. The fraction not eaten from the cut part is $\frac{2}{3} - \frac{5}{12} = \frac{8}{12} - \frac{5}{12} = \frac{3}{12} = \frac{1}{4}$. Then total remaining is $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$? Wait, no. Wait, the set aside is $\frac{1}{3}$, and the remaining from the cut part is $\frac{2}{3} - \frac{5}{12}$. Let's recalculate: $\frac{2}{3} = \frac{8}{12}$, $\frac{8}{12} - \frac{5}{12} = \frac{3}{12} = \frac{1}{4}$. Then total remaining is $\frac{1}{3} + \frac{1}{4}$. Find a common denominator, which is 12. $\frac{1}{3} = \frac{4}{12}$, $\frac{1}{4} = \frac{3}{12}$, so $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$. Wait, but let's check again. Alternatively, total pizza: 1. Eaten: $\frac{5}{12}$, set aside: $\frac{1}{3} = \frac{4}{12}$. So remaining is $1 - \frac{5}{12} - \frac{4}{12} = \frac{3}{12} = \frac{1}{4}$? Wait, no, I messed up. Wait, the set aside is $\frac{1}{3}$, the part that was cut is $\frac{2}{3}$. Of that $\frac{2}{3}$, 5 slices are eaten. Each slice is $\frac{2}{3} \div 8 = \frac{1}{12}$, so 5 slices is $\frac{5}{12}$. So the part eaten is $\frac{5}{12}$, the part set aside is $\frac{1}{3} = \frac{4}{12}$. So total eaten and set aside? No, set aside is not eaten. So remaining is set aside plus (cut part - eaten part). Cut part is $\frac{2}{3}$, eaten part is $\frac{5}{12}$. So cut part remaining is $\frac{2}{3} - \frac{5}{12} = \frac{8}{12} - \frac{5}{12} = \frac{3}{12} = \frac{1}{4}$. Set aside is $\frac{1}{3} = \frac{4}{12}$. So total remaining is $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$. Wait, but when we do 1 - eaten - (1 - set aside - eaten)? No, better to do:

Total pizza: 1.

Set aside: $\frac{1}{3}$.

Remaining to cut: $1 - \frac{1}{3} = \frac{2}{3}$.

Cut into 8 slices, so each slice: $\frac{2}{3} / 8 = \frac{1}{12}$.

Eaten: 5 slices, so $\frac{5}{12}$.

So remaining is set aside + (remaining in cut part) = $\frac{1}{3} + (\frac{2}{3} - \frac{5}{12})$.

Calculate $\frac{2}{3} - \frac{5}{12} = \frac{8}{12} - \frac{5}{12} = \frac{3}{12} = \frac{1}{4}$.

$\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}$.

Yes, that's correct.

Answer:

$\frac{7}{12}$