Let's break this problem down into steps to understand how much of the whole pie Pascal ate.
1. Determine the portion of the pie given to Pascal:
Pascal's mom gave him [tex]\(\frac{3}{4}\)[/tex] of the pie. This means that out of the whole pie, Pascal received 0.75 (or 75%) of it.
2. Determine the portion of what was given that Pascal ate:
Pascal ate [tex]\(\frac{2}{3}\)[/tex] of the portion given to him. This means that out of the [tex]\(\frac{3}{4}\)[/tex] of the pie he received, he ate approximately 0.6667 (or about 66.67%) of it.
3. Calculate the portion of the whole pie that Pascal ate:
To find out how much of the entire pie Pascal ate, we multiply the portion of the pie he was given by the portion he ate of that given amount:
[tex]\[
\text{Portion of the whole pie eaten} = \left( \frac{3}{4} \right) \times \left( \frac{2}{3} \right)
\][/tex]
In decimal form, this calculation is:
[tex]\[
0.75 \times 0.6667 = 0.5
\][/tex]
Therefore, Pascal ate [tex]\(\frac{1}{2}\)[/tex] of the entire pie, or 50% of the whole pie.
