two sisters have bought $2$ quarter pizzas, like the one shown in the diagram. Their brother arrives unexpectedly for dinner. The easiest way to divide the $2$ quater pizzas equally in three is to cut each pizza twice.is that correct?

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Q. two sisters have bought

2

quarter pizzas, like the one shown in the diagram. Their brother arrives unexpectedly for dinner. The easiest way to divide the

2

quater pizzas equally in three is to cut each pizza twice.is that correct?

Understand the problem: Understand the problem. $\newline$ We have two quarter pizzas, which means each pizza is a quarter of a whole pizza. We need to divide these $2$ quarter pizzas equally among $3$ people.
Determine total pizza: Determine the total amount of pizza. $\newline$ Since we have two quarter pizzas, the total amount of pizza we have is $2 \times \left(\frac{1}{4}\right) = \frac{1}{2}$ of a whole pizza.
Amount per person: Determine the amount of pizza each person should get. $\newline$ To divide the half pizza equally among three people, each person should get $\frac{1}{2}$ divided by $3$ , which is $(\frac{1}{2}) \times (\frac{1}{3}) = \frac{1}{6}$ of a whole pizza.
Proposed solution: Consider the proposed solution. $\newline$ The proposed solution is to cut each quarter pizza twice. This implies making two cuts on each quarter pizza, but we need to understand how these cuts will be made to ensure equal portions.
Visualize the cuts: Visualize the cuts. $\newline$ If we cut each quarter pizza into three equal parts, we would have $6$ pieces in total. However, since each quarter pizza is $\frac{1}{4}$ of a whole, cutting it into three equal parts would give us pieces that are each $\frac{1}{12}$ of a whole pizza.
Calculate total after cutting: Calculate the total amount of pizza after cutting. $\newline$ If we have $6$ pieces that are each $\frac{1}{12}$ of a whole pizza, the total amount of pizza we have is $6 \times \left(\frac{1}{12}\right) = \frac{6}{12} = \frac{1}{2}$ of a whole pizza, which is what we started with.
Equal portions check: Determine if the cuts result in equal portions for three people. $\newline$ Each person would get two pieces of $\frac{1}{12}$ pizza, which is $2 \times \left(\frac{1}{12}\right) = \frac{2}{12} = \frac{1}{6}$ of a whole pizza. This is the correct amount each person should get as calculated in Step $3$ .
Solution correctness: Conclude if the proposed solution is correct. $\newline$ Since each person gets $\frac{1}{6}$ of a whole pizza, which is the fair share for each person, the proposed solution of cutting each quarter pizza twice to divide the pizzas equally among three people is correct.