To determine the total amount of sugar needed to make 4 cakes, when each cake requires [tex]\(\frac{2}{3}\)[/tex] of a cup of sugar, we can follow these steps:
1. Identify the amount of sugar needed per cake: The recipe specifies that [tex]\(\frac{2}{3}\)[/tex] cup of sugar is needed for each cake.
2. Identify the number of cakes: The task is to make 4 cakes.
3. Multiply the sugar per cake by the number of cakes:
[tex]\[
\text{Total sugar needed} = \left(\frac{2}{3} \text{ cup/cake}\right) \times 4 \text{ cakes}
\][/tex]
4. Perform the multiplication:
[tex]\[
\frac{2}{3} \times 4 = \frac{2 \times 4}{3} = \frac{8}{3} \text{ cups}
\][/tex]
5. Simplify the result:
[tex]\[
\frac{8}{3} = 2 + \frac{2}{3} = 2.6666666666666665 \text{ cups}
\][/tex]
Thus, the total amount of sugar needed to make 4 cakes is [tex]\(2.6666666666666665\)[/tex] cups.
