To determine the part of the whole watermelon each child would get when 8 children share two-thirds of the watermelon equally, let's consider the problem step by step.
1. We start with the total amount of the watermelon that needs to be shared, which is two-thirds of the watermelon. This can be written as [tex]\(\frac{2}{3}\)[/tex].
2. We need to divide this [tex]\(\frac{2}{3}\)[/tex] among 8 children equally. This translates to dividing [tex]\(\frac{2}{3}\)[/tex] by 8.
3. In fractional terms, dividing a fraction by a whole number involves multiplying the fraction by the reciprocal of that whole number. Therefore, dividing [tex]\(\frac{2}{3}\)[/tex] by 8 is equivalent to multiplying [tex]\(\frac{2}{3}\)[/tex] by [tex]\(\frac{1}{8}\)[/tex].
[tex]\[
\frac{2}{3} \div 8 = \frac{2}{3} \times \frac{1}{8}
\][/tex]
4. We multiply the numerators and the denominators:
[tex]\[
\frac{2 \times 1}{3 \times 8} = \frac{2}{24}
\][/tex]
5. Simplifying the fraction [tex]\(\frac{2}{24}\)[/tex]:
[tex]\[
\frac{2}{24} = \frac{1}{12}
\][/tex]
Thus, each child gets [tex]\(\frac{1}{12}\)[/tex] of the whole watermelon.
The correct answer is:
b. [tex]\(\frac{2}{3} \div 8\)[/tex]
