To determine if John and Ben had the same amount of cool drink, we need to compare the fractions of the cool drink each consumed.
1. Identify John's Portion:
John had four eighths of the cool drink. We represent this fraction as:
[tex]\[
\frac{4}{8}
\][/tex]
2. Simplify John's Fraction:
To simplify [tex]\(\frac{4}{8}\)[/tex], we divide both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor, which is 4:
[tex]\[
\frac{4 \div 4}{8 \div 4} = \frac{1}{2}
\][/tex]
Thus, John's portion of the cool drink, when simplified, is:
[tex]\[
\frac{1}{2}
\][/tex]
3. Identify Ben's Portion:
Ben had half of the cool drink. This is directly represented as:
[tex]\[
\frac{1}{2}
\][/tex]
4. Compare the Fractions:
Now, we compare the simplified fraction of John's portion with Ben's portion:
[tex]\[
\frac{1}{2} \text{ (John's) } = \frac{1}{2} \text{ (Ben's)}
\][/tex]
Since both fractions are equal, John and Ben had the same amount of cool drink.
In conclusion, both John and Ben had [tex]\(\frac{1}{2}\)[/tex] (or half) of the cool drink each. Therefore, they indeed had the same amount of cool drink.
