Question

An athlete drank 6 1/4 bottles of sports drink in the first half of a match and another 1/3 of a bottle in the second half. How much did he drink in all?

Write your answer as a fraction or as a whole or mixed number.

bottles

Answer 1

To find out how much the athlete drank in total, we need to add the amounts he drank in both halves of the match.

First, let's convert the mixed number \( 6 \frac{1}{4} \) into an improper fraction.

\[
6 \frac{1}{4} = 6 + \frac{1}{4} = \frac{6 \times 4}{4} + \frac{1}{4} = \frac{24}{4} + \frac{1}{4} = \frac{25}{4}
\]

Next, we need to add the \( \frac{1}{3} \) of a bottle to this amount. To do this, we need a common denominator for \( \frac{25}{4} \) and \( \frac{1}{3} \). The least common multiple of 4 and 3 is 12.

Now we convert both fractions to have a denominator of 12:

\[
\frac{25}{4} = \frac{25 \times 3}{4 \times 3} = \frac{75}{12}
\]
\[
\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}
\]

Now we can add these two fractions:

\[
\frac{75}{12} + \frac{4}{12} = \frac{75 + 4}{12} = \frac{79}{12}
\]

Now, let's convert \( \frac{79}{12} \) into a mixed number. We divide 79 by 12:

\[
79 \div 12 = 6 \quad \text{(whole part)}
\]
\[
79 - (12 \times 6) = 79 - 72 = 7 \quad \text{(remainder)}
\]

So the improper fraction \( \frac{79}{12} \) can be written as the mixed number:

\[
6 \frac{7}{12}
\]

Thus, the total amount the athlete drank is

\[
\boxed{6 \frac{7}{12}} \text{ bottles.}
\]