Lisa drank $\frac{7}{16}$ of a bottle of water during the soccer game. Julianne drank $\frac{2}{3}$ of the water in a bottle that was the same size as Lisa's. Who drank more water and by exactly how much? Show all of your work.
To determine who drank more water, we need to compare the two fractions representing the amount consumed by Lisa and Julianne. Lisa drank \(\frac{7}{16}\) of her bottle, and Julianne drank \(\frac{2}{3}\) of her bottle. Since both bottles are the same size, we can directly compare these two fractions.
To compare \(\frac{7}{16}\) and \(\frac{2}{3}\), we find a common denominator. The least common multiple of 16 and 3 is \(16 \times 3 = 48\). Converting each fraction:
Comparing the numerators, we see that \(32 > 21\), so \(\frac{32}{48} > \frac{21}{48}\). Thus, Julianne drank more water.
To find out by how much more Julianne drank, we subtract Lisa's portion from Julianne's portion:
\[\frac{32}{48} - \frac{21}{48} = \frac{32 - 21}{48} = \frac{11}{48}\].
So, Julianne drank \(\frac{11}{48}\) of a bottle more than Lisa.
In daily life, comparing fractions is essential when sharing resources or preparing recipes. For instance, if you and a friend both have identical containers of juice, and you have consumed \(\frac{7}{16}\) while they have consumed \(\frac{2}{3}\), knowing the exact difference (\(\frac{11}{48}\)) helps you understand how much more juice they finished compared to you. This skill is vital for managing supplies and ensuring fair distribution of items in various practical settings.