Matthew read $\frac{2}{3}$ of a book. Craig read $\frac{4}{5}$ of the same book. Who read more? How much more? Show your work using numbers, sketches, or words.
We are comparing the portion of a book read by two people, Matthew and Craig. Matthew read \(\frac{2}{3}\) of the book, while Craig read \(\frac{4}{5}\) of the same book. To determine who read more and by what amount, we must compare the two fractions \(\frac{2}{3}\) and \(\frac{4}{5}\). Comparing fractions is easiest when they share a common denominator.
To compare \(\frac{2}{3}\) and \(\frac{4}{5}\), we find a common denominator, which is the least common multiple of 3 and 5. Since 3 and 5 are prime numbers, their least common multiple is \(3 \times 5 = 15\). Now, we convert both fractions to have a denominator of 15:
Comparing the numerators, 12 is greater than 10, which means \(\frac{12}{15} > \frac{10}{15}\). Therefore, Craig read more of the book than Matthew.
To find out how much more Craig read, we subtract Matthew's portion from Craig's portion:
\[\frac{4}{5} - \frac{2}{3} = \frac{12}{15} - \frac{10}{15} = \frac{12 - 10}{15} = \frac{2}{15}.\]
Thus, Craig read \(\frac{2}{15}\) more of the book than Matthew.
In daily life, comparing fractions is essential when dealing with shared tasks or resources. For instance, if you and a friend are tasked with painting a wall, and you have painted \(\frac{2}{3}\) of your assigned section while your friend has painted \(\frac{4}{5}\) of theirs, you can use the same method to determine who has completed a larger share of their work and by how much. This helps in coordinating progress, managing time effectively, and ensuring fair distribution of duties.