Question

1. jared has mowed \\(\frac{2}{5}\\) of the yard. abby says that jared has mowed \\(\frac{4}{6}\\) of the yard. is abby correct? explain.

Explanation:

Step1: Simplify \(\frac{4}{6}\)

To simplify \(\frac{4}{6}\), we divide the numerator and the denominator by their greatest common divisor, which is 2. So, \(\frac{4\div2}{6\div2}=\frac{2}{3}\).

Step2: Compare \(\frac{2}{5}\) and \(\frac{2}{3}\)

When two fractions have the same numerator, the fraction with the smaller denominator is larger. Here, the numerators are both 2, and \(5>3\), so \(\frac{2}{5}<\frac{2}{3}\). Also, we can find a common denominator, which is 15. \(\frac{2}{5}=\frac{2\times3}{5\times3}=\frac{6}{15}\) and \(\frac{2}{3}=\frac{2\times5}{3\times5}=\frac{10}{15}\). Since \(\frac{6}{15}
eq\frac{10}{15}\), \(\frac{2}{5}\) is not equal to \(\frac{4}{6}\) (which simplifies to \(\frac{2}{3}\)).

Answer:

Abby is not correct. Because \(\frac{4}{6}\) simplifies to \(\frac{2}{3}\), and \(\frac{2}{5}\) (the fraction of the yard Jared actually mowed) is not equal to \(\frac{2}{3}\) (the fraction Abby claims he mowed). We can show this by simplifying \(\frac{4}{6}\) to \(\frac{2}{3}\) or by finding a common denominator (15) and seeing that \(\frac{2}{5}=\frac{6}{15}\) and \(\frac{2}{3}=\frac{10}{15}\), and \(\frac{6}{15}
eq\frac{10}{15}\).