Question

lets play more
umber line disc golf\! this time, the number line is divided into twelfths, and a basket is located at 1. starting at \\(\frac{8}{12}\\), get the disc to the basket in one throw. meis turn: from \\(\frac{8}{12}\\), mei throws the disc \\(\frac{10}{12}\\). compare where her disc lands to 1. \\(\frac{8}{12} + \frac{10}{12}\\) is ?

Explanation:

Step1: Add the numerators

To add the fractions \(\frac{8}{12}\) and \(\frac{10}{12}\), we add the numerators since the denominators are the same. So, \(8 + 10 = 18\).

Step2: Write the sum as a fraction

The sum of the fractions is \(\frac{18}{12}\).

Step3: Simplify the fraction (optional, but to compare with 1)

We can simplify \(\frac{18}{12}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 6. So, \(\frac{18\div6}{12\div6}=\frac{3}{2}\) or \(1\frac{1}{2}\). Now, comparing \(\frac{3}{2}\) (or \(1\frac{1}{2}\)) with 1, we see that \(\frac{3}{2}>1\) (since \(1\frac{1}{2}\) is one and a half, which is greater than 1). But first, let's just find the sum: \(\frac{8}{12}+\frac{10}{12}=\frac{8 + 10}{12}=\frac{18}{12}=\frac{3}{2}\) (or \(1.5\)).

Answer:

The sum \(\frac{8}{12}+\frac{10}{12}\) is \(\frac{18}{12}\) (or simplified to \(\frac{3}{2}\) or \(1\frac{1}{2}\)), and \(\frac{3}{2}>1\) (so Mei's disc lands at \(\frac{18}{12}\) (or \(\frac{3}{2}\)) which is greater than 1). The value of \(\frac{8}{12}+\frac{10}{12}\) is \(\frac{18}{12}\) (or \(\frac{3}{2}\) or \(1.5\)).