Question

meis turn: from $1\frac{4}{8}$, mei throws the disc back $\frac{2}{8}$. compare where her disc lands to 1. $1\frac{4}{8} - \frac{2}{8}$ is ?

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \(1\frac{4}{8}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(1\frac{4}{8}\), we have \(a = 1\), \(b = 4\), \(c = 8\). Then \(\frac{1\times8 + 4}{8}=\frac{8 + 4}{8}=\frac{12}{8}\).

Step2: Subtract the fractions

Now we need to calculate \(\frac{12}{8}-\frac{2}{8}\). When subtracting fractions with the same denominator, we subtract the numerators and keep the denominator the same. So \(\frac{12 - 2}{8}=\frac{10}{8}\).

Step3: Simplify the result

Simplify \(\frac{10}{8}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So \(\frac{10\div2}{8\div2}=\frac{5}{4}\), and converting \(\frac{5}{4}\) back to a mixed number gives \(1\frac{1}{4}\). We can also compare it to 1. Since \(1\frac{1}{4}=1.25\) and \(1.25>1\), the result of \(1\frac{4}{8}-\frac{2}{8}\) is \(1\frac{2}{8}\) (or simplified as \(1\frac{1}{4}\)) which is greater than 1. But for the calculation of \(1\frac{4}{8}-\frac{2}{8}\), the result is \(\frac{10}{8}=1\frac{2}{8}=1\frac{1}{4}\). If we just want the result of the subtraction (not the comparison part for the question " \(1\frac{4}{8}-\frac{2}{8}\) is? "), we can also do it by subtracting the fractional parts first. The whole number part is 1, and the fractional part is \(\frac{4}{8}-\frac{2}{8}=\frac{2}{8}\), so \(1+\frac{2}{8}=1\frac{2}{8}=1\frac{1}{4}\) or \(\frac{5}{4}\).

Answer:

\(1\frac{2}{8}\) (or simplified as \(1\frac{1}{4}\) or \(\frac{5}{4}\))