Question

1 (\frac{1}{5}) = (\frac{\text{yellow rectangle}}{\text{yellow rectangle}}), 6 (\frac{1}{7}) = (\frac{\text{yellow rectangle}}{\text{yellow rectangle}})

Explanation:

Step1: Convert mixed number to improper fraction (first case)

To convert \(1\frac{1}{5}\) to an improper fraction, use the formula \(a\frac{b}{c}=\frac{a\times c + b}{c}\). Here, \(a = 1\), \(b = 1\), \(c = 5\). So, \(1\times5 + 1=6\), and the fraction is \(\frac{6}{5}\).

Step2: Convert mixed number to improper fraction (second case)

For \(6\frac{1}{7}\), using the same formula \(a\frac{b}{c}=\frac{a\times c + b}{c}\) with \(a = 6\), \(b = 1\), \(c = 7\). Then, \(6\times7+1 = 43\), so the fraction is \(\frac{43}{7}\).

Answer:

\(1\frac{1}{5}=\frac{6}{5}\), \(6\frac{1}{7}=\frac{43}{7}\)