Question

$\frac{1}{10} < \frac{\square}{4}$

Explanation:

Step1: Cross - multiply the inequality

We have the inequality \(\frac{1}{10}<\frac{x}{4}\) (let the unknown numerator be \(x\)). Cross - multiplying gives us \(1\times4 < 10\times x\), which simplifies to \(4 < 10x\).

Step2: Solve for \(x\)

Divide both sides of the inequality \(4 < 10x\) by 10. We get \(\frac{4}{10} 0.4\). Since \(x\) is a positive integer (because it is the numerator of a fraction in this context), the smallest positive integer greater than \(0.4\) is \(1\). We can check: \(\frac{1}{10}=0.1\) and \(\frac{1}{4} = 0.25\), and \(0.1<0.25\). Also, if we try \(x = 1\), the inequality holds. If we consider other positive integers, like \(x = 2\), \(\frac{2}{4}=0.5\) also satisfies \(0.1 < 0.5\), but the smallest positive integer that works is \(1\).

Answer:

\(1\)