Question

find a numerator that makes the statement true. there may be more than one correct answer. the fraction you make must be greater than 0 and less than 1. the numerator must be a whole number. \\(\frac{1}{4} < \frac{square}{10}\\)

Explanation:

Step1: Let the numerator be \( x \). The inequality is \( \frac{1}{4} < \frac{x}{10} \), where \( 0 < x < 10 \) (since the fraction is between 0 and 1, \( x \) is a whole number less than 10).

Step2: Solve the inequality \( \frac{1}{4} < \frac{x}{10} \). Cross - multiply (since 4 and 10 are positive, the inequality sign remains the same): \( 10\times1 < 4\times x \), which simplifies to \( 10 < 4x \). Then divide both sides by 4: \( x > \frac{10}{4}=2.5 \).

Step3: Since \( x \) is a whole number and \( x < 10 \) (because \( \frac{x}{10}<1\) implies \( x < 10 \)), the possible values of \( x \) are 3, 4, 5, 6, 7, 8, 9. We can choose one of them, for example, \( x = 3 \).

Answer:

3 (Other possible answers: 4, 5, 6, 7, 8, 9)