Question

complete the expression so its difference is greater than 1. hint: there is more than one correct answer. $1\frac{4}{10}-\frac{?}{10}$

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \(1\frac{4}{10}\) 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 \(1\frac{4}{10}\), we have \(a = 1\), \(b = 4\), \(c = 10\). Then \(1\frac{4}{10}=\frac{1\times10 + 4}{10}=\frac{14}{10}\).

Step2: Set up the inequality

Let the numerator of the second fraction be \(x\). The expression is \(\frac{14}{10}-\frac{x}{10}\), and we want this difference to be greater than \(1\) (which is \(\frac{10}{10}\)). So we set up the inequality:
\[
\frac{14 - x}{10}> \frac{10}{10}
\]
Since the denominators are the same, we can compare the numerators: \(14 - x>10\).

Step3: Solve the inequality for \(x\)

Subtract \(14\) from both sides: \(-x>10 - 14\), which simplifies to \(-x>- 4\). Multiply both sides by \(- 1\) (and remember to reverse the inequality sign), we get \(x < 4\). Since \(x\) is a non - negative integer (as it is the numerator of a fraction with denominator \(10\) in this context), possible values of \(x\) are \(0\), \(1\), \(2\), \(3\). Let's take \(x = 3\) as an example.

Answer:

\(3\) (Other possible answers are \(0\), \(1\), \(2\))