Question

e if each expression is less than 1 or greater than 1.
less than 1
$1\frac{2}{5} - \frac{4}{5}$
greater than 1
$1\frac{9}{12} - \frac{5}{12}$
$1\frac{4}{6} - \frac{2}{6}$

Explanation:

Step1: Analyze \(1\frac{2}{5} - \frac{4}{5}\)

First, convert the mixed number to an improper fraction: \(1\frac{2}{5}=\frac{5 + 2}{5}=\frac{7}{5}\). Then subtract: \(\frac{7}{5}-\frac{4}{5}=\frac{7 - 4}{5}=\frac{3}{5}\). Since \(\frac{3}{5}=0.6<1\), this expression is less than 1.

Step2: Analyze \(1\frac{9}{12} - \frac{5}{12}\)

Convert the mixed number: \(1\frac{9}{12}=\frac{12 + 9}{12}=\frac{21}{12}\). Subtract: \(\frac{21}{12}-\frac{5}{12}=\frac{21 - 5}{12}=\frac{16}{12}=\frac{4}{3}\approx1.33>1\), so this is greater than 1.

Step3: Analyze \(1\frac{4}{6} - \frac{2}{6}\)

Convert the mixed number: \(1\frac{4}{6}=\frac{6 + 4}{6}=\frac{10}{6}\). Subtract: \(\frac{10}{6}-\frac{2}{6}=\frac{10 - 2}{6}=\frac{8}{6}=\frac{4}{3}\approx1.33>1\), so this is greater than 1.

Answer:

• Less than 1: \(1\frac{2}{5} - \frac{4}{5}\)
• Greater than 1: \(1\frac{9}{12} - \frac{5}{12}\), \(1\frac{4}{6} - \frac{2}{6}\)