Question

determine 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: Simplify \(1\frac{2}{5} - \frac{4}{5}\)

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 \(\frac{3}{5}<1\), this expression is less than 1.

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

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

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

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

Answer:

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