Question

determine if each expression is less than 1 or greater than 1. less than 1 greater than 1 $1\frac{2}{5}-\frac{4}{5}$

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \(1\frac{2}{5}\) 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 \(1\frac{2}{5}\), we have \(a = 1\), \(b = 2\), \(c = 5\). Then \(1\frac{2}{5}=\frac{1\times5 + 2}{5}=\frac{7}{5}\).

Step2: Subtract the fractions

Now we have the expression \(\frac{7}{5}-\frac{4}{5}\). When subtracting fractions with the same denominator, we subtract the numerators and keep the denominator the same. So \(\frac{7 - 4}{5}=\frac{3}{5}\).

Step3: Compare with 1

We know that \(\frac{3}{5}=0.6\), and \(0.6<1\).

Answer:

The expression \(1\frac{2}{5}-\frac{4}{5}\) is less than 1.