Question

find the difference.
$4\frac{2}{10} - 2\frac{5}{10} = $
□
\frac{?}{?}

Explanation:

Step1: Subtract the whole numbers and fractions separately

First, handle the whole numbers: \(4 - 2 = 2\). Then, handle the fractions: \(\frac{2}{10}-\frac{5}{10}\). But \(\frac{2}{10}<\frac{5}{10}\), so we need to borrow 1 from the whole number part of \(4\frac{2}{10}\). So \(4\frac{2}{10}\) becomes \(3 + 1+\frac{2}{10}=3+\frac{10}{10}+\frac{2}{10}=3\frac{12}{10}\).

Step2: Now subtract the mixed numbers

Now subtract the whole numbers: \(3 - 2 = 1\). Subtract the fractions: \(\frac{12}{10}-\frac{5}{10}=\frac{12 - 5}{10}=\frac{7}{10}\).

Step3: Combine the results

Combine the whole number and the fraction: \(1+\frac{7}{10}=1\frac{7}{10}\). Wait, no, wait. Wait, original problem: \(4\frac{2}{10}-2\frac{5}{10}\). Let's do it again. Wait, maybe I made a mistake. Wait, \(4\frac{2}{10}\) is \(4 + \frac{2}{10}\), \(2\frac{5}{10}\) is \(2+\frac{5}{10}\). So \(4\frac{2}{10}-2\frac{5}{10}=(4 - 2)+(\frac{2}{10}-\frac{5}{10})=2+(-\frac{3}{10})\). But since we can't have a negative fraction in a mixed number without adjusting, we borrow 1 from the 2 (the whole number part). So 2 becomes 1, and we add \(\frac{10}{10}\) to \(-\frac{3}{10}\), so \(1+(\frac{10}{10}-\frac{3}{10})=1\frac{7}{10}\)? Wait, no, wait. Wait, \(4\frac{2}{10}-2\frac{5}{10}\). Let's convert to improper fractions. \(4\frac{2}{10}=\frac{4\times10 + 2}{10}=\frac{42}{10}\), \(2\frac{5}{10}=\frac{2\times10+5}{10}=\frac{25}{10}\). Then \(\frac{42}{10}-\frac{25}{10}=\frac{42 - 25}{10}=\frac{17}{10}=1\frac{7}{10}\). Wait, no, 42 - 25 is 17? Wait, 42 - 25 is 17? Wait, 25 + 17 is 42? Yes. So \(\frac{17}{10}=1\frac{7}{10}\). Wait, but that seems wrong. Wait, no, 4\frac{2}{10} is 4.2, 2\frac{5}{10} is 2.5, 4.2 - 2.5 = 1.7, which is 1\frac{7}{10}. Yes, that's correct.

Answer:

\(1\frac{7}{10}\) (or as a fraction \(\frac{17}{10}\))