Question

find the difference.
$3\frac{1}{5}-1\frac{4}{5}=\square\frac{?}{?}$

Explanation:

Step1: Subtract the whole numbers and the fractions separately

First, subtract the whole number parts: \(3 - 1 = 2\). Then subtract the fraction parts: \(\frac{1}{5}-\frac{4}{5}\). But \(\frac{1}{5}-\frac{4}{5}=\frac{1 - 4}{5}=\frac{- 3}{5}\). Since the fraction part is negative, we need to borrow 1 from the whole number part. So the whole number 2 becomes \(1\), and we add the denominator to the numerator of the fraction: \(1+\frac{5}{5}+\frac{1}{5}-\frac{4}{5}=1+\frac{6}{5}-\frac{4}{5}\). Wait, actually, a better way is to convert the mixed numbers to improper fractions. \(3\frac{1}{5}=\frac{3\times5 + 1}{5}=\frac{16}{5}\), \(1\frac{4}{5}=\frac{1\times5+4}{5}=\frac{9}{5}\). Then subtract: \(\frac{16}{5}-\frac{9}{5}=\frac{7}{5}\), and convert back to mixed number: \(\frac{7}{5}=1\frac{2}{5}\). Wait, let's do it step by step with mixed numbers.

Mixed number subtraction: \(3\frac{1}{5}-1\frac{4}{5}\). The fraction part: \(\frac{1}{5}-\frac{4}{5}\) is negative, so we take 1 from the whole number 3, making it 2, and add \(\frac{5}{5}\) to \(\frac{1}{5}\), so we have \(2\frac{6}{5}-1\frac{4}{5}\). Now subtract whole numbers: \(2 - 1 = 1\), subtract fractions: \(\frac{6}{5}-\frac{4}{5}=\frac{2}{5}\). So the result is \(1\frac{2}{5}\).

Step2: Verify the calculation

Convert \(3\frac{1}{5}\) to improper fraction: \(3\times5 + 1 = 16\), so \(\frac{16}{5}\). Convert \(1\frac{4}{5}\) to improper fraction: \(1\times5 + 4 = 9\), so \(\frac{9}{5}\). Subtract: \(\frac{16}{5}-\frac{9}{5}=\frac{7}{5}\). Convert \(\frac{7}{5}\) to mixed number: \(7\div5 = 1\) with remainder \(2\), so \(1\frac{2}{5}\).

Answer:

\(1\frac{2}{5}\) (So the whole number is \(1\), numerator is \(2\), denominator is \(5\))