Question

7\frac{3}{5} - 4\frac{3}{10}

Explanation:

Step1: Convert mixed numbers to improper fractions

To subtract mixed numbers, first convert them to improper fractions. For \(7\frac{3}{5}\), multiply the whole number \(7\) by the denominator \(5\) and add the numerator \(3\): \(7\times5 + 3=35 + 3 = 38\), so \(7\frac{3}{5}=\frac{38}{5}\). For \(4\frac{3}{10}\), multiply \(4\) by \(10\) and add \(3\): \(4\times10+3 = 40 + 3=43\), so \(4\frac{3}{10}=\frac{43}{10}\).

Step2: Find a common denominator

The denominators are \(5\) and \(10\). The least common denominator is \(10\). Convert \(\frac{38}{5}\) to a fraction with denominator \(10\) by multiplying numerator and denominator by \(2\): \(\frac{38\times2}{5\times2}=\frac{76}{10}\).

Step3: Subtract the fractions

Now subtract \(\frac{43}{10}\) from \(\frac{76}{10}\): \(\frac{76}{10}-\frac{43}{10}=\frac{76 - 43}{10}=\frac{33}{10}\).

Step4: Convert back to mixed number (optional, but common)

Convert \(\frac{33}{10}\) to a mixed number. Divide \(33\) by \(10\): \(33\div10 = 3\) with a remainder of \(3\), so \(\frac{33}{10}=3\frac{3}{10}\). Alternatively, we can also subtract the whole numbers and the fractions separately from the start. Let's check that way too. Subtract the whole numbers: \(7 - 4 = 3\). Subtract the fractions: \(\frac{3}{5}-\frac{3}{10}\). Convert \(\frac{3}{5}\) to \(\frac{6}{10}\), then \(\frac{6}{10}-\frac{3}{10}=\frac{3}{10}\). Then add the results: \(3+\frac{3}{10}=3\frac{3}{10}\).

Answer:

\(3\frac{3}{10}\)