Question

10 $6\frac{2}{5} - 3\frac{3}{4}$

Explanation:

Step1: Convert mixed numbers to improper fractions

To subtract mixed numbers, first convert them to improper fractions. For \(6\frac{2}{5}\), multiply the whole number 6 by the denominator 5 and add the numerator 2: \(6\times5 + 2 = 32\), so \(6\frac{2}{5}=\frac{32}{5}\). For \(3\frac{3}{4}\), multiply 3 by 4 and add 3: \(3\times4 + 3 = 15\), so \(3\frac{3}{4}=\frac{15}{4}\).

Step2: Find a common denominator

The denominators are 5 and 4, so the least common denominator (LCD) is \(5\times4 = 20\). Convert \(\frac{32}{5}\) to a fraction with denominator 20: \(\frac{32}{5}=\frac{32\times4}{5\times4}=\frac{128}{20}\). Convert \(\frac{15}{4}\) to a fraction with denominator 20: \(\frac{15}{4}=\frac{15\times5}{4\times5}=\frac{75}{20}\).

Step3: Subtract the fractions

Now subtract the two fractions: \(\frac{128}{20}-\frac{75}{20}=\frac{128 - 75}{20}=\frac{53}{20}\).

Step4: Convert back to a mixed number (optional)

Convert \(\frac{53}{20}\) back to a mixed number. Divide 53 by 20: \(53\div20 = 2\) with a remainder of 13, so \(\frac{53}{20}=2\frac{13}{20}\).

Answer:

\(2\frac{13}{20}\)