What is the value of ( \frac{3}{4}\times\frac{2}{5} )?

Correct answer: ( \frac{3}{10} )

Direct answer: Option B, \(\frac{3}{10}\). To multiply fractions, multiply the numerators together and multiply the denominators together. The numerators are 3 and 2, so the numerator becomes \(3\times2=6\). The denominators are 4 and 5, so the denominator becomes \(4\times5=20\). Thus the product is \(\frac{6}{20}\). Divide numerator and denominator by their common factor 2: \(\frac{6\div2}{20\div2}=\frac{3}{10}\). Option A, \(\frac{5}{9}\), comes from adding or combining numbers incorrectly and is not the product. Option B is correct because it is the simplified product. Option C, \(\frac{6}{9}\), uses neither the correct denominator nor correct simplification. Option D, \(\frac{1}{20}\), loses the factor 3 and is therefore too small. A safe check is that \(\frac34\) is less than 1 and \(\frac25\) is less than 1, so the answer should be positive and less than either factor; \(\frac3{10}\) fits. Remember: fraction multiplication is numerator times numerator and denominator times denominator.