Question

use the model to answer the question.
what is $\frac{2}{5} \times \frac{1}{4}$?
a. $\frac{3}{9}$
b. $\frac{3}{20}$
c. $\frac{2}{20}$
d. $\frac{2}{9}$

Explanation:

Step1: Recall fraction multiplication rule

To multiply two fractions \(\frac{a}{b}\) and \(\frac{c}{d}\), we use the rule \(\frac{a}{b} \times \frac{c}{d}=\frac{a\times c}{b\times d}\).

Step2: Apply the rule to \(\frac{2}{5}\times\frac{1}{4}\)

Here, \(a = 2\), \(b = 5\), \(c = 1\), \(d = 4\). So, \(\frac{2}{5}\times\frac{1}{4}=\frac{2\times1}{5\times4}=\frac{2}{20}\). We can also simplify \(\frac{2}{20}\) to \(\frac{1}{10}\), but looking at the options, \(\frac{2}{20}\) is option C. Wait, wait, let's check again. Wait, \(2\times1 = 2\), \(5\times4=20\), so \(\frac{2}{20}\) which is option C? Wait, no, wait, maybe I made a mistake. Wait, \(\frac{2}{5}\times\frac{1}{4}\): numerator \(2\times1 = 2\), denominator \(5\times4 = 20\), so \(\frac{2}{20}\), which is option C. But let's check the options again. Option C is \(\frac{2}{20}\), option B is \(\frac{3}{20}\), option A is \(\frac{3}{9}\) (simplified \(\frac{1}{3}\)), option D is \(\frac{2}{9}\). So the correct calculation gives \(\frac{2}{20}\), which is option C. Wait, but let's confirm the fraction multiplication. Yes, \(\frac{2}{5}\times\frac{1}{4}=\frac{2\times1}{5\times4}=\frac{2}{20}\). So the answer should be option C.

Answer:

C. \(\frac{2}{20}\)