Question

which fractions are equivalent to \\(\frac{4}{20}\\)?
hint: there may be more than one.
\\(\frac{1}{5}\\) \\(\frac{5}{16}\\) \\(\frac{3}{8}\\) \\(\frac{2}{10}\\)

Explanation:

Step1: Simplify the given fraction

Simplify \(\frac{4}{20}\) by dividing numerator and denominator by their greatest common divisor (GCD). The GCD of 4 and 20 is 4. So, \(\frac{4\div4}{20\div4}=\frac{1}{5}\).

Step2: Check each option

• For \(\frac{1}{5}\): We just simplified \(\frac{4}{20}\) to \(\frac{1}{5}\), so they are equivalent.
• For \(\frac{5}{16}\): Cross - multiply \(\frac{4}{20}\) and \(\frac{5}{16}\). \(4\times16 = 64\) and \(20\times5=100\). Since \(64

eq100\), \(\frac{4}{20}\) and \(\frac{5}{16}\) are not equivalent.

• For \(\frac{3}{8}\): Cross - multiply \(\frac{4}{20}\) and \(\frac{3}{8}\). \(4\times8 = 32\) and \(20\times3 = 60\). Since \(32

eq60\), \(\frac{4}{20}\) and \(\frac{3}{8}\) are not equivalent.

• For \(\frac{2}{10}\): Simplify \(\frac{2}{10}\) by dividing numerator and denominator by 2. \(\frac{2\div2}{10\div2}=\frac{1}{5}\), which is equivalent to \(\frac{4}{20}\) (since \(\frac{4}{20}=\frac{1}{5}\)). Also, we can cross - multiply: \(4\times10=40\) and \(20\times2 = 40\). So \(\frac{4}{20}\) and \(\frac{2}{10}\) are equivalent.

Answer:

A. \(\frac{1}{5}\), D. \(\frac{2}{10}\) (assuming the options are labeled as A. \(\frac{1}{5}\), B. \(\frac{5}{16}\), C. \(\frac{3}{8}\), D. \(\frac{2}{10}\))