Question

find 3 ratios that are equivalent to the given ratio
\frac{5}{2}

find three ratios that are equivalent to the given ratio
\square a. \frac{15}{4} \square b. \frac{10}{4}
\square c. \frac{15}{6} \square d. \frac{20}{8}
\square e. \frac{20}{6} \square f. \frac{10}{6}
\square g. \frac{15}{8} \square h. \frac{10}{8}

Explanation:

To find equivalent ratios to \(\frac{5}{2}\), we can multiply or divide both the numerator and the denominator by the same non - zero number.

Step 1: Analyze Option B (\(\frac{10}{4}\))

We multiply the numerator and denominator of \(\frac{5}{2}\) by 2.
Using the formula for equivalent fractions \(\frac{a}{b}=\frac{a\times k}{b\times k}\) (where \(k = 2\), \(a = 5\), \(b=2\))
\(\frac{5\times2}{2\times2}=\frac{10}{4}\), so \(\frac{10}{4}\) is equivalent to \(\frac{5}{2}\)

Step 2: Analyze Option C (\(\frac{15}{6}\))

We multiply the numerator and denominator of \(\frac{5}{2}\) by 3.
Using the formula \(\frac{a}{b}=\frac{a\times k}{b\times k}\) (where \(k = 3\), \(a = 5\), \(b = 2\))
\(\frac{5\times3}{2\times3}=\frac{15}{6}\), so \(\frac{15}{6}\) is equivalent to \(\frac{5}{2}\)

Step 3: Analyze Option D (\(\frac{20}{8}\))

We multiply the numerator and denominator of \(\frac{5}{2}\) by 4.
Using the formula \(\frac{a}{b}=\frac{a\times k}{b\times k}\) (where \(k=4\), \(a = 5\), \(b = 2\))
\(\frac{5\times4}{2\times4}=\frac{20}{8}\), so \(\frac{20}{8}\) is equivalent to \(\frac{5}{2}\)

Answer:

B. \(\frac{10}{4}\), C. \(\frac{15}{6}\), D. \(\frac{20}{8}\)