To determine whether the two ratios \( \frac{3}{x} \) and \( \frac{6}{10} \) are equivalent, we can set them equal to each other and solve for \(x\).

\[
\frac{3}{x} = \frac{6}{10}
\]

Now, we solve for \(x\) by cross-multiplying:

\[
3 \times 10 = 6 \times x
\]

\[
30 = 6x
\]

Now, divide both sides by 6:

\[
x = \frac{30}{6} = 5
\]

So, \( \frac{3}{5} \) is equivalent to \( \frac{6}{10} \).

Would you like more details or have any questions?

Here are five related questions for practice:
1. What is \( \frac{4}{x} = \frac{8}{16} \)?
2. Simplify the ratio \( 12:16 \).
3. How do you convert a ratio to a fraction?
4. Is \( \frac{5}{10} \) equivalent to \( \frac{7}{14} \)?
5. Solve for \( x \) in \( \frac{9}{x} = \frac{12}{20} \).

**Tip:** When comparing two ratios, cross-multiplication is a useful method for checking equivalency.

Learn how to solve the ratio problem 'Is 3:5 equivalent to 6:10?' using cross-multiplication. This example covers the concept of equivalent ratios and proportional reasoning, suitable for students in Grades 5-7.

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