Which fractions are equivalent to $$ \frac{6}{10} $$ ? Hint: There may be more than one.

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Fractions equivalent to $$ \frac{6}{10} $$ are those that represent the same value when simplified or scaled by multiplying both the numerator and the denominator by the same non-zero integer. Here are several examples:

1. **Simplified Form:**
   $$
   \frac{6}{10} = \frac{3}{5}
   $$
   (Both numerator and denominator are divided by 2.)

2. **Multiples:**
   $$
   \frac{6 \times 2}{10 \times 2} = \frac{12}{20}
   $$
   $$
   \frac{6 \times 3}{10 \times 3} = \frac{18}{30}
   $$
   $$
   \frac{6 \times 4}{10 \times 4} = \frac{24}{40}
   $$
   $$
   \frac{6 \times 5}{10 \times 5} = \frac{30}{50}
   $$
   $$
   \frac{6 \times 6}{10 \times 6} = \frac{36}{60}
   $$
   $$
   \frac{6 \times 7}{10 \times 7} = \frac{42}{70}
   $$
   $$
   \frac{6 \times 8}{10 \times 8} = \frac{48}{80}
   $$
   $$
   \frac{6 \times 9}{10 \times 9} = \frac{54}{90}
   $$
   $$
   \frac{6 \times 10}{10 \times 10} = \frac{60}{100}
   $$
   
3. **Negative Equivalents:**
   $$
   \frac{-6}{-10} = \frac{6}{10} = \frac{3}{5}
   $$

4. **Non-Integer Multiples (for completeness):**
   While less common in basic fractions, you can also have equivalent fractions by using fractions to multiply:
   $$
   \frac{6 \times \frac{1}{2}}{10 \times \frac{1}{2}} = \frac{3}{5}
   $$
   $$
   \frac{6 \times \frac{3}{2}}{10 \times \frac{3}{2}} = \frac{9}{15}
   $$

**General Rule:**
To find equivalent fractions, multiply or divide both the numerator and the denominator by the same non-zero integer. This maintains the value of the fraction while changing its appearance.

**Summary of Examples:**
- $$ \frac{3}{5} $$
- $$ \frac{12}{20} $$
- $$ \frac{18}{30} $$
- $$ \frac{24}{40} $$
- $$ \frac{30}{50} $$
- $$ \frac{36}{60} $$
- $$ \frac{42}{70} $$
- $$ \frac{48}{80} $$
- $$ \frac{54}{90} $$
- $$ \frac{60}{100} $$
- $$ \frac{-6}{-10} $$

These are just a few examples; there are infinitely many fractions equivalent to $$ \frac{6}{10} $$.
Equivalent fractions to $$ \frac{6}{10} $$ include $$ \frac{3}{5} $$, $$ \frac{12}{20} $$, $$ \frac{18}{30} $$, $$ \frac{24}{40} $$, $$ \frac{30}{50} $$, $$ \frac{36}{60} $$, $$ \frac{42}{70} $$, $$ \frac{48}{80} $$, $$ \frac{54}{90} $$, and $$ \frac{60}{100} $$.

Which fractions are equivalent to \( \frac{6}{10} \) ? Hint: There may be more than one.

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