To find fractions that are equivalent to \( \frac{2}{3} \), you can multiply the numerator and the denominator by the same non-zero number.
For example:
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If you multiply both the numerator and the denominator by 2, you get: \[ \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \]
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If you multiply both by 3, you get: \[ \frac{2 \times 3}{3 \times 3} = \frac{6}{9} \]
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If you multiply both by 4, you get: \[ \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \]
So, \( \frac{4}{6} \), \( \frac{6}{9} \), and \( \frac{8}{12} \) are all equivalent to \( \frac{2}{3} \).
In general, any fraction of the form \( \frac{2n}{3n} \) (where \( n \) is a non-zero integer) will be equivalent to \( \frac{2}{3} \).