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Divide. Write your answer in simplest form. (2)/(5)÷(2)/(3)=" ? "

Divide.\newlineWrite your answer in simplest form.\newline25÷23=? \frac{2}{5} \div \frac{2}{3}=?

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Full solution

Q. Divide.\newlineWrite your answer in simplest form.\newline25÷23=? \frac{2}{5} \div \frac{2}{3}=?
  1. Flip fraction: Flip the second fraction to find its reciprocal, so (23)(\frac{2}{3}) becomes (32)(\frac{3}{2}).
  2. Multiply fractions: Now multiply the first fraction by the reciprocal of the second fraction: (25)×(32)(\frac{2}{5}) \times (\frac{3}{2}).
  3. Multiply numerators: Multiply the numerators together: 2×3=62 \times 3 = 6.
  4. Multiply denominators: Multiply the denominators together: 5×2=105 \times 2 = 10.
  5. Write result: Write the result as a single fraction: 610.\frac{6}{10}.
  6. Simplify fraction: Simplify the fraction by dividing both the numerator and the denominator by their greatest common factor, which is 22: 6÷2=36 \div 2 = 3 and 10÷2=510 \div 2 = 5.
  7. Final simplified fraction: The simplified fraction is 35.\frac{3}{5}.

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