quotient of $$ \frac{3}{5} \div \frac{2}{3} ? $$ Prove

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To find the quotient of $$\frac{3}{5} \div \frac{2}{3}$$, we can follow these steps:

### Step 1: Understand Division of Fractions
Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of a fraction is obtained by swapping its numerator and denominator.

### Step 2: Apply the Reciprocal
Given:
$$
\frac{3}{5} \div \frac{2}{3}
$$
We take the reciprocal of $$\frac{2}{3}$$, which is $$\frac{3}{2}$$, and multiply:
$$
\frac{3}{5} \times \frac{3}{2}
$$

### Step 3: Multiply the Numerators and Denominators
Multiply the numerators together and the denominators together:
$$
\frac{3 \times 3}{5 \times 2} = \frac{9}{10}
$$

### Step 4: Simplify (if necessary)
In this case, $$\frac{9}{10}$$ is already in its simplest form.

### Proof Using the Definition of Division
To reinforce the solution, let's use the definition of division:

Let $$x = \frac{3}{5} \div \frac{2}{3}$$. By definition:
$$
x \times \frac{2}{3} = \frac{3}{5}
$$
To solve for $$x$$, multiply both sides by the reciprocal of $$\frac{2}{3}$$, which is $$\frac{3}{2}$$:
$$
x = \frac{3}{5} \times \frac{3}{2} = \frac{9}{10}
$$

### Conclusion
The quotient of $$\frac{3}{5} \div \frac{2}{3}$$ is:
$$
\boxed{\dfrac{9}{10}}
$$
The quotient of $$\frac{3}{5} \div \frac{2}{3}$$ is $$\frac{9}{10}$$.

quotient of \( \frac{3}{5} \div \frac{2}{3} ? \) Prove

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