Complete the division 3/5 divided by 2/3.

Step-by-step solution

1. 1

   Recall why dividing by a fraction flips it. Dividing by $\tfrac{2}{3}$ asks how many two-thirds fit into $\tfrac35$; since $\tfrac23\cdot\tfrac32=1$, multiplying by $\tfrac32$ undoes multiplying by $\tfrac23$. Formally,

   $\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\cdot\frac{d}{c}.$

2. 2

   Rewrite the division as a multiplication by the reciprocal. Only the second fraction is flipped:

   $\frac{3}{5}\div\frac{2}{3}=\frac{3}{5}\cdot\frac{3}{2}.$

3. 3

   Multiply straight across.

   $\frac{3\cdot 3}{5\cdot 2}=\frac{9}{10}.$

4. 4

   Check whether the result reduces. $9=3^2$ and $10=2\cdot 5$ share no common factor, so $\tfrac{9}{10}$ is already in lowest terms.

5. 5

   Sanity-check the size. Dividing by a number smaller than $1$ must make the result larger than what you started with, and indeed $\tfrac{9}{10}=0.9$ is bigger than $\tfrac35=0.6$. Numerically $0.6\div 0.6\overline{6}=0.9$ ✓.