Work out 0•36×2•4 over 0•9×0•6

$$0.36 \times 2.4$$

Multiply $36 \times 24$:
$36 \times 20 = 720$
$36 \times 4 = 144$
$720 + 144 = 864$
Since there are two decimal places in 0.36 and one in 2.4, there will be $2+1=3$ decimal places in the product.
So, $0.36 \times 2.4 = 0.864$.

$$0.9 \times 0.6$$

Multiply $9 \times 6 = 54$.
Since there is one decimal place in 0.9 and one in 0.6, there will be $1+1=2$ decimal places in the product.
So, $0.9 \times 0.6 = 0.54$.

$$\frac{0.864}{0.54}$$

To simplify the division, we can multiply both the numerator and the denominator by 1000 to remove the decimals.

$$\frac{0.864 \times 1000}{0.54 \times 1000} = \frac{864}{540}$$

We can simplify this fraction. Both are divisible by 10:

$$\frac{86.4}{54}$$

Now, perform the division:

$$86.4 \div 54$$ $$86 \div 54 = 1 \text{ with a remainder of } 32$$

Bring down the 4, making it 324.

$$324 \div 54 = 6$$

So, $86.4 \div 54 = 1.6$.

Alternatively, we can write:

$$\frac{0.864}{0.54} = \frac{864}{540}$$

Divide both by 10:

$$\frac{86.4}{54}$$

Divide 86.4 by 54:

$$54 \times 1 = 54$$ $$86.4 - 54 = 32.4$$ $$54 \times 0.6 = 32.4$$

So, $1 + 0.6 = 1.6$.

The final answer is 1.6.