Answer :

To solve the division

[tex]$$
\frac{12}{38.4},
$$[/tex]

we can go through the following detailed steps:

1. Express the Division as a Fraction:
Write the division in fraction form:

[tex]$$
\frac{12}{38.4}.
$$[/tex]

2. Eliminate the Decimal:
To avoid working with decimals, multiply both the numerator and the denominator by 10. This gives:

[tex]$$
\frac{12 \times 10}{38.4 \times 10} = \frac{120}{384}.
$$[/tex]

3. Simplify the Fraction:
Next, simplify the fraction by finding a common factor. Notice that both 120 and 384 are divisible by 8:

[tex]$$
\frac{120 \div 8}{384 \div 8} = \frac{15}{48}.
$$[/tex]

Now, simplify further by dividing both the numerator and the denominator by 3:

[tex]$$
\frac{15 \div 3}{48 \div 3} = \frac{5}{16}.
$$[/tex]

4. Convert to a Decimal:
Finally, convert the simplified fraction to a decimal. Since

[tex]$$
\frac{5}{16} = 0.3125,
$$[/tex]

we find that

[tex]$$
\frac{12}{38.4} = 0.3125.
$$[/tex]

Thus, the final result of the division is

[tex]$$
\boxed{0.3125}.
$$[/tex]

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