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------------------------------------------------ Divide 147 by 2.25.

[tex]
\[
\begin{array}{r}
147 \\
\div 2.25 \\
\hline
\end{array}
\]
[/tex]

We start with the expression

[tex]$$
147 \div 2.25
$$[/tex]

Step 1. Convert the Decimal to a Fraction.

Notice that

[tex]$$
2.25 = \frac{9}{4}.
$$[/tex]

Step 2. Rewrite Division as Multiplication by the Reciprocal.

Dividing by a number is the same as multiplying by its reciprocal. Thus,

[tex]$$
147 \div 2.25 = 147 \times \frac{4}{9}.
$$[/tex]

Step 3. Multiply the Numbers.

Multiply the numerator by the reciprocal:

[tex]$$
147 \times \frac{4}{9} = \frac{147 \times 4}{9}.
$$[/tex]

Step 4. Simplify the Expression.

It is often easier to simplify before doing the multiplication. Notice that [tex]$147$[/tex] and [tex]$9$[/tex] have a common factor:

- Divide [tex]$147$[/tex] by [tex]$9$[/tex]:

[tex]$$
\frac{147}{9} = \frac{49}{3} \quad \text{since } 147 = 49 \times 3.
$$[/tex]

Now substitute back:

[tex]$$
\frac{147 \times 4}{9} = \frac{49 \times 3 \times 4}{9} = 49 \times \frac{4}{3}.
$$[/tex]

Then perform the multiplication:

[tex]$$
49 \times \frac{4}{3} = \frac{196}{3}.
$$[/tex]

Step 5. Convert to a Decimal (if needed).

Divide:

[tex]$$
\frac{196}{3} \approx 65.3333\ldots
$$[/tex]

Thus, the result is

[tex]$$
147 \div 2.25 = \frac{196}{3} \approx 65.3333.
$$[/tex]

This is the final answer.