Answer :
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.
[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.
