The problem is to calculate the result of the division: $4.65 \div 3.5$.

1. Problem Description

The problem is to calculate the result of the division: $4.65 \div 3.5$.

2. Solution Steps

To divide $4.65$ by $3.5$, we can rewrite the division as a fraction:

$\frac{4.65}{3.5}$

To get rid of the decimal points, we can multiply both the numerator and the denominator by 100:

$\frac{4.65 \times 100}{3.5 \times 100} = \frac{465}{350}$

Now we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Both 465 and 350 are divisible by 5:

$\frac{465 \div 5}{350 \div 5} = \frac{93}{70}$

Now we perform long division to find the decimal representation of $\frac{93}{70}$.

$93 \div 70 = 1$ with a remainder of $23$.

So, $\frac{93}{70} = 1 + \frac{23}{70}$.

Now, convert the remainder into a decimal: $\frac{23}{70} = \frac{230}{700}$.

$230 \div 70 = 3$ with a remainder of $20$.

So we have $1.3$ so far. The remainder is $20$, so we can write it as $200$ and divide by $70$.

$200 \div 70 = 2$ with a remainder of $60$.

So we have $1.32$ so far. The remainder is $60$, so we can write it as $600$ and divide by $70$.

$600 \div 70 = 8$ with a remainder of $40$.

So we have $1.328$ so far. The remainder is $40$, so we can write it as $400$ and divide by $70$.

$400 \div 70 = 5$ with a remainder of $50$.

So we have $1.3285$ so far.

$4.65 \div 3.5 = 1.32857...$

We can perform the division:

4. 65 / 3.5 = 1.32857142857...

Rounding to two decimal places gives 1.

3

3. However, the question doesn't mention rounding so we'll leave the exact value by writing as a fraction or continuing the division until we see repetition.

We have $\frac{93}{70}$.

Performing the long division:

1. 3285714...

We can write the number as 1.3285714 repeating.

Another approach:

$\frac{4.65}{3.5} = \frac{465}{350} = \frac{93}{70}$.

Dividing 93 by 70, we get 1.328571428571...

A good approximation is 1.

3

3. Let's find the precise answer. We want $\frac{465}{350}$. Multiplying the numerator and denominator by 2, we get $\frac{930}{700}$. This gives $1 \frac{230}{700} = 1 \frac{23}{70}$. This is equal to 1.3285714...

3. Final Answer

1. 328571428571... or $\frac{93}{70}$