To determine which given expression equals [tex]\(\frac{53462}{14}\)[/tex], we'll start by examining the quotient and remainder when 53462 is divided by 14.
Here are the four options:
1. [tex]\(3810 \times 14 + 12\)[/tex]
2. [tex]\(3810 \times 14 \times 12\)[/tex]
3. [tex]\(3818 \times 14 \times 10\)[/tex]
4. [tex]\(3818 \times 14 + 10\)[/tex]
We need to check each option to see which one matches the value of [tex]\(\frac{53462}{14}\)[/tex].
First, let's dismiss options that inherently won't give us a correct division result because they involve multiplication beyond the scope we need:
- Option 2: [tex]\(3810 \times 14 \times 12\)[/tex]
- Option 3: [tex]\(3818 \times 14 \times 10\)[/tex]
Both of these options involve multiplying by an additional factor without adding a remainder, so these cannot be correct as they far exceed the target result.
Now let's check the remaining options:
### Option 1: [tex]\(3810 \times 14 + 12\)[/tex]
```
Evaluating:
3810 \times 14 + 12
= 53340 + 12
= 53352
```
The result of Option 1 is 53352, which does not equal 53462.
### Option 4: [tex]\(3818 \times 14 + 10\)[/tex]
```
Evaluating:
3818 \times 14 + 10
= 53452 + 10
= 53462
```
The result of Option 4 is 53462, which matches the desired value exactly.
Thus, the correct expression that equals [tex]\(\frac{53462}{14}\)[/tex] is:
[tex]\[ 3818 \times 14 + 10 \][/tex]
Therefore, the correct option is:
[tex]\[ \boxed{4} \][/tex]
