To solve the question of which expression is equal to [tex]\( 53462 \div 14 \)[/tex], we will evaluate each given option to find the one that matches the result [tex]\( 3818.714285714286 \)[/tex].
1. Evaluate [tex]\( 3818 \times 14 \times 10 \)[/tex]:
[tex]\[
3818 \times 14 \times 10 = (3818 \times 14) \times 10 = 53452 \times 10 = 534520
\][/tex]
This result is [tex]\( 534520 \)[/tex].
2. Evaluate [tex]\( 3810 \times 14 + 12 \)[/tex]:
[tex]\[
3810 \times 14 + 12 = (3810 \times 14) + 12 = 53340 + 12 = 53352
\][/tex]
This result is [tex]\( 53352 \)[/tex].
3. Evaluate [tex]\( 3810 \times 14 \times 12 \)[/tex]:
[tex]\[
3810 \times 14 \times 12 = (3810 \times 14) \times 12 = 53340 \times 12 = 640080
\][/tex]
This result is [tex]\( 640080 \)[/tex].
4. Evaluate [tex]\( 3818 \times 14 + 10 \)[/tex]:
[tex]\[
3818 \times 14 + 10 = (3818 \times 14) + 10 = 53452 + 10 = 53462
\][/tex]
This result is [tex]\( 53462 \)[/tex].
After evaluating each expression:
- The first expression [tex]\( 3818 \times 14 \times 10 \)[/tex] results in [tex]\( 534520 \)[/tex].
- The second expression [tex]\( 3810 \times 14 + 12 \)[/tex] results in [tex]\( 53352 \)[/tex].
- The third expression [tex]\( 3810 \times 14 \times 12 \)[/tex] results in [tex]\( 640080 \)[/tex].
- The fourth expression [tex]\( 3818 \times 14 + 10 \)[/tex] results in [tex]\( 53462 \)[/tex].
The expression [tex]\( 53462 \div 14 \)[/tex] is approximately [tex]\( 3818.714285714286 \)[/tex], and among the evaluated results, the closest match is [tex]\( 53462 \)[/tex].
Therefore, the expression that is equal to [tex]\( 53462 \div 14 \)[/tex] is:
[tex]\[ 3818 \times 14 + 10 \][/tex]
