Verified Answer :

  • The division of 13714 by 72 yields an integer quotient and a remainder.
  • By performing the long division, we find 72 goes into 13714 exactly 190 times with a remainder of 34.
  • In decimal form, the division is approximately \(190.4722\).
  • The final result is \(\boxed{190.4722...}\) or \(\boxed{190 \frac{17}{36}}\).

Explanation

  1. Division Analysis

We are tasked with dividing 13714 by 72. To find the result, we perform long division.
First, we look at the dividend 13714 and the divisor 72. We determine how many times 72 fits into the leading digits of 13714.

  • 72 goes into 137 once: \(137 - 72 = 65\).
  • Bring down the next digit, 1, to make 651. 72 goes into 651 nine times: \(72 \times 9 = 648\). Subtracting gives \(651 - 648 = 3\).
  • Bring down the next digit, 4, to make 34. 72 goes into 34 zero times.

Thus, the integer quotient is 190 with a remainder of 34. Expressed as a decimal, this is \(190 + \frac{34}{72}\), which simplifies to \(190 + \frac{17}{36} \approx 190.4722\).

Examples

Long division is an essential skill in everyday life, such as when you need to share resources equally. For instance, if you have a budget of \$13,714 to distribute among 72 departments in a large organization, you would need to perform this division to find out how much each department receives. Specifically, each department would receive \$190, with \$34 left over as a remainder to be allocated elsewhere. Mastering this process ensures accurate financial management and fair resource distribution.

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