$38 \overline{)27664}$
Answer (2)
The result of the long division 27664 ÷ 38 is 728 . This is obtained by dividing, multiplying, and subtracting systematically. The long division is complete with no remainder, confirming that the quotient is correct.
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Divide 276 by 38, which gives 7. Multiply 7 by 38 to get 266, and subtract from 276 to get 10.
Bring down the 6, resulting in 106. Divide 106 by 38, which gives 2. Multiply 2 by 38 to get 76, and subtract from 106 to get 30.
Bring down the 4, resulting in 304. Divide 304 by 38, which gives 8. Multiply 8 by 38 to get 304, and subtract from 304 to get 0.
The result of the long division is 728 .
Explanation
Understanding the Problem We are asked to perform the long division 38 v er t 27664 . This means we want to find the quotient when 27664 is divided by 38.
First Step: Dividing 276 by 38 First, we look at the first three digits of the dividend, 276. We want to find the largest whole number that, when multiplied by 38, is less than or equal to 276. We can estimate this by dividing 276 by 38. The result of this division is 7.
Multiplying and Subtracting Now, we multiply 7 by 38: 7 v er tt im es 38 = 266 . We subtract this from 276: 276 − 266 = 10 .
Bringing Down the Next Digit Next, we bring down the next digit from the dividend, which is 6. This gives us 106. We want to find the largest whole number that, when multiplied by 38, is less than or equal to 106. We can estimate this by dividing 106 by 38. The result of this division is 2.
Multiplying and Subtracting Again Now, we multiply 2 by 38: 2 v er tt im es 38 = 76 . We subtract this from 106: 106 − 76 = 30 .
Bringing Down the Last Digit Next, we bring down the last digit from the dividend, which is 4. This gives us 304. We want to find the largest whole number that, when multiplied by 38, is less than or equal to 304. We can estimate this by dividing 304 by 38. The result of this division is 8.
Final Multiplication and Subtraction Now, we multiply 8 by 38: 8 v er tt im es 38 = 304 . We subtract this from 304: 304 − 304 = 0 .
Final Answer Since the remainder is 0, the long division is complete. The quotient is 728. Therefore, 27664 ÷ 38 = 728 .
Examples
Long division is a fundamental arithmetic operation used to divide large numbers into smaller, more manageable parts. For example, if you have 27664 apples and want to distribute them equally among 38 people, long division helps you determine that each person would receive 728 apples. This method is widely used in various real-life scenarios, such as calculating unit prices, determining average speeds, and splitting costs among groups.
