how can you perform division with long numbers

Answer 1

Performing division with long numbers involves using the long division method. Here's a step-by-step guide to help you understand how to do it:

Step-by-Step Long Division

1. Set Up the Division: Write the dividend (the number you want to divide) under the long division symbol and the divisor (the number you are dividing by) outside, to the left.

2. Divide: Look at the leftmost digit (or group of digits) of the dividend. Determine how many times the divisor can fit into that number without exceeding it.

3. Multiply: Multiply the divisor by the quotient you just determined in the previous step. Write this result under the dividend.

4. Subtract: Subtract this result from the portion of the dividend you are working with. Write the result below.

5. Bring Down the Next Digit: Bring down the next digit from the dividend to the right of the subtraction result to form a new number.

6. Repeat: Repeat the process (divide, multiply, subtract, and bring down the next digit) until you have brought down all the digits from the dividend.

7. Remainder: If you reach a point where the divisor can no longer fit into the number you have (after bringing down all digits), you can either stop there or write the remaining number as a remainder. To express this, you would write your final answer followed by "R" and the remainder, or continue dividing to add decimal points.

Example of Long Division

Let’s look at an example: Divide 12345 by 67.

1. Set Up:

       ____
   67 | 12345
   

2. First Division:

   • How many times does 67 fit into 123? It fits 1 time.

3. Multiply:

   • 67 x 1 = 67

4. Subtract:

       ____
   67 | 12345
       - 67
       ------
         56
   

5. Bring Down:

   • Bring down the next digit (4), making it 564.

6. Repeat:

   • How many times does 67 fit into 564? It fits 8 times (since 67 x 8 = 536).

       ____
   67 | 12345
       - 67
       ------
         564
       - 536
       ------
          28
   

7. Bring Down Next Digit:

   • Bring down the last digit (5), making it 285.

8. Final Division:

   • How many times does 67 fit into 285? It fits 4 times (since 67 x 4 = 268).

       ____
   67 | 12345
       - 67
       ------
         564
       - 536
       ------
          285
       - 268
       ------
           17
   

Final Result:

The quotient is 184 with a remainder of 17. You could express that as:

• 184 R17 or as a decimal if you continue dividing:
  • 17 divided by 67 is approximately 0.25, so you could express the quotient as 184.25.

This method can be applied to any long numbers, and with practice, you can get more comfortable performing long division quickly!

Answer 2

make it a short summary

Answer 3

Long Division Summary:

1. Set Up: Write the dividend (number to be divided) under the long division symbol and the divisor (number doing the dividing) outside.

2. Divide: Determine how many times the divisor fits into the leftmost part of the dividend.

3. Multiply: Multiply the divisor by the quotient.

4. Subtract: Subtract this result from the current number.

5. Bring Down: Bring down the next digit from the dividend.

6. Repeat: Continue the process of dividing, multiplying, subtracting, and bringing down until you’ve used all digits.

7. Remainder: If you can't divide anymore, either stop or express as a remainder or decimal.

Example: For 12345 ÷ 67, the result is 184 with a remainder of 17 or approximately 184.25 if expressed as a decimal.