Multi Digit Division

Multi-digit division refers to the process of dividing a multi-digit number (dividend) by another number (divisor) to obtain a quotient and possibly a remainder. This process involves dividing each digit of the dividend by the divisor and iteratively determining the result.

Multi-digit division is an essential arithmetic operation and is used in various mathematical and real-world scenarios.

Here’s a step-by-step process of multi-digit division with an example:

Example: Divide 3256 by 8

            407  (Quotient)

       ________

         8 | 3256

         – 32

         ________

                056

            –  56

          ________

                0

In this example, the divisor is 8, and the dividend is 3256. The process starts by dividing the leftmost digits of the dividend (3) by the divisor (8), resulting in a quotient of 0 and a remainder of 3. The next digit (2) is brought down, making the new partial dividend 32. This is divided by the divisor, resulting in a quotient of 4 and a remainder of 0. Finally, the remaining digits (5 and 6) are brought down, and since there are no more digits left, the process is complete.

So, 3256 divided by 8 equals 407 with no remainder.

Another example:

Example: Divide 1298 by 12

         108  (Quotient)

      __________

 12 | 1298

      – 12

      __________

          098

        –   96

      __________

  2

In this example, 1298 divided by 12 equals 108 with a remainder of 2.

Multi-digit division can become more complex with larger numbers and longer divisions, but the fundamental process involves repeatedly dividing digits and determining the quotient and remainder until the entire dividend has been processed.

Questions

Example 1

Divide 3546 by 12

Solution:

          295  (Quotient)

      _______

 12 | 3546

     –  24

      _______

         114

       – 108

       _______

            66

        –   60

       _______

             6

Here, Dividend is 3456, divisor is 12, quotient is 295, and remainder is 6

Example 2

Divide 6897 by 23

Solution:

        299  (Quotient)

     _______

23 | 6897

    –  46

    _______

       229  

     – 207

     _______

         227

      –  207

     _______

          20

Here, Dividend is 6897 divisor is 23, quotient is 299, and remainder is 20

Example 3

Calculate the quotient and remainder of 1473 divided by 9

Solution:

       163  (Quotient)

    _______

9  | 1473

     –  9

     _______

        57

     –  54

     _______

         33

      –  27

     _______

           6

Here, Dividend is 1473 divisor is 9, quotient is 163, and remainder is 6

Example 4

Divide 82.08 by 24

Solution:

         3.42 (Quotient)

     ________

24 | 82.08

      -72

      ________

       100                 

        -96

      ________

           48

         – 48

      ________

            0

Here, Dividend is 82.08 divisor is 24, quotient is 3.42, and remainder is 0

Following word problems demonstrate how to apply multi-digit division in real-life situations.

Example 5

Bakery Orders: A bakery received a shipment of 732 cupcakes. The cupcakes need to be divided equally into boxes, with each box containing 12 cupcakes. How many boxes will the bakery need to pack all the cupcakes?

Solution:

To solve this problem, we need to perform a multi-digit division to find out how many boxes of 12 cupcakes can be formed from the total of 732 cupcakes.

         61  (Quotient)

     ______

12 | 732

    –  72

     _______

         12

      –  12

     _______

           0

The bakery will need 61 boxes to pack all 732 cupcakes equally, with no cupcakes left over.

Therefore, the answer is that the bakery will need 61 boxes to pack all the cupcakes.

Example 6:

Candy Distribution: A candy store has received a shipment of 3724 candies. The store manager wants to pack these candies into bags, each containing 892 candies. How many bags can the store manager fill, and will there be any candies left?

Solution:

To solve this problem, we need to divide the total number of candies (3724) by the number of candies per bag (892) to find out how many bags the store manager can fill.

            4  (Quotient)

       _______

892 | 3724

      –  3568

       _______

           156

The division process shows that the store manager can fill 4 bags with 892 candies each. There will be 156 candies left over.

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