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Thought-Process to Discover Knowledge

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mathsWhole NumbersWhole Numbers: Multiplication and Division

Division : Simplified Procedure for Large Numbers

This page extends the division in first principles into a simplified procedure for division of large numbers, which is called division by place-value with de-grouping.



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Consider the division `36-:3`.division two digit numbers Which of the following step helps in the division?

  • Split `36` into `3` parts and count one part
  • Split `36` into `3` parts and count one part
  • two digit number division is not possible

The answer is 'Split `36` into `3` parts and count one part'.

Considering the division `36-:3`.division two digit numbers Splitting `36` into `3` parts is shown in the figure. Only one part is chosen, and other parts are shaded.

What is the count in the part chosen?

  • `1+2=3`
  • `12`
  • `12`

The answer is '`12`'. There are `1` tens and `2` units which together form the value `12`.

Considering the division `36-:3`. The number `36` is given in the place value form in the figure.division two digit numbers place-value-form The splitting into equal parts is visualized and the division is performed as shown in the figure.

What is the result of the division?

  • `12`
  • `12`
  • `0`

The answer is '`12`'.

The tens place is divided first as `3-:3=1` and then the units place is divided as `6-:3=2`.

Consider the division `52-:2`. That is, `52` is split into two equal parts as shown in the figure.division with carryover two digit numbers `5` tens are distributed as `2` each in the two parts. `1` ten part remains in the dividend. The `2` units parts are distributed as `1` each in the two parts.

What can be done with the tens part remaining in dividend?

  • `1` ten is the remainder of this division
  • `1` ten is equivalently `10` units and so can be distributed as `5` units each
  • `1` ten is equivalently `10` units and so can be distributed as `5` units each

The answer is '`1` ten is equivalently `10` units and so can be distributed as `5` units each'. This is explained in the next page.

Considering the division `52-:2`. That is, `52` is split into two equal parts as shown in the figure.division two digit numbers Note that `1` ten remaining in dividend is de-grouped into `10` units and are placed `5` each. So the result of the division is `2` tens and `6` units, which is `26`.

Considering the division `52-:2`. The number `52` is given in the place value format in the figure.division of two digit numbers A simplified procedure, Division by Place-value is shown in the figure.

First the tens place division, `5-:2` is considered. `2xx2=4` and `1` ten remains.

The remaining `1` ten is converted to `10` units and combined with `2` units from units place of dividend. In the units place, `2xx6=12` is applied. The result is `26`.

Consider the division, `35-:4`. One `35` is shown in the figure.division of larger two digit numbers How to perform the division?

  • split the quantity into `4` equal parts
  • use the simplified procedure to divide in place-value form
  • either one of the above
  • either one of the above

The answer is 'either one of the above'.

Considering the division: `35-:4`. division of larger two digit numbers The `3` tens cannot be split into `4` equal parts.

Which of the following helps to proceed with the division?

  • de-group the `3` tens into `30` units and combine with the `5` units
  • de-group the `3` tens into `30` units and combine with the `5` units
  • `3` tens form the remainder

The answer is 'de-group the `3` tens into `30` units and combine with the `5` units'. This is explained in the next page.

Considering the division: `35-:4`. The value `35` is converted into `30` units and combined with the `5` units in the units place. Now, the units are distributed as shown in the figure.division of larger two digit numbers One part makes `8` units and `3` units of dividend is remaining.

What is the result of this division?

  • `83`
  • `8` quotient and `3` remainder
  • `8` quotient and `3` remainder

The answer is '`8` quotient and `3` remainder'.

Considering the division: `35-:4`. The numbers are given in place value in the figure.division of larger two digit numbers place value A simplified procedure is given in the figure.

What is the result of this division?

  • `83`
  • `8` quotient and `3` remainder
  • `8` quotient and `3` remainder

The answer is '`8` quotient and `3` remainder'.

Division by Place-value -- Simplified Procedure : A number is divided using long division method as shown in the figure.simplified process for division Note: The procedure de-groups remaining tens into equivalent number of `10` units.

Solved Exercise Problem:

What is the quotient and remainder of `1111 -: 4`

  • quotient `22` and remainder `33`
  • quotient `277` and remainder `3`
  • quotient `277` and remainder `3`

The answer is "quotient `277` and remainder `3`"

Solved Exercise Problem:

What is the quotient and remainder of `3001 -: 3`

  • quotient `1` and remainder `1`
  • quotient `1000` and remainder `1`
  • quotient `1000` and remainder `1`

The answer is "quotient `1000` and remainder `1`"

                            
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