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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

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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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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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