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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 addition and subtraction

### Addition: Simplified Procedure for Large Numbers

This page extends the addition in first principles into a simplified procedure for addition of large numbers, which is called as addition by place value with regrouping.

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Consider addition of 12 and 15. Which of the following step helps in the addition?

• Combine 12 and 15 together and count the combined quantity
• Combine 12 and 15 together and count the combined quantity
• two digit number addition is not possible

The answer is 'Combine 12 and 15 together and count the combined quantity'.

Considering addition of 12 and 15. Combining 12 and 15 is shown in the figure. The top shaded portion shows the numbers 12 and 15. The combined quantity is shown in the lower half.

What is the count shown in the combined quantity?

• 1215
• 27
• 27

The answer is '27'.

Consider the addition of 19 and 17. The quantities are illustrated in the figure. Counting the two quantities together, there are 2 tens and 16 units.

What is the sum?

• 216
• 36
• 36

The answer is '36'.

Considering the addition of 19 and 17. The combined sum is illustrated in the lower portion of the figure. Note that 10 units are combined together to form the 1 ten. So the result of the addition is 36.

10 units blocks are grouped into 1 ten. This is referred as regrouping.

Note that, the two numbers 19 and 17 were grouped already and when combined, the number representing the sum is regrouped.

Regrouping: In a place value position, when combining grouped numbers, 10 of a lower place-value can be regrouped into 1 of the next higher place-value.

Considering the addition of 19 and 17. A simplified procedure for addition is shown in the figure.

9 and 7 are added to 16. The 10 units are converted to 1 ten and moved to the tens position.

The sum is calculated as 36.

Consider the addition of 214 and 132. We can quickly count the combined quantity in the figure.

What is the sum?

• 216
• 346
• 346

The answer is '346'.

Considering the addition of 214 and 132. The numbers are given in the place-value form in the figure.

What is the sum?

• 216
• 346
• 346

The answer is '346'.

Considering the addition of 214 and 132. A simplified procedure Addition by Place-value is given in the figure.

The digits in the units place are added,
Then the digits in the tens place are added.
Then the digits in the hundreds place are added.

What is the sum as given in the figure?

• 216
• 346
• 346

The answer is '346'.

Consider the addition of 156 and 11. Which of the following is correct?
156+11=266 or
156+11 = 167.

• 266
• 167
• 167

The answer is '167'. The units are added with units, and tens are added with tens.

Consider the addition of 156 and 88. The simplified procedure Addition by Place-value with regrouping is given in the figure.

•  The digits in units place are added. 6+8=14. 14 units is modified as 1 ten and 4 units. The 1 ten is moved to the tens place as carry over. The 4 units is placed in the units place of sum.

•  The tens place is modified 1+5+8 = 14. 14 tens is modified as 1 hundred and 4 tens. The 1 hundred is moved to the hundreds place as carry over. The 4 tens is placed in the tens place of sum.

•  The hundreds place is modified 1+1 = 2. 2 hundreds is placed in the hundreds place of the sum.

What is the sum?

• 244
• 244
• 2+4+4 = 10

The answer is '244'.

Consider the addition of 675 and 896. The simplified procedure Addition by Place-value with regrouping is given in the figure. Note: the addition of place values and the carry over are highlighted in color.

What is the sum?

• 1571
• 1571
• 1751

The answer is '1571'.

Addition by Place-value with regrouping -- simplified procedure : Two numbers are added as follows:

•  the place-value positions are arranged units under units, 10s under 10s, etc.

•  the units are added and if the result has 10 numbers, then it is carried to the 10s place.

•  The addition is continued to the higher place-value position. Note: The carry over is the simplification of combining 10 of a place value to a higher place value.

Solved Exercise Problem:

What is the sum of 2314+2883?

• 4197
• 5297
• 5297

The answer is "5297"

Solved Exercise Problem:

What is the sum of 34+66?

• 100
• 100
• 910

The answer is "100"

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