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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

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Consider addition of, 12 and 15. The quantities are combined together and the combined quantity is counted.

Combining 12 and 15 is shown in the figure. The combined quantity is shown in the lower half. The combined quantity is: 2 tens and 7 units. The result 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. The units can be re-grouped into tens.

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 count the combined quantity in the figure. The combined quantity is counted as,

4 units and 2 units together is 6 units,

1 tens and 3 tens together is 4 tens,

2 hundreds and

1 hundred together is 3 hundreds.

So the combined count is 346.

The numbers 214 and 132 are given in the place-value form. Addition is carried out and

The result if 346.

The simplified procedure 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.

Considering the addition of 156 and 11. The result is 167, and not 266. The place value positions should be aligned correctly when employing the simplified procedure.

Considering 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 plus 8 equals 14. 14 units is modified to 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 plus 5 plus 8 ;; equals 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 plus 1 equals 2. 2 hundreds is placed in the hundred place of the sum.

Consider the addition of two numbers. 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.

The result of addition 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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