Lesson 6

ADDING WHOLE NUMBERS
AND DECIMALS

Addition with Regrouping

On adding the ones column, we get 9.  But on adding the tens column, we get 16.  Now,

16 tens = 10 tens + 6 tens

(Lesson 2).  Write 6, and regroup 10 tens onto the hundreds column -- because 10 tens are equal to 1 hundred.  Therefore when we add the hundreds, we have

1 + 6 + 4 + 5 + 8 = 24 hundreds.

But

24 hundreds = 20 hundreds + 4 hundreds.

Write 4, and regroup 20 hundreds onto the thousands column -- because 20 hundreds are equal to 2 thousands. (Lesson 2, Example 3c.)

When we add the thousands, then, we get

2 + 4 + 8 + 5 + 3 = 22.

The sum of those numbers is 22,469.  

Example 2.   Write in a column and add:  4,785 + 9 + 2.307

Solution..  The ones are shown:

4,785 + 9 + 2.307

(Lesson 3, Question 5.)  Therefore, align as follows:

Example 3.   Write in a column and add:  .58 + 5.8 + 58

Solution.  Here are the ones:

_.58 + 5.8 + 58

As for .58, the ones are at the first place to the left of the decimal point.

Align as follows:

When the decimal points are aligned, the decimal point in the answer will fall in the same place.  (But that is true only in addition and subtraction, not in multiplication.   Lesson 10.)

As for a whole number such as 58, to help with alignment we may imagine a decimal point after the 8.

58 = 58.

Whole numbers, however, are normally written without a decimal point, because the decimal point means "and." Here come the fractions

Example 4.    .5 + .5 + .5

Choose the correct answer:

a)  15

b)  .15

c)  1.5

d)  .015

Answer.    c)  1.5   

For, if we aligned them and wrote .5 as 0.5 --

-- we would see that the 1 (of 15 tenths) carries over into the next column.

The point is:

Example 5.   .007 + .003 + .004

Answer.    .014

The numbers being added have three decimal digits.  Therefore the answer also will have three decimal digits.

Example 6.   Perimeters.   The perimeter of a plane (flat) figure is its boundary.  

This figure is a rectangle, which is a four-sided figure in which all the angles are right angles.  In a rectangle, the opposite sides are equal. Therefore the perimeter of that rectangle is:

Example 7.    Add:

Technique.  Do not break up each column into separate sums.  Do not say -- or write -- "3 plus 9 is 12.  12 plus 6 is 18."  And so on.  Rather, let your eye go down each column and say -- do not write -- each partial sum. (See Lesson 5, Question 2.)   To add the column on the right, say

Write 6, carry 2.   To add the middle column, say

Write 1, carry 2.   To add the last column, say

Write 25.

We may write the decimal point in the answer when we come to it; that is, after adding the middle column.

Please "turn" the page and do some Problems.

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