## NUMBERS AND OPERATIONS The addition is the mathematical composition operation that consists of combining, joining or adding two or more numbers to obtain a final or total quantity.

In the additive expression, four fundamental properties are always satisfied:

1) Commutative property:

A modification in the order of its elements (addends) will not modify the result; for example: 3 + 2 = 2 + 3

2) Associative property:

When three or more numbers are added, the order of the addends does not influence the result; for example: 4 + (2 + 1) = (4 + 2) + 1

3) Property of the neutral element (or identity element):

Any number added to the number zero (0) will result in the same number; for example: 5 + 0 = 5

4) Distributive property (combines multiplication and addition):

The result of the sum of two numbers (A and B) multiplied by a third number (C) will be equivalent to the sum of their products (A x C + B x C); for example: 2 x (4 + 3) = 2 x 4 + 2 x 3

#### Properly place the terms of the addition in natural numbers up to 9,999,999

How to build the algorithm of a vertical sum?

Next you will learn to construct vertical sums by placing the symbols "+" and "=" and each of their terms (addends and result) in the corresponding place, practicing with the different printable educational worksheets that we have developed for whole numbers from 0 to 10,000,000.

Remember, with the 6-digit and 7-digit additions you must always align, according to their place value, the ones (1s), the tens (10s), the hundreds (100s), the thousands (1,000s), the ten thousands (10,000s), the hundred thousands (100,000s) and the millions (1,000,000s) before solving any addition operations.  #### Solve sums of two addends vertically without regrouping with natural numbers up to 9,999,999

We present a solved example as well as some printable PDF activities accompanied by their explanation so that you can easily learn how to add in vertical and without regrouping 6 and 7-digit numbers between 0 and the 10,000,000.

SPANISH ENGLISH HOW TO ADD SEVEN-DIGIT NUMBERS WITHOUT REGROUPING?

1st) We will write the addends vertically:

We will align the two addends by columns ordering their figures according to their place value, that is, the units with the units, the tens with the tens... and so on with each and every one of its figures.

2nd) We will add the ones column (O):

We will add the column of ones (blue color), that is, we will join the elements to form a single set:

3 ones + 3 ones = 6 ones

We will write the ones figure (6 ones) below the horizontal dividing line and aligned with the ones column. 3rd) We will add the tens column (T):

We will add the column of the tens (red color) and, again, we will join the elements to form a single set:

7 tens + 1 tens = 8 tens

We will write the result (8 tens) below the horizontal dividing line and aligned with the tens column.

4th) We will add the hundreds column (H):

We will add the hundreds column (green color) to form a single set:

5 hundreds + 1 hundred = 6 hundreds

We will write the result (6 hundreds) below the horizontal dividing line and in line with the hundreds column.

5th) We will add the column of thousand ones (Th):

We will add the column of the thousands (orange color), and we will group its elements to generate a unique set:

1 + 6 = 7 thousands

We will write the result obtained (7 units of a thousand) below the horizontal dividing line and in line with the thousands column.

6th) We will add the column of the tens of thousands (Tth):

We will add the column of the tens of thousands (purple color) to form a single set:

0 + 9 = 9 ten thousands

We will write the result (9 tens of thousands) below the dividing horizontal line and in line with the ten thousands column. 7th) We will add the column of the hundreds of thousands (Hth):

We will add the column of the hundreds of thousands (dark blue color) to form a single set:

6 + 2 = 8 hundred thousands

We will write the result (8 hundreds of thousands) below the dividing horizontal line and in line with the column of the hundreds of thousands.

8º) We will add the column of Millions (M):

We will add the column of the units of million (dark red color) to form a single set:

4 + 3 = 7 one millions

We will write the result (7 units of a million) below the horizontal dividing line and in line with the column of units of million.

We did it! The result of the sum of 4,601,573 + 3,296,113 = 7,897,686 #### Solve sums of two addends vertically with regrouping with natural numbers up to 9,999,999

Practice the 6 and 7-digits addition with regrouping with the whole numbers from 0 to 10,000,000 from our printable worksheets and become a mathematical expert.

If you need a little preparation, watch our video lessons where we provide you with some solved examples following the vertical resolution method by columns.

SPANISH ENGLISH HOW TO ADD SEVEN-DIGIT NUMBERS WITH REGROUPING?

1st) We will write the addends vertically:

We will align the two addends by columns ordering their figures according to their place value, that is, the units with the units, the tens with the tens... and so on with each and every one of its figures.

2nd) We will add the ones column (O):

We will add the column of ones (blue color), that is, we will join the elements to form a single set:

6 ones + 6 ones = 12 ones

If we decompose the 12 ones, we will obtain 1 ten (10 ones) and 2 ones; therefore, we will perform the following steps:

- We will write the ones figure (2 ones) below the horizontal dividing line and aligned with the ones column.

- We will transfer the remaining ten (1 ten) to the tens column (red column) and we will add it in the next step. 3rd) We will add the tens column (T):

We will add the column of the tens (red color) and, again, we will join the elements to form a single set:

1 + 3 + 4 = 8 tens

We will write the result (8 tens) below the horizontal dividing line and aligned with the tens column.

4th) We will add the hundreds column (H):

We will add the hundreds column (green color) to form a single set:

5 tens + 8 tens = 13 tens

If we decompose the 13 hundreds, we will obtain 1 thousand (10 hundreds) and 3 hundreds; therefore, we will carry out the following steps:

- We will write the result (3 hundreds) below the horizontal dividing line and in line with the hundreds column.

- We will transfer the remaining thousand (1 one of thousand) to the thousands column (orange column) and we will add it in the next step.

5th) We will add the column of thousand ones (Th):

We will add the column of the thousands (orange color), and we will group its elements to generate a unique set:

1 + 2 + 3 = 6 thousands

We will write the result obtained (6 ones of a thousand) below the horizontal dividing line and aligned with the column of thousands.

6th) We will add the column of the tens of thousands (Tth):

We will add the column of the tens of thousands (purple color) to form a single set:

3 + 9 = 12 tens of thousands

If we decompose the 12 tens of thousands, we will get 1 hundred thousand (10 tens of thousands) and 2 tens of a thousand.

We will write the 2 tens of thousands and we will transfer the hundreds of thousands to their corresponding columns. 7th) We will add the column of the hundreds of thousands (Hth):

We will add the column of the hundreds of thousands (dark blue color) to form a single set:

1 + 4 + 2 = 7 hundreds of thousands

We will write the result (7 hundreds of thousands) below the dividing horizontal line and in line with the column of the hundreds of thousands.

8º) We will add the column of Millions (M):

We will add the column of the units of million (dark red color) to form a single set:

2 + 1 = 3 Millions

We will write the result (3 units of a million) below the horizontal dividing line and in line with the column of units of million.

We have finally made it! The result of the sum of 2,432,536 + 1,293,846 = 3,726,382 We also provide you with a set of interactive games so that you can practice six and seven-digit sums with carry from the personal computer (or desktop computer), the tablet and / or the mobile phone:

#### Solve sums of three addends vertically without regrouping with whole numbers up to 9,999,999

We explain step by step how to perform the calculations and how to find the result easily in the sums with three addends without carrying up to the millions.

1st) We will write the three addends vertically:

We will orderly align the three addends vertically and by columns, taking into account the positional value of each of their figures. We will add, separately, each of the columns to generate a single set, that is, the units with the units, the tens with the tens... and so on.

Remember to write the result of each of the columnar sums below the horizontal dividing line. #### Solve sums of three addends vertically with regrouping with whole numbers up to 9,999,999

Practice the addition of three addends with seven digits and carried from our printable worksheets and with the natural numbers from 0 to 9,999,999.

1st) We will write the three addends vertically:

We will orderly align the three addends vertically and by columns, taking into account the positional value of each of their figures. We will add, separately, each of the columns to generate a single set, that is, the units with the units, the tens with the tens... and so on.

Remember to write the results in each column (below the dividing line) and do not forget to transfer to the next column (from right to left) the remaining figures ("the figures that we take away"). #### Mentally solve simple addition facts with natural numbers up to 9,999,999

Show your logical-mathematical skills by solving our exercises with hidden or missing whole numbers and using mental calculation (also known as "mental math"). #### Solve addition word problems without regrouping with natural numbers up to 9,999,999

We have made some exercises so that you can practice solving addition word problems no carrying with the numbers from 0 to 10,000,000.

To make it easier for you, we provide you a step-by-step explanation through a video tutorial with 6 and 7-digits adding word problems without regrouping.

SPANISH ENGLISH  #### Solve addition word problems with regrouping with whole numbers up to 9,999,999

Show that you are a math genius by solving each of our arithmetic problems using the basic operation of addition with carryover from 0 to 10,000,000.

If you need a little preparation, watch our video lessons where we provide you with some solved examples using the vertical column method.

SPANISH ENGLISH  #### Apply the commutative property of addition with natural numbers up to 9,999,999

Do you know what the Commutative Property of Addition is?

The Commutative Property of Addition is that universal mathematical law that states that "even if we change the order in which the addends are added, the result is always the same".

SPANISH ENGLISH   #### Apply the associative property of addition with natural numbers up to 9,999,999

Do you know what the Associative Property of the Addition is?

The Associative Property of addition is that universal mathematical law that tells us that "if we add three or more numbers, the result will always be the same regardless of the order in which we group the addends".

SPANISH ENGLISH   Select more exercises, worksheets and activities of Mathematics for each of the 4 learning blocks of the Educational Curriculum ("Numbers and Operations", "Quantities and Measurements", "Geometric and Spatial Reasoning" and "Data Analysis and Probability") aimed at improving the logical-mathematical competencies and skills that are developed throughout "Grade 4" or "Year 5":