**Subtraction** is an arithmetic operation that is represented by a "minus" sign (-) and symbolizes the operation of removing objects from a collection.

__It fulfills the property of the neutral element:__

Any natural number subtracted by the number zero (0) results in the same number; for example: 8 - 0 = 8

__It fulfills the distributive property:__

The result of the subtraction of two numbers (A and B) multiplied by a third number (C) will be equivalent to the subtraction of their products (A x C - B x C); for example: 2 x (6 - 3) = 2 x 6 - 2 x 3

__Subtraction is anti-commutative__

A modification in the order of its elements (minuend and subtrahend) will modify the sign of the answer; for example: 6 - 4 ≠ 4 - 6.

__Subtraction is non-associative__

When three or more numbers are subtracted, the order in which the subtraction is performed always influences; for example: 5 - (3 - 2) ≠ (5 - 3) - 2.

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

What is the "minuend", the "subtrahend" and the "difference" in a subtraction?

- ** Minuend**: Represents the total collection or initial set of elements.

- ** Subtrahend**: Symbolizes the number or quantity of elements in which the minuend will be reduced.

- ** Difference or Rest**: It corresponds to the unique set formed by separating or reducing the amount of the subtrahend on the minuend.

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How to build the algorithm of a vertical subtraction?

Next you will learn ** to construct vertical subtractions ** placing the symbols "-" e "=" and each of its terms (minuend, subtrahend and difference) in the corresponding place practicing with the different ** printable educational worksheets** that we have elaborated for the natural numbers from 0 to 10,000,000 following the method based on vertical columns.

Remember, with the 6-digit and 7-digit subtractions 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 subtraction operations.

#### Solve subtractions of two elements vertically without regrouping with whole numbers up to 9,999,999

How to subtract numbers up to seven digits without borrowing?

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

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#### Solve subtractions of two elements vertically with regrouping with whole numbers up to 9,999,999

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

We are going to explain ** how to solve any two-digit subtraction by regrouping** using the __ the most taught methods in school__: Austrian and American Method.

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SUBTRACT BY COMPENSATION

The ** Austrian Method ** (also called "by compensation") proposes the resolution of subtractions with borrowing __ "adding units to both the minuend and the subtrahend"__ when the minuend figure is less than the digit of the subtrahend:

1st) ** Can we subtract 3 - 7 in the ones column? **

No, because 3 is less than 7 ( 3 < 7 ), therefore, we must ask for help in the tens column.

2nd) ** We add 1 ten to the subtrahend figure and 10 units to the minuend figure ** to __ compensate by equivalence__ the place value of its figures:

__Subtrahend__:

1 ten + * 1 ten * = 2 tens

__Minuend__:

3 ones + * 10 ones (1 ten) * = 13 ones

3rd) ** We subtract the ones column ** because 13 is greater than 7:

13 - 7 = 6

4th) Next, ** we will subtract the tens column ** without having to borrow from the hundreds because 6 is greater than 2:

6 - 2 = 4

5th) And finally, ** we will subtract the hundreds column: **

5 - 2 = 3

SUBTRACT BY GROUPING

The ** American Method ** (also called "by grouping") proposes the resolution of the subtractions __ "by borrowing units between the minuend figures from left to right"__:

1st) ** Can we subtract 7 - 3 in the ones column? **

Yes, because 7 is greater than 3 and therefore we don't need to borrow from the tens column.

7 - 3 = 4

2nd) ** Can we subtract 2 - 5 in the tens column? **

No, because 2 is less than 5 and, therefore, we must ask the hundreds column for help.

3rd) ** We reduce 1 hundred of the minuend figure (hundreds column) and we borrow it to the minuend figure of the tens column ** taking into account that 1 hundred equals to 10 tens:

__Minuend (hundreds column)__:

4 hundreds - * 1 hundred * = 3 hundreds

__Minuend (tens column)__:

2 tens + * 10 tens (1 hundred) * = 12 tens

4th) ** We subtract the tens column ** because 12 is greater than 5:

12 - 5 = 7

5th) Finally, ** we will subtract the hundreds column**:

3 - 1 = 2

6th) ** We already have the solution! **

427 - 153 = 274

#### Solve subtractions of three elements vertically without regrouping with whole numbers up to 9,999,999

How to subtract 3 or more 6 and 7-digit numbers without borrowing?

We explain step by step ** how to perform the calculations and how to find the result ** easily in the ** subtractions with three elements no regrouping up to 7 digits**.

#### Mentally solve simple subtraction 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 subtraction word problems without regrouping with natural numbers up to 9,999,999

We have made some **exercises** so that you can practice ** solving subtraction word problems no borrowing ** 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 2 digit word problems without regrouping.

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#### Solve subtraction 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 ** subtraction by borrowing** 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 column method.

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#### Check the subtraction using addition to verify the accuracy of calculations

How to check if the result of a subtraction is correct?

Cheking subtraction using addition helps us __ recognize if we have correctly solved any subtraction__.

__ Once we have obtained the difference__ (or result), we can make sure if we have subtracted correctly ** using the addition ** and applying the following ** mathematical formula**:

*Minuend = Subtrahend + Difference*

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Do you want access to more Fourth Grade learning?

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"**:

##### NUMBERS AND OPERATIONS

##### QUANTITIES AND MEASUREMENTS

##### GEOMETRIC AND SPATIAL REASONING

##### DATA ANALYSIS AND PROBABILITY

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Hesiod