Modulative Property Example

The modulative property is a property of the natural numbers by which, when doing any of the basic operations: addition, subtraction, multiplication or division, of any number, gives us the result original number. For this to happen, a neutral factor is necessary, that is, when performing the mathematical operation with that factor, it will always give us the other number as a result.

Add and subtract. For addition and subtraction, the factor or neutral number is the number zero. In any sum in which we add 0, the result will always be the number of the other adding:

• 1 + 0 = 1
• 13 + 0 = 13

The same happens in subtraction. By having 0 as subtrahend, the result will always be the minuend:

• 1 – 0 = 1
• 13 – 0 = 13

Multiplication and division. In multiplication and division, the neutral factor is 1. Any number that we multiply by 1 will always give us the same number:

• 1 X 1 = 1
• 13 X 1 = 13

The same thing happens in division. Division is equivalent to separating a number (dividend) into as many parts as the divisor indicates. Being only a part, it means that the result will always be the dividend:

• 1 ÷ 1 = 1
• 13 ÷1 = 13

Examples of modulative property in addition:

0 + 0 = 0
1+ 0 =1
2 + 0 = 2
5 + 0 = 5
10 + 0 = 10
50 + 0 = 50
100 + 0 = 100
500 + 0 = 500
1000 + 0 = 1000
10,000 + 0 = 10,000

Examples of modulative property in subtraction:

0 - 0 = 0
1 - 0 = 1
2 - 0 = 2
5 - 0 = 5
10 - 0 = 10
50 - 0 = 50
100 – 0 = 100
500 – 0 = 500
1000 – 0 = 1000
10,000 – 0 = 10,000

Examples of modulative property in multiplication

0 x 1 = 0
1 x 1 = 1
2 x 1 = 2
5 x 1 = 5
10 x 1 = 10
50 x 1 = 50
100 x 1 = 100
500 x 1 = 500
1000 x 1 = 1000
10,000 x 1 = 10,000

Examples of modulative property in division:

1 ÷ 1 =1
2 ÷ 1 = 2
5 ÷ 1 = 5
10 ÷ 1 = 10
50 ÷ 1 = 50
100 ÷ 1 = 100
500 ÷ 1 = 500
1000 ÷ 1 = 1000
10,000 ÷ 1 = 10,000

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