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Laws of arithmetic

Lecture



let's take the basic laws of arithmetic , which are otherwise called the properties of addition and multiplication.

Commutation law of addition


From changing the terms of the sum does not change.
(The value of the sum does not change when the terms are rearranged.)

  Laws of arithmetic

Examples:

  • 90 + 20 = 20 + 90 = 110

Combined addition law


The value of the sum does not depend on how the items are grouped.
(The order of the actions in calculating the sum does not affect the final result.)

  Laws of arithmetic

For example:

  • 6 + 4 + (3 + 2) = 6 + (4 + 3) + 2 = (6 + 4) + 3 + 2 = 15

Please note that this law is valid only if all actions in the example are addition!

The transfer law of multiplication


From the change of places of multipliers the product does not change.
(The value of the product does not change when the factors are rearranged.)

  Laws of arithmetic

Examples:

  • 11 • 4 = 4 • 11 = 44

The combined law of multiplication


The value of the product does not depend on how the factors are grouped.
(The procedure for performing actions during the calculation does not affect the final result.)

  Laws of arithmetic

By tradition, an example:

  • 2 • (4 • 3) = (2 • 4) • 3 = 8 • 3 = 24

Distribution law of multiplication with respect to addition


To multiply the amount by a number, you can multiply each of the terms by this number, and then add the resulting works.

  Laws of arithmetic

For example:

  • 8 • (6 + 5) = 8 • 6 + 8 • 5 = 48 + 40 = 88
created: 2014-09-22
updated: 2021-01-10
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Arithmetic

Terms: Arithmetic