Rational numbers and commutative law

Thread starter bips2010
Start date Oct 23, 2010
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In summary, rational numbers are numbers that can be expressed as a ratio of two integers, and differ from irrational numbers in that they have a finite number of non-repeating decimals. The commutative law for rational numbers states that the order of addition or multiplication does not affect the result, and is used in mathematics to simplify equations. This law can be applied to all operations except for subtraction and division.

Oct 23, 2010

bips2010

How can i prove that addition and mulitiplication of rational numbers follow commutative and associative law?

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Oct 23, 2010

fzero

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If you can assume those properties for integers, then you might want to figure out how to incorporate multiplication by the common denominator for your rational expressions.

FAQ: Rational numbers and commutative law

What are rational numbers?

Rational numbers are numbers that can be expressed as a ratio of two integers, where the denominator is not equal to 0.

How are rational numbers different from irrational numbers?

Rational numbers can be expressed as a ratio of two integers, while irrational numbers cannot be expressed as a ratio and have an infinite number of non-repeating decimals.

What is the commutative law for rational numbers?

The commutative law for rational numbers states that the order in which two rational numbers are added or multiplied does not affect the result. For example, a + b = b + a and a x b = b x a.

How is the commutative law used in mathematics?

The commutative law is used in mathematics to simplify calculations and equations. It allows us to change the order of operations without changing the final result.

Can the commutative law be applied to all operations?

Yes, the commutative law can be applied to addition, subtraction, multiplication, and division of rational numbers. However, it does not apply to subtraction and division as the order of operands can change the result.