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Sum/Product - Rationals or Irrationals starrkingschool.net

Topical outline | Algebra 1 rundown | MathBits" Teacher resources regards to Use contact Person: Donna Roberts


"The amount of 2 rational number is rational."

By definition, a rational number deserve to be expressed as a fraction with integer values in the numerator and denominator (denominator not zero). So, including two rationals is the same as including two such fractions, which will an outcome in another portion of this same form since integers space closed under addition and multiplication. Thus, including two rational numbers produces another rational number.

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Proof:

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"The product of two rational number is rational."

Again, by definition, a reasonable number deserve to be expressed together a portion with integer values in the numerator and also denominator (denominator no zero). So, multiplying 2 rationals is the very same as multiplying 2 such fractions, i beg your pardon will result in another fraction of this same form since integers room closed under multiplication. Thus, multiplying two rational number produces an additional rational number.

Proof:

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watch out! This next part gets tricky!!

"The amount of two irrational number is occasionally irrational."

The amount of 2 irrational numbers, in part cases, will certainly be irrational. However, if the irrational components of the numbers have actually a zero amount (cancel each various other out), the amount will it is in rational.

See more: How Do You Know If A Pattern Of Stressed And Unstressed Syllables Called?

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"The product of 2 irrational numbers is sometimes irrational."

The product of 2 irrational numbers, in part cases, will certainly be irrational. However, the is feasible that some irrational numbers might multiply to type a reasonable product.

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Topical rundown | Algebra 1 outline | starrkingschool.net | MathBits" Teacher sources Terms the Use contact Person: Donna Roberts