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Sum/Product - Rationals or Irrationals sommos.net

Topical rundown | Algebra 1 outline | MathBits\" Teacher resources terms of Use contact Person: Donna Roberts


\"The amount of 2 rational number is rational.\"

By definition, a rational number deserve to be expressed together a fraction with integer values in the numerator and denominator (denominator no zero). So, including two rationals is the very same as including two such fractions, i beg your pardon will an outcome in another portion of this same type since integers space closed under enhancement and multiplication. Thus, adding two rational number produces one more rational number.

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Proof:

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\"The product of 2 rational number is rational.\"

Again, by definition, a reasonable number have the right to be expressed together a portion with integer worths in the numerator and also denominator (denominator no zero). So, multiplying two rationals is the exact same as multiplying 2 such fractions, which will result in another fraction of this same form since integers room closed under multiplication. Thus, multiplying two rational numbers produces one more rational number.

Proof:

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look out! This next part gets tricky!!

\"The sum of two irrational numbers is sometimes 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 sum (cancel each various other out), the sum will it is in rational.

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\"The product of 2 irrational numbers is occasionally 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 kind a rational product.

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Topical rundown | Algebra 1 summary | sommos.net | MathBits\" Teacher resources Terms that Use contact Person: Donna Roberts