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Sum/Product - Rationals or Irrationals lungemine.com

Topical synopsis | Algebra 1 summary | MathBits" Teacher sources regards to Use call Person: Donna Roberts


"The sum of two rational number is rational."

By definition, a reasonable number have the right to be expressed as a fraction with integer worths in the numerator and denominator (denominator not zero). So, including two rationals is the same as including two together fractions, which will result in another portion of this same form since integers room closed under enhancement and multiplication. Thus, including two rational number 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 rational number have the right to be expressed together a fraction with integer worths in the numerator and also denominator (denominator not zero). So, multiplying two rationals is the exact same as multiplying 2 such fractions, which will result in another portion 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 component gets tricky!!

"The amount of two irrational numbers is sometimes irrational."

The amount of two 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 amount will be rational.

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"The product of two irrational numbers is periodically irrational."

The product of two irrational numbers, in some cases, will certainly be irrational. However, it is possible that part irrational numbers might multiply to kind a rational product.

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Topical summary | Algebra 1 synopsis | lungemine.com | MathBits" Teacher sources Terms that Use contact Person: Donna Roberts