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Sum/Product - Rationals or Irrationals ptcouncil.net

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


"The sum of 2 rational numbers is rational."

By definition, a reasonable number deserve to be expressed as a fraction with integer worths in the numerator and also denominator (denominator not zero). So, including two rationals is the very same as adding two together fractions, which will result in another fraction of this same kind since integers space closed under enhancement and multiplication. Thus, adding two rational numbers produces one more rational number.

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Proof:

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"The product of two rational numbers is rational."

Again, through definition, a reasonable number deserve to be expressed together a fraction with integer values in the numerator and also denominator (denominator no zero). So, multiplying two rationals is the exact same as multiplying two such fractions, i m sorry will result in another portion of this same type since integers room closed under multiplication. Thus, multiplying 2 rational numbers produces another rational number.

Proof:

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watch out! This next part gets tricky!!

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

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

See more: How Many Cups In A Bottle Of Water Is In A Water Bottle? Read The Best Answer

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

The product of 2 irrational numbers, in part cases, will be irrational. However, the is possible that some irrational numbers might multiply to kind a rational product.

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Topical outline | Algebra 1 overview | ptcouncil.net | MathBits" Teacher sources Terms that Use contact Person: Donna Roberts