** Sum/Product - Rationals or Irrationals** rewildtv.com

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

**"The amount of 2 rational numbers is rational."**

By definition, a reasonable number deserve to be expressed together a portion with integer values in the numerator and denominator (denominator no zero). So, adding two rationals is the same as adding two such 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 an additional rational number.

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** Proof:**

**"The product of two rational numbers is rational."**

Again, by definition, a rational number can be expressed as a portion with integer worths in the numerator and also denominator (denominator no zero). So, multiplying two rationals is the same as multiplying 2 such fractions, which will result in another portion of this same kind since integers space closed under multiplication. Thus, multiplying 2 rational number produces an additional rational number.

**Proof:**

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** "The amount of 2 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 amount (cancel each other out), the sum will be rational.

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** "The product of two irrational number is sometimes irrational."**

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

Topical synopsis | Algebra 1 overview | rewildtv.com | MathBits" Teacher resources Terms that Use** contact Person:** Donna Roberts