** Sum/Product - Rationals or Irrationals** juniorg8.com

Topical synopsis | Algebra 1 summary | 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 as a portion with integer worths in the numerator and denominator (denominator no zero). So, including two rationals is the exact same as including two together fractions, i m sorry will an outcome in another portion of this same kind since integers are closed under enhancement and multiplication. Thus, including two rational number produces another rational number.

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** Proof:**

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

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

**Proof:**

watch out! This next component gets tricky!!

** "The amount of 2 irrational number is occasionally irrational."**

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

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** "The product of two irrational numbers is occasionally irrational."**

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

Topical summary | Algebra 1 rundown | juniorg8.com | MathBits" Teacher resources Terms of Use** call Person:** Donna Roberts