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

Topical summary | Algebra 1 overview | MathBits" Teacher resources regards to Use** contact Person:** Donna Roberts

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

By definition, a rational number have the right to be expressed as a portion with integer values in the numerator and also denominator (denominator not zero). So, including two rationals is the exact same as including two such fractions, i beg your pardon will result in another portion of this same type since integers room closed under addition and multiplication. Thus, including two rational numbers produces one more rational number.

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** Proof:**

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

Again, by definition, a rational number deserve to be expressed as a portion with integer worths in the numerator and denominator (denominator no zero). So, multiplying 2 rationals is the very same as multiplying 2 such fractions, i m sorry will an outcome in another fraction of this same form since integers room closed under multiplication. Thus, multiplying two rational number produces one more rational number.

**Proof:**

watch out! This next component gets tricky!!

** "The sum of 2 irrational number is sometimes irrational."**

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

See more: For A Standard Normal Distribution, What Is The Probability That Z Is Greater Than 1.75?

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

The product of 2 irrational numbers, in some cases, will certainly be irrational. However, the is feasible that some irrational numbers may multiply to kind a rational product.

Topical rundown | Algebra 1 summary | discoverhotmail.com | MathBits" Teacher sources Terms the Use** call Person:** Donna Roberts