 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.

You are watching: The sum of two rational numbers is rational

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