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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.

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

Proof:

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"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:

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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.

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