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Sum/Product - Rationals or Irrationals historicsweetsballroom.com

Topical summary | Algebra 1 rundown | MathBits" Teacher resources regards to Use call Person: Donna Roberts


"The amount of 2 rational number is rational."

By definition, a rational number can be expressed as a fraction with integer values in the numerator and denominator (denominator no zero). So, adding two rationals is the exact same as including two together fractions, which will result in another fraction of this same form since integers are closed under enhancement and multiplication. Thus, adding two rational numbers produces an additional rational number.

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

Proof:

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"The product of two rational number is rational."

Again, through definition, a reasonable number can be expressed together a portion with integer worths in the numerator and denominator (denominator not zero). So, multiplying 2 rationals is the same as multiplying 2 such fractions, i beg your pardon will an outcome in another fraction of this same form since integers room closed under multiplication. Thus, multiplying 2 rational number produces one more rational number.

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"The amount of two irrational numbers is occasionally 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 sum (cancel each various other out), the sum will it is in rational.

See more: How Many Pints Are In 32 Fluid Ounces To Pints Conversion (Fl Oz To Pt)

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

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

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Topical summary | Algebra 1 rundown | historicsweetsballroom.com | MathBits" Teacher sources Terms that Use call Person: Donna Roberts