Sum/Product - Rationals or Irrationals yellowcomic.com

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"The sum of two rational numbers is rational."

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

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Proof:

"The product of two rational number is rational."

Again, by definition, a rational number have the right to be expressed together a fraction with integer worths in the numerator and also denominator (denominator not zero). So, multiplying two rationals is the same as multiplying two such fractions, which will result in another fraction of this same type since integers room closed under multiplication. Thus, multiplying two rational number produces an additional rational number.

Proof:

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"The sum of 2 irrational number is periodically irrational."

The sum of 2 irrational numbers, in some cases, will be irrational. However, if the irrational parts of the numbers have actually a zero amount (cancel each various other out), the amount 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, the is possible that some irrational numbers may multiply to kind a reasonable product.

Topical overview | Algebra 1 outline | yellowcomic.com | MathBits" Teacher resources Terms the Use call Person: Donna Roberts