** Sum/Product - Rationals or Irrationals** snucongo.org

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

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

By definition, a reasonable number can be expressed together a fraction with integer worths in the numerator and also denominator (denominator not zero). So, adding two rationals is the very same as adding two together fractions, i m sorry will result in another portion of this same form since integers are closed under addition and multiplication. Thus, including two rational number produces another rational number.

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** Proof:**

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

Again, by definition, a rational number have the right to be expressed as a portion with integer values in the numerator and denominator (denominator no zero). So, multiplying 2 rationals is the same as multiplying two such fractions, i m sorry will an outcome in another portion of this same type since integers are closed under multiplication. Thus, multiplying 2 rational number produces an additional rational number.

**Proof:**

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

The amount of two irrational numbers, in part cases, will certainly be irrational. However, if the irrational components of the numbers have actually a zero amount (cancel each other out), the amount will be rational.

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** "The product of two irrational numbers is sometimes 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 reasonable product.

Topical outline | Algebra 1 rundown | snucongo.org | MathBits" Teacher sources Terms of Use** contact Person:** Donna Roberts