** Sum/Product - Rationals or Irrationals** jajalger2018.org

Topical overview | Algebra 1 outline | MathBits" Teacher resources terms of Use** contact Person:** Donna Roberts

**"The sum of two rational numbers is rational."**

By definition, a reasonable number can be expressed as a portion with integer worths in the numerator and also denominator (denominator not zero). So, including two rationals is the very same as including two such fractions, which will an outcome in another portion of this same kind since integers are closed under addition and multiplication. Thus, adding two rational number produces an additional rational number.

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** Proof:**

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

Again, through definition, a reasonable 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, which will result in another portion of this same kind since integers are closed under multiplication. Thus, multiplying 2 rational number produces another rational number.

**Proof:**

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** "The sum of 2 irrational number is occasionally irrational."**

The sum of 2 irrational numbers, in part cases, will be irrational. However, if the irrational components of the numbers have actually a zero sum (cancel each other out), the amount will it is in rational.

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** "The product of two irrational number is sometimes irrational."**

The product of 2 irrational numbers, in part cases, will be irrational. However, it is possible that part irrational numbers might multiply to form a rational product.

Topical outline | Algebra 1 synopsis | jajalger2018.org | MathBits" Teacher resources Terms the Use** call Person:** Donna Roberts