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Sum/Product - Rationals or Irrationals gimpppa.org

Topical rundown | Algebra 1 overview | MathBits" Teacher sources regards to Use contact Person: Donna Roberts


"The sum of two rational numbers is rational."

By definition, a rational number have the right to be expressed as a portion with integer worths in the numerator and denominator (denominator not zero). So, including two rationals is the exact same as adding two together fractions, i m sorry will an outcome in another fraction of this same type since integers are closed under addition and multiplication. Thus, including two rational numbers produces an additional rational number.

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Proof:

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"The product of two rational numbers is rational."

Again, by definition, a reasonable number have the right to be expressed together a fraction with integer values in the numerator and also denominator (denominator no zero). So, multiplying 2 rationals is the exact same as multiplying 2 such fractions, which will result in another fraction of this same type since integers room closed under multiplication. Thus, multiplying 2 rational number produces an additional rational number.

Proof:

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watch out! This next part gets tricky!!

"The sum of two irrational number is sometimes irrational."

The sum 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 various other out), the amount will be rational.

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"The product of 2 irrational number is sometimes irrational."

The product of two irrational numbers, in some cases, will be irrational. However, it is feasible that part irrational numbers might multiply to type a reasonable product.

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Topical summary | Algebra 1 synopsis | gimpppa.org | MathBits" Teacher sources Terms the Use contact Person: Donna Roberts