 # Rational and Irrational Numbers

Videos and lessons to help High School students explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a non-zero rational number and an irrational number is irrational.

• Add, subtract, and multiply real numbers.
• Explain why adding and multiplying two rational numbers results in a rational number.
• Explain why adding a rational number to an irrational number results in an irrational number.
• Explain why multiplying a nonzero number to an irrational number results in an irrational number.

Rational + Rational = Rational
Rational + Irrational = Irrational
Irrational + Irrational = Irrational

Rational × Rational = Rational
Rational × Irrational = Irrational
Irrational × Irrational = Rational or Irrational

Common Core: HSN-RN.B.3

Related Topics:
Common Core (The Real Number System)

Common Core for Mathematics

Rational vs. Irrational Numbers
This video explains the difference between rational and irrational numbers and how to identify rational and irrational numbers.

Irrational Numbers
Although the Greeks initially thought all numeric qualtities could be represented by the ratio of two integers, i.e. rational numbers, we now know that not all numbers are rational. How do we know this.

Rational + Rational = Rational
Rational + Irrational = Irrational.

Product & quotient of 2 rationals, 2 irrationals or 1 of each
Rational × Rational = Rational
Rational × Irrational = Irrational
Irrational × Irrational = Rational or Irrational

Rational ÷ Rational = Rational
Rational ÷ Irrational = Irrational
Irrational ÷ Irrational = Rational or Irrational

Sums and products of rationals and irrationals - Song
This is a song that teaches about adding and multiplying rational numbers and irrational numbers. The song lines up with the following high school common core standard : CCSS.Math.Content.HSN-RN.B.3
Rational + Rational = Rational
Rational + Irrational = Irrational
Rational × Rational = Rational
Rational × Irrational = Irrational

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