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Common Core (The Real Number System)

Common Core for Mathematics

Common Core: HSN-RN.B.3

**Sum and product of rational numbers**

Learn that the sum or the product of two rational numbers is always a rational number.

Rational + Rational = Rational

Rational × Rational = Rational

**Sums and products of irrational numbers**

Sums and products of irrational numbers maybe rational or irrational.

Irrational + Irrational = Can be Rational or Irrational

Irrational × Irrational = Can be Rational or Irrational

**Proof that sum of rational and irrational is irrational**

Rational + Irrational = Irrational

**Proof that rational times irrational is irrational**

Rational × Irrational = Irrational

**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 qualities 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.**Adding Rational and Irrational Numbers**

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

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Common Core (The Real Number System)

Common Core for Mathematics

Examples, solutions, 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.

- Simplify radical expressions.
- 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 = Can be Rational or Irrational
Rational × Rational = Rational
Rational × Irrational = Irrational
Irrational × Irrational = Can be Rational or Irrational
**

Common Core: HSN-RN.B.3

The following diagram shows the sum and product of rational and irrational numbers. Scroll down the page for proofs, examples, and solutions on using the sum and product of rational and irrational numbers.

Learn that the sum or the product of two rational numbers is always a rational number.

Rational + Rational = Rational

Rational × Rational = Rational

Sums and products of irrational numbers maybe rational or irrational.

Irrational + Irrational = Can be Rational or Irrational

Irrational × Irrational = Can be Rational or Irrational

Rational + Irrational = Irrational

Rational × Irrational = Irrational

This video explains the difference between rational and irrational numbers and how to identify rational and irrational numbers.

Although the Greeks initially thought all numeric qualities 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.

Rational × Rational = Rational

Rational × Irrational = Irrational

Irrational × Irrational = Rational or Irrational

Rational ÷ Rational = Rational

Rational ÷ Irrational = Irrational

Irrational ÷ Irrational = Rational or Irrational

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

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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