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## Multiplying and Adding Rational and Irrational Numbers

#### High School - HSN-RN.B.3

How to Multiply Rational and Irrational Numbers? Rational numbers are the ones that can be written in the form of a ratio of two integers. Every fraction number is a rational number. There are some numbers that we cannot write in the form of a ratio between two integers, and we call them irrational numbers! You can apply all basic arithmetic operations on both rational and irrational numbers. However, students might find the operation of multiplication a bit tricky! Multiplication of Two Rational Numbers Consider the following set of rational numbers! 2/5 and 1/2 To multiply these two rational numbers, you multiply the numerators of both numbers and denominators of both numbers. 2/5 × 1/2 = 2/10 = 1/5 A rational number multiplied with a rational number gives a rational number. Multiplication of Rational Number with Irrational Number Consider two numbers; 1/2 and ℼ Here, the fraction is a rational number, and π is an irrational number. When you multiply these two numbers, you get an irrational number. 1/2 × 3.1415926535897932384626433832795=1.5707963267945… Multiplication of Irrational Number with Irrational Number You can multiply two irrational numbers, but you cannot determine whether the resulting number will be rational or irrational. Case 1: √2 × √5 These are two rational numbers. When you multiply these two numbers, you get; √2 × √5 = √10 √10 is 3.162… which is a non-repeating and a non-terminating number, hence irrational number. Case 2: 5√3 × √3 Both these numbers are irrational. When you multiply these numbers, you get; 5√3 × √3 = 5 × 3 = 15 15 is a rational number! These worksheets and lessons will help students learn how to find the sum or product when rational and irrational numbers are involved.

### Printable Worksheets And Lessons  #### Homework Sheets

These are mostly identification questions. Calculations will follow.

• Homework 1 - A rational number can be written as a ratio of two numbers.
• Homework 2 - Irrational numbers can't be written as simple fractions.
• Homework 3 - When adding rational numbers the sum is rational.

#### Practice Worksheets

We got a great review from Teacher Place on this batch of sheets.

• Practice 1 - Determine whether the final value of this problem will be rational or irrational.
• Practice 2 - When adding a rational number to an irrational number, the sum is irrational, so the answer is irrational.
• Practice 3 - An integer is a rational number, so both are rational numbers and the product of two rational numbers is also a rational number.

#### Math Skill Quizzes

Expand the problems and classify them.

• Quiz 1 - Classify all of these products or sums.
• Quiz 2 - Make a push to find the right value.
• Quiz 3 - Put all of it together.