# Multiplying and Adding Rational and Irrational Numbers Worksheets

This is one of those topics that students see and sense they are purely academic, like challenges that teachers just threw in their direction test their wits. Students normally do not see this type of material until they are late in their high school career and ready to enter college. That is because this is type of material is more based on theoretical math that lends itself more to applied math in areas of science and engineering. It also has many different applications to construction and geometric modeling because many the geometric ratios are based on the use of irrational numbers. These worksheets and lessons will help students learn how to find the sum or product when rational and irrational numbers are involved.

### Aligned Standard: HSN-RN.B.3

- Irrational or Rational Step-by-step Lesson- You will look at radical sums and products. We ask you to classify their outcome.
- Guided Lesson - More on classifying the sums and products of some out there radicals.
- Guided Lesson Explanation - We go over the standard rules and trains of thought on the classification system.
- Practice Worksheet - It's like a huge ten question line up. You can go right down the list.
- Matching Worksheet - Find the sum or product of the radicals and real numbers. Then your job is to classify the end result.

- Answer Keys - These are for all the unlocked materials above.

### 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.

### How to Perform Operations with 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!

**Adding Rational with Irrational Numbers** - An irrational number in decimal form goes on infinitely without repeating. These non-terminating, non-repeating number go on forever and when you add a number that terminates to a number that does not and there is no rounding taking place, you will end up with a sum that repeats forever as well. Therefore, when you find the sum of a rational and irrational number, it will be irrational as well.

**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 and 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 and 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!