Introduction to Rational and Irrational Numbers

Rational and irrational numbers are two of the most fundamental concepts in mathematics. Rational numbers are any number that can be written as a fraction, such as 3/2, 5/7, and 8/3. Irrational numbers are numbers that cannot be written as a fraction, such as pi or the square root of 2. Understanding the difference between these two types of numbers is essential for mastering algebra. This worksheet is designed to help you solidify your understanding of rational and irrational numbers.

Identifying Rational and Irrational Numbers

The first step in understanding rational and irrational numbers is to be able to identify which is which. To do this, look at a given number and see if it can be written as a fraction. If it can, it is a rational number. If it cannot, it is an irrational number. For example, the number pi (3.14159...) is an irrational number because it cannot be written as a fraction. The number 6/7 is a rational number because it can be written as a fraction.

Working with Rational Numbers

Once you understand how to identify rational numbers, you can begin to work with them. When working with rational numbers, you can add, subtract, multiply, and divide just like any other number. The result will always be a rational number. For example, if you were to add the rational numbers 6/7 and 3/4, the result would be 9/7.

Working with Irrational Numbers

When working with irrational numbers, you must use a different set of rules. These numbers cannot be added, subtracted, multiplied, or divided like regular numbers. Instead, you must use special formulas to calculate the result. For example, if you were to multiply the irrational numbers pi and the square root of 2, the result would be 2.828427124...

Conclusion

Rational and irrational numbers are two of the most important concepts in algebra. Being able to identify which type of number a given number is, as well as how to work with each type of number, is essential for mastering algebra. This worksheet is designed to help you solidify your understanding of rational and irrational numbers so that you can be successful in your studies.