Rational and Irrational numbers and worksheet on various operations on rational numbers:

Rational and Irrational numbers are one of the most important concepts for mathematics students.

Rational numbers are derived from the word ratio in mathematics. A rational number is the one that can be expressed as a fraction or quotient of two numbers, say p/q. Here, p is the numerator, and q is the non-zero denominator. Every integer in the number series is a rational number. For Example, 5 is also a rational number, represent-able as 5/1.

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Rational and irrational number worksheet contains all the operations and applications of these numbers. For the students learning the concepts, the worksheet helps in having the best practice materials compiled together at a single place. Furthermore, rational number worksheet separately and rational number worksheet with answers are also available to help the students get the right study material according to their needs and preferences.

### Rational Coordinates and Curve:

There are other concepts also available related to rational numbers, like, a rational point is the one present on the number line with rational coordinates.

Rational Curve, on the other hand, is just a curve with parameters represented in terms of rational functions.

### Rational Number Decimal Expansion and Worksheets:

Rational Numbers with decimal expansion either begin with a repetition of the sequence of digits with finite behaviour or would terminate after certain limited digits. Thus, Rational numbers might carry any form of repetition or termination of the decimals.

If any rational number represents in terms of decimal numbers like the fraction 10/3, its last digits will recur indefinitely. Like, 10/2 is equal to 3.333... and so on.

For the students to get a clear idea about how to represent numbers in the form of x/y, with y being a non-zero integer and x an integer, we precisely designed the ration number worksheet. Based on various operations on the numbers, worksheets are also available as adding and subtracting rational number worksheet and multiplying and dividing rational number worksheet.

### Subtracting and Adding Rational Numbers Worksheet:

To perform addition or subtraction of rational numbers, say a/b and c/d, the below given procedure must be followed:

a/b + c/d = (a/b)*(d/d) + (c/d)*(b/b)

=>((ad)+(bc))/bd

Similarly the whole process goes for subtraction of the rational numbers.

Here are some problems on subtraction and addition of rational numbers worksheet:

1. Perform addition of the following:

½ +2/5

3/8+9/7

2. Perform removal of the following rational numbers:

5/2 – ½

¼ - 1/5

### Dividing and Multiplying Rational Numbers Worksheet:

To perform multiplication of two numbers a/b and c/d, we must follow the below-mentioned set of steps:

a/b * c/d = (ac) /(bd)

And to divide two rational numbers a/b and c/d, the second number must be flipped first and then the multiplication is to be followed.

(a/b)/(c/d) = (a/b)*(d/c) = ad/bc

Here are some problems on multiplying and dividing rational numbers worksheet:

1. Perform multiplication and division operations as stated:

(1/2) / (3/4)

(3/4)*(1/2)

### Fun Facts on Rational Numbers:

Pythagoras, an ancient Greek mathematician, believed that all the numbers available in the number line are rational. However, one of his intelligent students, Hippasus concluded using geometry that writing the square root of 2 is practically impossible as a fraction, thus it is an irrational number.

Still, the loyal followers of the prominent mathematician, Pythagoras, could not accept the concept of irrational numbers’ existence, and it is also known that the gods drowned Hippasus as a punishment.

Q1: Differentiate Between Rational and Irrational Numbers.

Ans. There are several differences between rational and irrational numbers, such as:

One can represent rational numbers as a ratio of two numbers in p/q form. But, we cannot represent irrational numbers as a ratio of two numbers.

Rational numbers are the finite and recurring numbers. In contrast, irrational numbers are non-terminating and non-repeating numbers.

Rational Numbers contain perfect squares, like 4, 25, 16, and so on. Irrational numbers include surds, like √2, √3, and so on.

Both numerator and denominator come under whole numbers in the rational numbers, and here, the denominator is not equal to zero. In the case of irrational numbers, no one can write them in the fractional form.

Examples of rational numbers are 3/2, 3.67, 5, etc. Examples of irrational numbers are √5, √11, etc.

Q2: List the Properties that a Rational Number Satisfies.

Ans. Properties that rational numbers satisfy are as follows:

Closure property – Rational numbers are closed under addition, subtraction, multiplication, and division.

Commutative property – For given two rational numbers a and b, addition is commutative, i.e. a+b = b+a, and multiplication is commutative, i.e. a*b=b*a.

Associative property – Given three rational numbers follow associative property for addition and multiplication, such that, a+(b+c)=(a+b)=c and a(bc)=(ab)c.

Distributive property – Distributive property for rational numbers is as mentioned here. A* (B+C)= (A*B) + (A*C)

Identity – For the rational numbers, 0 is additive, and 1 is the multiplicative identity.

Inverse – For a given rational number x/y, the additive inverse is –x/y and the multiplicative inverse is y/x.