Rational Number Worksheet with Answers and Step by Step Solutions
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.
FAQs on Rational Number Worksheet Practice and Solved Questions
1. What is a rational number?
A rational number is any number that can be written in the form p/q, where p and q are integers and q ≠ 0. This means:
- Both positive and negative fractions are rational numbers.
- All integers (like 5 or −3) are rational because they can be written as 5/1 or −3/1.
- Terminating decimals (0.75) and repeating decimals (0.333...) are also rational numbers.
2. How do you identify a rational number?
A number is a rational number if it can be expressed as a fraction of two integers with a non-zero denominator. To identify it:
- Check if it is an integer (e.g., 8 = 8/1).
- Check if it is a fraction (e.g., 3/4).
- Check if it is a terminating decimal (0.2 = 1/5).
- Check if it is a repeating decimal (0.666... = 2/3).
3. What is the formula for a rational number?
The standard form of a rational number is p/q, where p and q are integers and q ≠ 0. In simplest form:
- The numerator and denominator have no common factor except 1.
- The denominator is kept positive.
4. How do you add and subtract rational numbers?
To add or subtract rational numbers, first make the denominators the same, then combine the numerators. Steps:
- Find the LCM of the denominators.
- Convert each fraction to equivalent fractions.
- Add or subtract the numerators.
- Simplify the result.
5. How do you multiply rational numbers?
To multiply rational numbers, multiply the numerators together and the denominators together. Formula:
(a/b) × (c/d) = (ac)/(bd)
- Simplify before or after multiplying if possible.
6. How do you divide rational numbers?
To divide rational numbers, multiply by the reciprocal of the second fraction. Formula:
(a/b) ÷ (c/d) = (a/b) × (d/c)
- Flip the second fraction.
- Multiply numerators and denominators.
- Simplify the result.
7. What is the difference between rational and irrational numbers?
The key difference is that rational numbers can be written as p/q, while irrational numbers cannot. Differences:
- Rational numbers have terminating or repeating decimals (e.g., 0.25, 0.333...).
- Irrational numbers have non-terminating, non-repeating decimals (e.g., √2, π).
- All integers and fractions are rational.
8. Can zero be a rational number?
Yes, 0 is a rational number because it can be written as 0/1. Since 0 can be expressed in the form p/q where q ≠ 0, it satisfies the definition of a rational number.
9. How do you simplify a rational number?
To simplify a rational number, divide the numerator and denominator by their greatest common divisor (GCD). Steps:
- Find the GCD of numerator and denominator.
- Divide both by the GCD.
10. What are some examples of rational numbers?
Examples of rational numbers include integers, fractions, and certain decimals. Common examples:
- 5 (can be written as 5/1)
- −3/4
- 0.75 (equals 3/4)
- 0.222... (equals 2/9)
