In this worksheet, you'll get the opportunity to practice and prepare for your Class 8 math exam on rational numbers. With practice questions, sample answers, and supplemental resources for further reading, this worksheet can help make sure you understand rational numbers before you take the test.
Understand the Basics of Rational Numbers.
Before you begin the worksheet, it will be helpful to understand some of the basics about rational numbers. Rational numbers are fractions that can be expressed as fractions or as decimals. For example, 1/2 is a rational number because it can also be written as 0.5. Understanding this concept is essential for answering some of the questions on the worksheet correctly.
Practice Adding and Subtracting Rationals Using Targeted Worksheet Questions.
Start the worksheet by practicing your addition and subtraction of rational numbers. This set of questions will help strengthen your knowledge of these concepts and become proficient in using fractional forms, decimal forms, and mixed number forms correctly when adding and subtracting. The worksheet includes several practice questions that are designed to help you master this concept before the midterm or final test.
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The worksheets on rational numbers for Class 8 are available with answers that help students evaluate their performance. The questions in these worksheets cover all the fundamental concepts such as what are rational numbers, types of rational numbers, their properties, operations on rational numbers, and many more. The worksheets also include word problems and MCQs that test a student's reasoning skills.
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Class 8th Rational Numbers important formulas.
A number that can be expressed in the form of p/q where q is not equal to 0 is called a rational number.
Simplification of Rational Numbers:
To simplify a rational number, divide the numerator and denominator by their HCF.
Addition of Rational Numbers:
To add two rational numbers, convert them to like fractions by finding their LCM and then add the numerators. The denominator remains the same.
Question: Find the sum of -3/4 and 2/3.
Answer: To add these two rational numbers, we need to find a common denominator.
The common denominator of 4 and 3 is 12. So, we can rewrite -3/4 and 2/3 as -9/12 and 8/12, respectively. Adding these two fractions, we get:
-9/12 + 8/12 = -1/12
Therefore, the sum of -3/4 and 2/3 is -1/12.
Subtraction of Rational Numbers:
To subtract two rational numbers, convert them to like fractions by finding their LCM and then subtract the numerators. The denominator remains the same.
Question: What is the difference between 5/8 and 3/4?
Answer: To subtract these two rational numbers, we need to find a common denominator.
The common denominator of 8 and 4 is 8. So, we can rewrite 5/8 and 3/4 as 5/8 and 6/8, respectively.
Subtracting these two fractions, we get:
5/8 - 6/8 = -1/8
Therefore, the difference between 5/8 and 3/4 is -1/8.
Multiplication of Rational
Numbers: To multiply two rational numbers, multiply the numerators and denominators separately and then simplify the resulting fraction.
Question: What is the product of 2/3 and 5/7?
Answer: To multiply these two rational numbers, we just need to multiply their numerators and denominators. So, we have:
(2/3) x (5/7) = (2 x 5) / (3 x 7) = 10/21
Therefore, the product of 2/3 and 5/7 is 10/21.
Division of Rational Numbers:
To divide two rational numbers, multiply the first fraction with the reciprocal of the second fraction.
Question: Divide 7/12 by 3/4.
Answer: To divide these two rational numbers, we need to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 3/4 is 4/3. So, we have:
(7/12) ÷ (3/4) = (7/12) x (4/3) = (7 x 4) / (12 x 3) = 28/36
Decimal Representation of Rational Numbers:
Any rational number can be represented in decimal form by dividing the numerator by the denominator.
Comparison of Rational Numbers:
To compare two rational numbers, convert them to like fractions by finding their LCM and then compare their numerators.
Compare 3/4 and 2/3.
To compare these two fractions, we need to convert them so that they have a common denominator. The least common multiple of 4 and 3 is 12, so we can convert both fractions to have a denominator of 12:
3/4 = (3/4) x (3/3) = 9/12
2/3 = (2/3) x (4/4) = 8/12
Now we can compare the two fractions by comparing their numerators:
9/12 > 8/12
Therefore, 3/4 is greater than 2/3.
Answer: 3/4 > 2/3.
Properties of Rational Numbers:
- Closure Property: The sum, difference, product or quotient of any two rational numbers is always a rational number.
- Commutative Property: The addition and multiplication of rational numbers is commutative i.e. a + b = b + a and a × b = b × a.
- Associative Property: The addition and multiplication of rational numbers is associative i.e. (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c).
- Distributive Property: The multiplication of a rational number with a sum or difference of two rational numbers is distributive i.e. a × (b + c) = a × b + a × c.
What is a rational number?
A rational number is a number that can be expressed in the form of a/b, where a and b are integers and b is not equal to 0.
What are the examples of rational numbers?
Examples of rational numbers include 1/2, -3/4, 5/1, 0, 2, and -7.
What is the difference between a rational and an irrational number?
A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a fraction and has an infinite non-repeating decimal representation.
How do you add or subtract rational numbers?
To add or subtract rational numbers, you need to make sure they have a common denominator. Once the denominators are the same, you can add or subtract the numerators and simplify the resulting fraction.
How do you multiply or divide rational numbers?
To multiply rational numbers, multiply the numerators and denominators separately and simplify the resulting fraction. To divide rational numbers, multiply the first fraction by the reciprocal of the second fraction and simplify the resulting fraction.
What is the absolute value of a rational number?
The absolute value of a rational number is the distance between the number and zero on the number line, regardless of its sign. The absolute value of a rational number is always positive.
Can a rational number be negative?
Yes, a rational number can be negative. For example, -3/4 is a rational number.
What is a mixed fraction?
A mixed fraction is a combination of a whole number and a fraction. It is written in the form of a whole number and a fraction, such as 2 1/2.
How do you convert a decimal to a rational number?
To convert a decimal to a rational number, you need to express the decimal as a fraction in its simplest form. For example, 0.75 can be expressed as 3/4.
How do you convert a fraction to a decimal?
To convert a fraction to a decimal, divide the numerator by the denominator using long division or a calculator. For example, 3/4 can be converted to 0.75.