Exercise 1.1 class 8 solution -students can click here to download the entire pdf chapterwise .here free pdf can be download for NCERT solution .class 8 Exercise are available here. These solutions are available in downloadable PDF format as well. it will help students in getting rid of all the doubts about those particular topics that are covered in the exercise. The NCERT textbook provides plenty of questions for the students to solve and practise. Solving and practising is more than enough to score high in the Class 8 examinations. Moreover, students should make sure that they practise every problem given in the textbook . exercise 1.2 class 8 solution Pdf can be downloaded free here.
A rational number is any number that can be expressed in the form of a fraction p/q, where p and q are integers (whole numbers), and q is not equal to zero.
Examples: Examples of rational numbers include 1/2, -3/4, 5, -7, 0, and so on. Whole numbers and integers are also considered rational numbers because they can be expressed as fractions with a denominator of 1 (e.g., 5 = 5/1, -7 = -7/1).
Operations: In 8th grade, students learn how to perform various operations with rational numbers, including addition, subtraction, multiplication, and division. These operations are typically taught with fractions, decimals, and mixed numbers.
Exercise 1.1 class 8 solution – exercise preview
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Exercise 1.1 class 8 solution-solution pdf
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Exercise 1.1 class 8 solution-how to do addition of rational numbers
Adding rational numbers is a fundamental mathematical operation. Rational numbers are numbers that can be expressed as a ratio (fraction) of two integers, where the denominator is not zero. To add rational numbers, you follow these steps:
- Ensure a Common Denominator: If the rational numbers you want to add have different denominators, you need to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators.
- Express Fractions with the Common Denominator: Rewrite each fraction so that they all have the same denominator (the common denominator). To do this, multiply the numerator and denominator of each fraction by the same number so that they have the common denominator.
- Add the Numerators: Once you have all the fractions with the same denominator, add the numerators together. The denominator remains the same.
- Simplify (if necessary): If the resulting fraction can be simplified, simplify it by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.
- Here’s a step-by-step example:
- Let’s add 3/4 and 1/6.
- Find the common denominator. In this case, it’s 12, as it’s the least common multiple of 4 and 6.
- Express the fractions with the common denominator:
- 3/4 becomes (3/4) * (3/3) = 9/12
- 1/6 becomes (1/6) * (2/2) = 2/12
- Add the numerators: 9/12 + 2/12 = 11/12.
- Simplify (if necessary). In this case, 11/12 cannot be simplified further, so it’s your final answer.
- So, 3/4 + 1/6 = 11/12.
Exercise 1.1 class 8 solution-commutative property of addition of rational numbers .-
The commutative property of addition is a fundamental property of rational numbers, just as it is for integers and real numbers. This property states that when you add two or more rational numbers, the order in which you add them does not affect the sum. In other words, you can add rational numbers in any order, and the result will be the same.
Formally, the commutative property of addition for rational numbers can be stated as:
For any rational numbers a and b, a + b = b + a.
This property holds true for all rational numbers. For example, if you have the rational numbers 2/3 and 5/6:
2/3 + 5/6 = 5/6 + 2/3
Regardless of the order in which you add them, the result will be the same. This property simplifies calculations and allows you to freely rearrange the terms in addition expressions without changing the outcome.
4.associative property of addition of rational numbers-
The associative property of addition is another fundamental property that holds true for rational numbers, just as it does for integers and real numbers. This property states that when you are adding three or more rational numbers, the way you group them does not affect the sum. In other words, you can regroup rational numbers and add them in any order, and the result will remain the same.
Formally, the associative property of addition for rational numbers can be stated as follows:
For any rational numbers a, b, and c, (a + b) + c = a + (b + c).
This property holds true for all rational numbers. For example, if you have the rational numbers 1/3, 1/4, and 1/6:
(1/3 + 1/4) + 1/6 = 1/3 + (1/4 + 1/6)
No matter how you group and add these rational numbers, the sum will be the same. This property is very useful in simplifying calculations involving addition, as it allows you to change the grouping of numbers without affecting the final result.