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# CBSE Maths Chapter 1 Real Numbers Formulas for Class 10

Last updated date: 23rd Jul 2024
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## Real Numbers Formulas for Class 10 CBSE Maths

The world of numbers is vast and fascinating, and real numbers are the foundation upon which much of mathematics is built. Real numbers are a mix of rational and irrational numbers. Real Numbers Formulas for Class 10 play a crucial role in various important concepts. Clear understanding of real numbers is essential before diving into these formulas. This article presents a short list of formulas with examples to aid students in learning and memorizing them.

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## CBSE Maths Chapter 1 List of Real Numbers Formulas for Class 10

CBSE Class 10 Maths Chapter 1 all formulas on Real Numbers cover fundamental concepts in number theory. The chapter includes important formulas related to prime numbers, Euclid's division lemma, and the Fundamental Theorem of Arithmetic. Students will explore these key mathematical principles to build a strong foundation in the understanding of real numbers.

 S No Type of Real Numbers Description 1 Natural Numbers N = {1,2,3,4,5  >It is the counting numbers 2 Whole Numbers W= {0,1,2,3,4,5>It is the counting numbers + zero 3 Integers All whole numbers, including negative numbers + Positive numbers like -4,-3,-2,-1,0,1,2,3,4,5… so on.Like whole numbers, integers don’t include fractions or decimals. 4 Positive Integers Z+ = 1,2,3,4,5, …… 5 Negative Integers Z– = -1,-2,-3,-4,-5, …… 6 Rational Numbers A number is called rational if it can be expressed in the form of p/q where p and q are integers (q> 0).For example, P/q, ⅘. 7 Irrational Number A number is called irrational if it cannot be expressed in the form of p/q where p and q are integers (q> 0).For example, √3. 8 Prime Numbers Rule If 'x' is a prime number and 'x' divides $a^2$, then 'x' also divides 'a', where 'x' is a positive integer. 9 Real Numbers A real number is a number that can be found on the number line. Real Numbers are the numbers that we normally use and apply in real-world applications.Real numbers include Natural Numbers, Integers, Whole Numbers, Rational Numbers, Fractions, and Irrational Numbers.

### Properties of Real Number Formula for Class 10:

 S No Properties of Real Numbers Description 1 Closure Addition, subtraction, multiplication, and division of real numbers (except division by zero) yield real numbers. 2 Commutative Addition and multiplication are commutative:$a + b = b + a$$a \times b = b \times a 3 Associative Addition and multiplication are associative:(a + b) + c = a + (b + c)$$(a \times b) \times c = a \times (b \times c)$ 4 Distributive Multiplication over addition is distributive $a \times (b + c) = a \times b + a \times c$ 5 Identity Addition has an identity element (0: a + 0 = a) and multiplication has an identity element (1: a $\times$ 1 = a) 6 Inverse Every non-zero real number has an additive inverse (-a) and a multiplicative inverse (1/a)

### How Chapter 1 Maths Class 10 Formulas on Real Numbers Will Help Students?

• The formulas help students to simplify calculations easily.

• Knowing the  CBSE Class 10 Maths Chapter 1all Formulas on Real Numbers will help students to prepare more effectively for the exams.

• It helps students to save valuable time in solving questions in the exam.

• Silly mistakes can be avoided while solving problems related to real numbers.

To help students get good scores in Class 10th board exams,  we have put together some of the important CBSE Real Numbers formulas for Class 10 that will further help them prepare well for the exams. Candidates can download the formula page PDF from the link given on this page.

## Conclusion

In Class 10 Maths Chapter 1 formula, we dove into the world of Real Numbers, unraveling essential formulas to grasp their essence. These foundational formulas equip us to understand and manipulate real numbers effectively. From Euclid's Division Lemma to the Fundamental Theorem of Arithmetic, each formula unveils a unique aspect of real numbers. These concepts, like the HCF and LCM, lay the groundwork for more advanced mathematical explorations. By mastering the Chapter 1 Maths Class 10 formulas, we not only comprehend the intricacies of real numbers but also pave the way for a solid mathematical journey ahead. Explore, practice, and let these formulas be your guiding lights in the realm of numbers.

## FAQs on CBSE Maths Chapter 1 Real Numbers Formulas for Class 10

1. What are the important Real Numbers formulas for Class 10?

1. Euclid’s Division Lemma: For positive integers a and b, there are whole numbers m and n such that a = bm + n, where 0 ≤ n < b.

2. Euclid’s Division Algorithm: Based on Euclid’s division lemma, it finds the Highest Common Factor (HCF) of positive integers a and b.

1. Apply division lemma to find m and n: a = bm + n, where 0 ≤ n < b.

2. If n = 0, HCF is b. If n ≠ 0, apply Euclid’s lemma to b and n.

3. Repeat until remainder is zero; the divisor is HCF of (a, b). HCF(a, b) = HCF(b, n).

3. Prime Divisibility: If 'x' is a prime number and 'x' divides a², then 'x' divides 'a', where 'x' is a positive integer.

2. Why is it Important to Solve Problems Related to Real Number Formulas for Class 10?

Solving these problems helps understand essential concepts with applications in arithmetic.

Examples include proving irrationality using the Fundamental Theorem of Arithmetic and determining termination of decimal expansion in rational numbers.

3. What are Important Concepts Covered under class 10 maths chapter 1 formula on Real Numbers?

• Properties of real numbers.

• Equation for Euclid's Lemma and its proof.

• Fundamental Theorem of Arithmetic.

• Finding HCF and LCM via Prime Factorization Method.

4. How Many Formulas are There in Real Numbers Formulas for Class 10?

There are three primary formulas covering properties and theorems of real numbers, applicable in various mathematical levels.

5. How can I Memorize chapter 1 maths class 10 formula on Real Numbers?

• Read notes in the textbook to understand the formula concept.

• Write down the formula multiple times with explanations for better understanding.

• Save formula images on devices for quick revision.

• By mastering these formulas, students not only solve class 10 questions effectively but also build a foundation for advanced mathematics