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CBSE Class 6 Mathematics Chapter 6 Revision Notes – Integers
What is an integer? Are they used in calculations? Where are they placed in a number line? Are arithmetic operations possible without them?
Class 6 Mathematics Chapter 6 Notes clear all the doubts from students’ minds so that they can answer all the questions in the board exams with confidence.
Class 6 Mathematics Chapter 6 Notes are prepared by subject matter experts at Extramarks to help the students gain conceptual clarity about the topics. Students do not have to make extra effort to make exhaustive notes to revise before the exams. With these notes, students will be able to grasp all the important topics quickly and can practice questions for selfevaluation.
Revision Notes For CBSE Class 6 Mathematics Chapter 6
Revision Notes For CBSE Class 6 Mathematics Chapter 6
Integers
 The collection of natural numbers, negative numbers, and zero is regarded as integers.
 Fractions and decimals are not included in the category of integers.
 The positive numbers are called positive integers, and the negative numbers are called negative integers.
 Negative integers are placed on the left side of zero on the number line, and positive integers are placed on the right side of zero.
 Integers are important in daily life to measure the temperature, denote the water level, measure the height of a place from the surface of the ocean, or perform simple calculations.
 Some examples of integers are 3, 6, 8, 2, 5, 0, etc.
 Integers can be placed on a number line.
 As the number line goes in the rightward direction the integers become greater.
 The numbers decrease as we move in the leftward direction.
 Therefore, 1 is greater than 5, which is greater than 10. Again, +10 is greater than +5, which is greater than +1.
 Addition of Integers
 When two positive integers are added, the sum is always a positive integer. For example, (+5) + (+7) = +12.
 When two negative integers are added, the result is always a negative number. If 5 is added with 6, the result is 11.
 When a positive and a negative number are added, the result takes the sign of the greater number. For example, (7) + (2) = (5).
 Subtraction of Integers
 When the greater number is positive and the smaller number is negative, the result takes the positive sign. For example, 75 – 45 = 30.
 When a negative number is subtracted from a positive number, the rule is as follows:
 45 – (23) = 45 + 23 = 68.
 When a positive number is subtracted from a negative number, only the sign remains unchanged.
 73 – (+30) = 73 – 30 = 110.
 Properties of Addition and Subtraction of Integers
 Closure Property: The sum or subtraction of two given integers is always an integer. For example, 5 + 3 = 8; 5 – 3 = 2; both 8 and 2 are integers.
 Commutative Property: The sum of two positive integers does not depend on the order of placement of the integers. For instance, 5 + 9 = 9 + 5 = 14.
 Associativity of Addition: The sum of more than two positive integers does not depend on the grouping of the integers. For example: (5 + 3) + 6 = 5 + (3 +6) = (5 + 6) +3 = 14.
 Additive Identity: If an integer is added to zero, the result remains unchanged. If 5 is added to zero the sum is 5 which is the value of the given number.
 Multiplication of Integers
 When a positive integer is multiplied by another positive integer the product is always a positive integer. 13 X 2 = 26, where both the given numbers are positive integers, hence, the product is a positive integer.
 When a positive integer and a negative integer are multiplied, then the result is a negative integer. For example, 90 X 3 = 270.
 This point is noteworthy and important from the point of view of the exam. When two negative integers are multiplied then the product is always a positive integer. For example, 270 x 3 = 810.
 Properties of Multiplication of Integers
 Multiplication by Zero: If an integer is multiplied by zero the product is zero. 84 X 0 = 0.
 Multiplication by 1: If an integer is multiplied by 1, the product is the given number itself. Any number multiplied by 1 will produce the same number This is known as the identity property of multiplication. For instance, the result of multiplying 5 by 1 will be 5.
 92 x 1 = 92.
 Division of Integers
 When one integer is divided by another integer and any one of them is a negative number, then the quotient must be a negative number. For example, 18/3 = 6, or 45/(5) = 9.
 When the dividend and the divisors are both positive numbers or both negative numbers, the quotient is always a positive number. For example: 77/11 =7; 36/6 = 6. In both cases, the quotients are positive integers.
 Properties of Division of Integers
 If an integer is divided by another integer, the quotient may not be an integer. For example: 22/7 = 3.14. Both 22 and 7 are integers but the quotient is a decimal.
 If an integer is divided by zero the result becomes undefined. 34/0 = undefined.
 If an integer is divided by 1, the given number itself becomes the quotient. For instance, 14/1 = 14.
Successors and Predecessors
 The number placed at the immediate right position of a number is a successor number.
 The number placed at the immediate left position of another number is the predecessor to that number.
 So, a successor number is the sum of one and the given number.
 If one is subtracted from a given number, the result is the predecessor number.
 For example, the predecessor number of ten is nine; 10 – 1 = 9.
 The successor number to ten is eleven; 10 + 1 = 11.
Revision Notes For CBSE Class 6 Mathematics Chapter 6
Class 6 Mathematics Chapter 6 Notes free PDF are available on the website of Extramarks. Students can download the file for further study. They can revise the notes at their convenient time and study offline as well.
CBSE Class 6 Chapter 6 Integers Revision Notes
The revision notes on Integers focus on what the integers are, where they lie on the number line, and what kind of arithmetic operations are possible with them. The subject experts have included all the major points and explained them with suitable examples so that students can understand the concepts easily.
Salient Features of Extramarks CBSE Class 6 Mathematics Chapter 6
There are many notes available in the market. What makes the notes provided by Extramarks unique or different?
 Class 6 Mathematics Chapter 6 Notes are prepared by mathematics experts at Extramarks.
 Special care has been taken by experts to cover all the concepts given in the NCERT book.
 The notes are wellstructured and the topics are arranged in a logical manner, so the students can understand the development of ideas.
 Simple and lucid language.
 The notes are written pointwise so that the students can quickly have a look at the major points.
 These notes are extremely helpful before the final exam to grasp all the topics in detail.
Why Refer to Extramarks for CBSE Class 6 Mathematics Notes PDF?
Extramarks is an online platform that helps students understand complicated concepts in a simple way. The online platform was built with the vision of helping the students perform better in the board exams. To turn their dream into a reality, Extramarks has appointed subject experts to make crisp and concise notes for the students as per CBSE guidelines so that they can revise all the chapters in less time before the exams. These notes will definitely clear all the doubts related to the concepts and help the students fetch extra marks in the exams.
Conclusion
The chapter on Integers is important for understanding basic operations using both positive and negative numbers. Without the knowledge of integers, it is impossible to keep track of calculations in daily life. Also, from the point of view of exams, this chapter is important. So, Extramarks brings you comprehensive notes that will help you not only gain indepth knowledge about the integers but also attempt different types of questions in the exams with ease. With the notes from Extramarks, give your preparation an extra edge.
FAQs (Frequently Asked Questions)
1. What are integers?
Integers are collections of numbers that include all the natural numbers, negative numbers, as well as zero.
2. .Write the integers that lie between 0 and 11. Write them in increasing order.
When we move leftward on the number line, the numbers become greater. Therefore, 11 is the smallest number between 0 and 11. The other numbers are 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, and 0.
3. What are the properties of zero?
Zero is neither a positive number nor a negative number nor a natural number. It is a whole number and an integer.
4. Can integers be fractions?
Integers comprise whole numbers and their negative counterparts. So, integers can never be fractions.
5. Are negative numbers integers?
Integers include positive numbers as well as negative numbers.
6. Is the product of a positive integer and a negative integer greater than the integers given?
The product of a positive integer and a negative integer can never be greater than the individual numbers. Suppose, (5) and (6) are the given numbers. Their product (30) is far less than the two given numbers.
7. What is the sum of 5 and 5?
The sum of 5 and 5 is zero.