CBSE Class 7 Maths Revision Nnotes Chapter 1

CBSE Class 7 Mathematics Revision Notes Chapter 1 – Integers

Some of the basic concepts of integers are introduced in CBSE Class 7 Mathematics Chapter 1. Students must have a solid grasp of these fundamental integer concepts because they will use them in other chapters of Mathematics. Subject matter experts have prepared Class 7 Chapter 1 Mathematics Notes for a better understanding of students.

Class 7 Mathematics Chapter 1 Notes are available from Extramarks for students to use while they are studying. In this chapter, crucial ideas like whole numbers, natural numbers, the properties of addition and subtraction of integers, the number line, etc., are explained.

Some of the important topics covered in CBSE Class 7 Mathematics Chapter 1 Integers are as follows. 

• Introduction to Numbers

1. Natural Numbers
2. Whole Numbers

• Properties of Addition and Subtraction of Integers

1. Closure under Addition and Subtraction
2. Commutative Property for Addition
3. Associativity Property for Addition 

• Additive Identity and Additive Inverse
• Properties of Multiplication of Integers

1. Closure under Multiplication
2. Commutative Property of Multiplication
3. Multiplication by Zero
4. Multiplicative Identity
5. Associative Property of Multiplication
6. Distributive Property of Integers

• Division of Integers
• Number Line
• Addition and Subtraction of Integers
• Introduction to Zero
• Properties of Division of Integers
• Multiplication of Integers

Revision Notes for CBSE Class 7 Mathematics Chapter 1 – Free Download

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Definition of Integers

Integers are a set of numbers that represent a whole number, such as 3 or 4 but not 3.5 and are made up of all whole numbers and their negatives.

Whole numbers are those that contain a zero. Therefore, we can write integers as …, -2, -1, 0, 1, 2, …

Representation on the Number Line

Let’s review how to add, subtract, and represent integers on a number line by using the following examples.

(i) Integers (−3) and 4 can be represented on the number line as shown below.

(ii) Addition of integers is performed as below.

2 + 3 = 5

(−3) + (−4) = (−7)

(−10) + 1 = (−9)

(iii) Subtraction of integers is performed as below.

2 − 3 = (−1)

(−3) − (−4) = 1

(−4) − 10 = (−14)

Properties of Addition and Subtraction of Integers

Following are the properties of addition and subtraction of integers.

(a) Both addition and subtraction on integers are closed. In other words, if a and b are both integers, then a + b and a – b must also be integers.

(b) For integers, addition is commutative. a + b = a + b for all integers a and b.

(c) For integers, addition is associative. a + b + c = a + (b + c) for all integers a, b, and c.

(d) Addition of the integer 0 to any integer ‘a’ results in the integer ‘a’. So, a + 0 = a = 0 + a. Hence, 0 is the additive identity of integers, according to this definition.

Multiplication of Integers

Positive and negative integers, as well as whole numbers, were taught to be multiplied. The following are some examples.

(i) A negative integer is produced when a positive and a negative integer are multiplied. For example, −6 × 2 = −12.

(ii) A positive integer is produced when two positive or negative integers are multiplied. For example, −5 × −3 = 15 and 6 × 3 = 18.

(iii) The outcome is positive when an even number of negative numbers are multiplied together.  For example, −2 × −3 × −4 × −5 = 120.

(iv) The outcome is negative when an odd number of negative integers are multiplied together. For example, −2 × −3 × −4 = −24.

Properties of Multiplication of Integers

Let’s examine the characteristics that integer multiplication satisfies.

(A) Multiplication on integers is closed. a × b is also an integer for any two integers a and b.

(b) For integers, multiplication is commutative. For any two integers a and b, a × b = b × a.

(c) For integers, multiplication is associative. For any three integers a, b and c, (a × b) × c = a × (b × c).

(d) Any integer ‘a’ is equal to the integer ‘a’ when multiplied by the number 1. Therefore, 1 is an integer’s multiplicative identity.

Distributive Property

According to the distributive property, each of the integers outside the parentheses (brackets) is multiplied by the integers inside the parenthesis. The integers that result from the multiplication are later added or subtracted accordingly.

For any three integers a, b and c, a × (b + c) = a × b + a × c or a × (b − c) = a × b − a × c.

Addition and subtraction can be used to express the distributive property of multiplication. The distributive characteristics of addition and subtraction can be used to rewrite expressions for a variety of reasons. 

Division of Integers

Divide both positive and negative integers, as explained. Here are a few instances:

(a) A negative integer is the quotient when a positive integer is divided by a negative integer, and vice versa. For example, −24 ÷ 3 = −8.

(b) A positive integer is the quotient when a negative integer is divided by another negative integer or when a positive integer is divided by another positive integer. For example, −35 ÷ −5 = 7 and 121 ÷ 11 = 11.

Properties of Division of Integers

The division of integers does not adhere to the associative and commutative properties.

If ‘a’ is an integer,

(a) a ÷ 0 is not defined

(b) 0 ÷ a = 0, a ≠ 0

(c) a ÷ 1 = a

(d) a ÷ (−1) = −a

Class 7 Integers Notes

In integers, students encounter the set of negative whole number values and their representation on the number line. The property of negative numbers using integers is introduced, which broadens the definition of the number line beyond whole and natural numbers. The different properties of integers, including addition, subtraction, multiplication, and division, shall also be helpful in future to comprehend the number system and understand the chapters relating to rational and irrational numbers.

Extramarks’ Chapter 1 Mathematics Class 7 Notes will help students easily revise the concepts before the exams. These notes will also assist them with quick concepts before beginning the chapters introduced in the higher grade.

Why Should You Go for Integers Class 7 Notes?

Extramarks Class 7 Mathematics Notes Chapter 1 will benefit students in the following ways.

Students can quickly review all the concepts of the chapter with the help of the Class 7 Mathematics Chapter 1 Notes.

Students will be able to solve problems more quickly by referring to the concepts explained in the notes. 

Extramarks Class 7 Mathematics Chapter 1 Notes are written in a descriptive and illustrative manner. Therefore, students can easily memorise the concepts, formulas, or properties explained in the chapter before any test or exam. 

While it is important to gather all the resources needed for one chapter, it requires a lot of time and effort. With these Class 7 Chapter 1 Mathematics Notes, students can focus on practising the sums, which is also important for understanding and mastering the concepts. 

Extramarks recommends that students review Class 7 Chapter 1 Mathematics Notes before beginning problem-solving. The Class 7 Chapter 1 Mathematics Notes are created in such a way that, with regular revisions, students will be able to maximise their performance in the exams.

Tips for Studying Class 7 Mathematics Chapter 1 Notes

Here are some tips for students to study and plan ahead.

• They must revise every point and relate it to the provided solved examples.
• It is advised that students revise the concepts every time before working on a question from the chapter.
• These revision notes can be used for a quick review of the basic concepts for other chapters on the number system in higher grades. Numbers can be rational and irrational.
• Students can revise all of the integer operation properties as necessary.

Conclusion

To sum up, NCERT Class 7 Mathematics Chapter 1 Revision Notes are extremely helpful for learning concepts, practising them, and revising for exams. Extramarks Class 7 Mathematics Chapter 1 Notes were created to guide students’ conceptual understanding that will help them better understand all the theorems, formulas, derivations, properties, and other concepts by connecting them to real-world applications. Students will be able to master the concepts and score better grades if they consult the Class 7 Mathematics Chapter 1 Notes for their studies.