# NCERT Solutions for Class 7 Maths Chapter 1 Integers

NCERT Solutions for Class 7 Maths Chapter 1 Integers- We have learned about integers and whole numbers in Class 6. We know that integers are a large collection of numbers which is formed by the whole numbers and negative numbers. In NCERT Class 7 Maths Chapter 1 Integers, we will discuss more the integers, their properties, and operations. There is a total of 4 exercises with 30 questions. The NCERT Solutions for Class 7 Maths Chapter 1 Integers are created by our subject experts with keeping in mind the understanding level of class 7 students and as per the syllabus prescribed by the CBSE. These NCERT solutions of class 7 are the detailed explanation of each and every problem of NCERT maths textbook and these NCERT solutions help students in their preparation of CBSE final examination.

NCERT Class 7 Maths Chapter 1 Integers is an important chapter for a maths student. All the topics included in this chapter are extremely important for the students because these basic concepts of integers are also included in the higher classes. In this chapter, we will study important topics like properties of addition, subtraction, multiplication, and division of Integers, multiplication of a positive integer with a negative integer, multiplication of two or more than two negative integers and also learn closure under addition, subtraction and multiplication. We know that whole numbers are starting from 0 and counting up forever and whole numbers do not contain negative numbers, decimals or fractions for example {0, 1, 2, 3, 4, 5, 6, 7, 8,....99, 100,.....}. On the other hand, Integers are also like the whole numbers, but integers also include negative numbers but still, no decimals or fractions allowed. So, integers are positive {1, 2, 3, 4,... }, negative {-1, -2,-3, -4,... }, or zero {0}.

Important points of Class 7 Maths Chapter 1 Integers-

• Integers are closed for both addition and subtraction. That is, if a and b are any integers then a + b and a – b are also integers.
• The addition is commutative for the integers, such that $\dpi{100} a + b = b + a$ for all integers 'a' and 'b'.
• The addition is associative for the integers, such that, $\dpi{100} (a + b) + c = a + (b + c)$ for all the integers 'a', 'b' and 'c'.
•  Integer 0 is the identity under addition. That is, $\dpi{100} a + 0 = 0 + a = a$  for every integer 'a'.
• Integers are closed under multiplication. That is,$\dpi{100} a \times b$ is an integer for any two integers 'a' and 'b'.
• Multiplication is commutative for the integers. That is, $\dpi{100} a \times b= b \times a$ for any integers 'a' and 'b.'
• The integer 1 is the identity under multiplication, such that, $\dpi{100} 1 \times a= a \times 1 = a$ for any integer 'a'.
• Multiplication is associative for the integers, such that, $\dpi{100} (a \times b) \times c = a \times (b \times c)$ for any three integers a, b and c.

## Topics of NCERT Grade 7 Maths Chapter 1 Integers-

1.1  Introduction

1.2  Recall

1.3   Properties of Addition and Subtraction of Integers

1.3.2  Closure under Subtraction

1.3.3  Commutative Property

1.3.4  Associative Property

1.4  Multiplication of Integers

1.4.1  Multiplication of a Positive and a Negative Integers

1.4.2  Multiplication of two Negative Integers

1.4.3  Product of three or more Negative Integers

1.5  Properties of Multiplication of Integers

1.5.1  Closure under Multiplication

1.5.2  Commutativity of Multiplication

1.5.3  Multiplication by Zero

1.5.4  Multiplicative Identity

1.5.5  Associativity for Multiplication

1.5.6  Distributive Property

1.5.7  Making Multiplication Easier

1.6 Division of Integers

1.7 Properties of Division of Integers

## NCERT Solutions for Class 7 Maths - Chapter-wise

 Chapter No. Chapter Name Chapter 1 Integers Chapter 2 Fractions and Decimals Chapter 3 Data Handling Chapter 4 Simple Equations Chapter 5 Lines and Angles Chapter 6 The Triangle and its Properties Chapter 7 Congruence of Triangles Chapter 8 Comparing Quantities Chapter 9 Rational Numbers Chapter 10 Practical Geometry Chapter 11 Perimeter and Area Chapter 12 Algebraic Expressions Chapter 13 Exponents and Powers Chapter 14 Symmetry Chapter 15 Visualising Solid Shapes