# NCERT Solutions for Class 7 Maths Chapter 1 Exercise 1.3

NCERT Solutions for Class 7 Maths Chapter 1 Exercise 1.3 (Ex. 1.3) Integers in Hindi Medium and English Medium updated for CBSE academic session 2021-2022. All the solutions are useful for state board students also.

Class 7 math exercise 1.3 illustrate the variety of questions based on Distributive Property, Commutative Property, and Associative Property. Some word problems based on daily life are also given at the end of exercise 1.3, which are interesting to solve.## Class 7 Maths Chapter 1 Exercise 1.3 Solution

### CBSE NCERT Class 7 Maths Chapter 1 Exercise 1.3 Solution in Hindi and English Medium

Class: 7 | Mathematics |

Chapter: 1 | Integers |

Exercise: 1.3 | NCERT Book’s Solutions |

### Class 7 Maths Chapter 1 Exercise 1.3 Solution in Videos

#### Multiplication of Integers

Rule 1. To find the product of two integers with unlike signs, we find the product of their values regardless of their signs and give a minus sign to the product.

#### Properties of Multiplication of Integers

##### I. Closure Property for Multiplication:

The product of two integers is always an integer.

Example:

(i) 7 x 5 = 35, which is an integer.

(ii) (- 8) x 4 = 32, which is an integer.

(iii) 9 x (- 6) = – 54, which is an integer.

(iv) (- 8) x (- 7) = 56, which is an integer.

For any two integers a and b, we have: (a x b) = (b x a).

Example:

(i) 5 x (- 8) = – 40 and (- 8) x 5 = – 40.

So, 5 x (- 8) = (- 8) x 5.

(ii) (- 9) x (- 7) = 63 and (- 7) x (- 9) = 63.

So, (- 9) x (- 7) = (- 7) x (- 9).

##### III. Associative Law for Multiplication:

For any integers a, b and c, we have: (a x b) x c = a x (b x c).

Example:

(i) Consider the integers 3, – 5 and – 8.

We have: {3 x (- 5)} x (- 8) = (- 15) x (- 8) = 120

and 3 x {(- 5) x (- 8)} = (3 x 40) = 120.

So, {3 x (- 5)} x (- 8) = 3 x {(- 5) x (- 8)}.

(ii) Consider the integers (- 8), (- 6) and (- 5).

We have:

{(- 8) x (- 6)} x (- 5) = 48 x (- 5) = – 240.

And (- 8) x {(- 6) x (- 5)} = (- 8) x 30 = – 240.

So, {(- 8) x (- 6)} x (- 5) = (- 8) x {(- 6) x (- 5)}.

##### IV. Distributive Law of Multiplication over Addition:

For any integers a, b and c, we have: a x (b + c) = (a x b) + (a x c).

Example:

(i) Consider the integers 5, (- 6) and (- 8). We have:

5 x {(- 6) + (- 8)} = 5 x (- 14) = -70

And {5 x (- 6)} + {5 x (- 8)} = (- 30) + (- 40) = – 70.

So, 5 x {(- 6) + (- 8)} = {(5 x (- 6)} + {5 x (- 8)}.

##### V. Existence of Multiplicative Identity:

For every integer a, we have: (a x 1) = (1 x a) = a. 1 is called the multiplicative identity for integers.

Examples:

(i) (12 x 1) = 12.

(ii) (- 16) x 1 = – 16.

##### VI. Existence of Multiplicative Inverse:

Multiplicative inverse of a non-zero integer a is the number

1/a, a.(1/a) = (1/a). a = 1

Examples:

(i) Multiplicative inverse of 6 is 1/6.

(ii) Multiplicative inverse of – 6 is – 1/6.

##### VII. Property of Zero:

For every integer a, we have:

(a x 0) = (0 x a) = 0.

Example:

(i) 8 x 0 = 0 x 8 = 0.

(ii) (- 6) x 0 = 0 x (- 6) = 0.

### Class 7 Maths Exercise 1.3 Important Questions

##### Find each of the following products: (i) 6 x (- 5) (ii) (- 7) x 9 (iii) 35 x (- 18) (iv) (- 42) x20

We have:

(i) 6 x (- 5) = – 30.

(ii) (- 7) x 9 = – 63.

(iii) 35 x (- 18) = – (35 x 18) = -630.

(iv) (- 42) x 20 = – (42 x 20) = -840.

##### What are the properties of multiplication of integers?

The properties of multiplication of integers are:

- Closure property.
- Commutative property.
- Multiplication by zero.
- Multiplicative identity.
- Associative property.
- Distributive property

##### How do you multiply positive and negative integers?

There are two simple rules to remember: When you multiply a negative number by a positive number then the product is always negative. When you multiply two negative numbers or two positive numbers then the product is always positive. 3 times 4 equals 12.

##### Simplify: (i) 8 x (- 15) + 8 x 6 (ii) (- 18) x 7 + (- 18 x (- 4)

Using the distributive laws, we get:

(i) 8 x (- 15) + 8 x 6 = 8 x {(- 15) + 6}

Because, [ a x b + a x c = a x (b + c)} = 8 x (- 9) = – 72.

(ii) (- 18) x 7 + (- 18) x (- 4) = (- 18) x {7 + (- 4)}

Because, [ a x b + a x c = a x (b + c)] = (- 18) x 3 = – 54.