# NCERT Solutions for Class 6 Maths Chapter 11 Exercise 11.3

NCERT Solutions for Class 6 Maths Chapter 11 Exercise 11.3 (Ex. 11.3) Algebra step by step question answers done by subject experts free to use online or download. All the solutions are prepared for the academic session 2020-2021.

Class 6 math exercise 11.3 provides a basic idea about the formation of algebraic expression. All the questions in ex. 11.3 of 8th math are simple to understand and easy to solve.## Class 6 Maths Chapter 11 Exercise 11.3 Solution

Class: 6 | Mathematics |

Chapter: 11 | Algebra |

Exercise: 11.3 | English and Hindi Medium |

### CBSE NCERT Class 6 Maths Chapter 11 Exercise 11.3 Solution in Hindi and English Medium

### Class 6 Maths Chapter 11 Exercise 11.3 Solution in Videos

#### Properties of Addition of Literals

Like numerals, addition of literal numbers have the following properties: For all literal numbers a, b and c:

(i) a + b = b + a

(ii) a + (b + c) = (a + b) + c

(iii) a + 0 = a = 0 + a However, subtraction of literals has none of these properties.

##### Laws of Addition and Subtraction of Literal Numbers

Integer Property | Addition | Subtraction |
---|---|---|

Commutative Property | x + y = y+ x | x – y ≠ y – x |

Associative Property | x + (y + z) = (x + y) + z | (x – y) – z ≠ x – (y – z) |

Identity Property | x + 0 = x =0 + x | x – 0 = x ≠ 0 – x |

Closure Property | x + y ∈ Z | x – y ∈ Z |

##### Write each of the following phrases using numbers, literals and the basic operation of subtraction: (i) Subtract 2 from x (ii) 9 less than a literal y (iii) Decrease x by 5 (iv) Decrease the sum of a and b by x (v) y less than the sum of x and 8.

(i) x – 2

(ii) y – 9

(iii) x – 5

(iv) (a + b) – x (v) (x + 8) – y

(v) y < x + 8

#### Multiplication of Literal Numbers

Multiplication can be indicated in several ways. To indicate the result of multiplying 2 by a, we can write as (i) 2 × a, (ii) 2.a or (iii) 2a. Thus, ab means a multiplied by b; 5a means a multiplied by 5.

The third form in which 2 and a are written side by side without the multiplication (×) sign or dot (.) between them is the one most extensively used.

##### Write each of the following phrases using numbers, literals and the basic operations of addition, subtraction and multiplication: (i) Multiply a by 6 (ii) 5 times b (iii) The product of x and 2 (iv) 7 times x added to a (v) y subtracted from 4 times x

(i) 6a

(ii) 5b

(iiii) 2x

(iv) 7x + a (v) 4x – y

##### Why is the commutative property of addition important?

Place value and commutative property are important to remember when understanding and solving addition and multiplication equations. The order of the numbers in the equation does not matter, as related to the commutative property, because the sum or product is the same.

##### When numbers literals are multiplied they are called?

A multiplying literal number or product of more literals in a term is called a literal factor.

##### How is linear algebra used in real life?

Linear algebra has many use in real life some examples are as:

The vibration frequencies of a violin strings (the “sound” of a violin)

Same for a drum.

The resonant frequencies of a bridge.

The energy levels of atoms.

The microwave energy distribution in a microwave oven.

You will also find hints of it in any systems that uses resonance, such as NMR and MRI, more at this place.