NCERT Solutions for Class 6 Maths Chapter 11 Exercise 11.4
NCERT Solutions for Class 6 Maths Chapter 11 Exercise 11.4 (Ex. 11.4) Algebra all question answers with proper explanation updated for CBSE session 2020-2021. Hindi Medium as well as English Medium contents are given here with videos solution.Class 6 math exercise 11.4 deals with the questions related to word problems or application based questions based on algebraic expression. Questions are done in simple manner so that every student can understand easily.
Class 6 Maths Chapter 11 Exercise 11.4 Solution
|Exercise: 11.4||NCERT Textbook’s Solution|
CBSE NCERT Class 6 Maths Chapter 11 Exercise 11.4 Solution in Hindi and English Medium
Class 6 Maths Chapter 11 Exercise 11.4 Solution in Videos
Properties of Multiplication of Literals
Like numerals, multiplication of literal numbers has the following properties:
For all literal numbers a, b and c:
(i) ab = ba
(ii) a (bc) = (ab)c
(iii) 1a = a = a1
(iv) 0a = 0 = a0
(v) a (b + c) = ab + ac; (b + c) a = ba + ca
(vi) a (b – c) = ab – ac; (b – c) a = ba – ca
Division of literal numbers
The division (÷) sign between two numbers means that the number on the left of it is to be divided by the number on the right.
In the case of literal numbers also, a ÷ b means that the literal number a is to be divided by the literal number b and is commonly written as a/b (b ≠ 0). For example, we write:
(i) a divided by 3 as a/3
(ii) one-fourth of a + b as (a + b)/4
(iii) one-half of the product of a and b as ab/2
(iv) 12 divided by x (x ≠ 0) as 12/x
The score of Rashmi in English is 15 more than the three-fourth of her score in Hindi. Determine her score in English if she scored x marks in Hindi.
We have, Score in Hindi = x
Three-fourth of score in Hindi = (¾)x
So, 15 more than three-fourth of score in Hindi = 3x/4 + 15
Hence, Rashmi’s score in English = (¾)x + 15
Variables and Constants
A symbol having a fixed numerical value is called a constant whereas a symbol which takes on various numerical values is called a variable.
For example, the perimeter P of a square is given by the formula P = 4s, where s is the length of side of a square. Here 4 is a fixed number and hence a constant but the literal numbers P and s depend on different sizes of the square and hence they are variables.
Similarly, the volume of a sphere is given by V = 4/3 πr3
Here 4/3 and π are fixed numbers, i.e., constants but the literal numbers V and r depend on different sizes of the sphere and hence they are variables.
A combination of constants and variables, connected by the symbols +, –, × and ÷ is called an algebraic expression.
The various parts of the algebraic expression separated by the sign + or – are called the terms of the expression.
Thus, (i) the algebraic expression 3x – 4y + 2xy has three terms, namely 3x, –4y and 2xy.
(ii) The algebraic expression 5a + 2b – 6 ab + 7 has four terms namely 5a, 2b, –6ab and 7.
What are mathematical literals?
In mathematical logic, a literal is an atomic formula (atom) or its negation. The definition mostly appears in proof theory (of classical logic), e.g. in conjunctive normal form and the method of resolution. Literals can be divided into two types: A positive literal is just an atom.
Mayank spends Rs. x daily and saves Rs y per week. What is his income in 5 weeks?
We have, 1 week = 7 days
So, 5 weeks = (7 × 5) days = 35 days
As Mayank spends Rs. x daily.
So, Total amount spent by him in 5 weeks (i.e., 35 days) = Rs (35 times x) = Rs 35x
He saves Rs. y per week.
So, Total amount saved by him in 5 weeks = Rs (5 times y) = Rs 5y
Now, income = expenditure + savings
So, His income in 5 weeks = Rs. (sum of 35x and 5y) = Rs (35x + 5y)
What is difference between literal and variable?
A literal is notation for representing a fixed (constant) value. A variable is storage location associated with a symbolic name (pointed to, if you’d like)