NCERT Solutions for Class 6 Maths Chapter 11 Exercise 11.5
NCERT Solutions for Class 6 Maths Chapter 11 Exercise 11.5 (Ex. 11.5) Algebra updated for academic session 2020-2021 in Hindi and English Medium free. All the contents are free to download or use online without any login or password.Practice the questions based on algebra and its basics in class 6 math exercise 11.5 including application based questions. If you have difficulty to understand solution through PDF solution, use video solution to solve your doubts.
Class 6 Maths Chapter 11 Exercise 11.5 Solution
|Exercise: 11.5||NCERT Book’s Solutions|
CBSE NCERT Class 6 Maths Chapter 11 Exercise 11.5 Solution in Hindi and English Medium
Class 6 Maths Chapter 11 Exercise 11.5 Solution in Videos
Expressions with Variables
To form expressions, we use all the four number operations of addition, subtraction, multiplication and division. For example, to form (2 × 10) + 3, we have multiplied 2 by 10 and then added 3 to the product. Examples of some of the other arithmetic expressions are:
(i) 3 + (4 × 5)
(ii) (– 3 × 40) + 5
Expressions can be formed from variables too. In fact, we already have seen expressions with variables, for example: 2n, 5m, x + 10, x – 3 etc.
These expressions with variables are obtained by operations of addition, subtraction, multiplication and division on variables. For example, the expression 2n is formed by multiplying the variable n by 2; the expression (x + 10) is formed by adding 10 to the variable x and so on.
Note: A number expression like (4 × 3) + 5 can be immediately evaluated as (4 × 3) + 5 = 12 + 5 = 17.
But an expression like (4x + 5), which contains the variable x, cannot be evaluated. Only if x is given some value, an expression like (4x + 5) can be evaluated. For example, when x = 3, 4x + 5 = (4 × 3) + 5 = 17 as found above.
Make up as many expressions with numbers as you can from three numbers 5, 7 and 8. Every number should be used not more than once. Use only addition, subtraction and multiplication.
We can make many expressions here three possible expressions are:
(i) 5 + (8 – 7)
(ii) 5 – (8 – 7)
(iii) (5 × 8) + 7
Using Expressions Practically
We have already come across practical situations in which expressions are useful.
(i) Raju’s father’s age is 2 years more than 3 times Raju’s age.
Let Raju’s age is x years, then his father age will be (3x + 2) years
(ii) The speed of a bus is 10 km/hour more than the speed of a truck going on the same road.
Let the speed of the truck be y km/hour.
The speed of the bus is (y + 10) km/hour.
In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.
Here, for example, 5x + 9 is the expression on the left-hand side, which is equal to the expression 24 on the right-hand side.
Solution of an Equation
The value of the variable in an equation which satisfies the equation is called a solution to the equation.
For example, let us take the equation x – 3 = 11
This equation is satisfied by x = 14, because for x = 14, LHS of the equation = 14 – 3 = 11 = RHS
Thus, x = 14 is a solution to the equation x – 3 = 11
What is an example of one solution?
On solving we have 7x = 35 or x = 5. The above linear equation is only true if x = 5 and hence the given linear equation has only one solution i.e. x = 5.
How many solutions do equations have?
A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line).
Which equation has no solution?
The solution x = 0 means that the value 0 satisfies the equation, so there is a solution. “No solution” means that there is no value, not even 0, which would satisfy the equation.
What are the 4 steps to solving an equation?
We have 4 ways of solving one-step equations: Adding, Subtracting, multiplication and division.