Students can go through AP Board 7th Class Maths Notes 3rd Lesson Simple Equations to understand and remember the concept easily.

## AP Board 7th Class Maths Notes 3rd Lesson Simple Equations

→ Bhaskara-II: Bhaskara-II is a famous mathematician of ancient India. He wrote Siddhanta Shiromani at the age of 36 in 1150 A.D. and this work (consisting of about 1450 verses) was divided into four parts.

- Lilavati (ARITHMETIC) has 278 verses.
- Bijaganit (ALGEBRA) has 213 verses.
- Goladhyaya (sphere/celestial globe) has 451 verses.
- Grahaganit (mathematics of the planets) has 501 verses.

Linear equations in one variable and several variables were one of the equations that Bhaskara II was interested in, and he presented many problems below one problem is an example to illustrate it.

MA fifth part of a swarm of bees came to rest on the flower of Kadamba, a third on the flower of Silinda. Three times the difference between these two numbers flew over a flower of Krutaja, and one bee alone remained in the air, attracted by the perfume of a jasmine in bloom. Tell me, beautiful girl, how many bees were in the swarm ?

→ An open sentence which contain sign “ = ” is called an equation.

→ An equation which involves only one variable whose highest power 1 is known as simple equation.

→ Solution of simple equation or root of simple equation: The value of the variable for which equation becomes true is called the solution or the root of the equation.

→ The equation remains unchanged if:

(a) The same number is added to both sides of the equation.

(b) The same number is subtracted from both sides of the equation.

(c) The same number is multiplied to both sides of the equation.

(d) The same non-zero number divides both sides of the equation.

→ The process of changing the term from one side of the equation to other side is called transposition.

→ So, by transposing a term we simply change its sign and carry it to the other side of the equation. Thus, in transposing terms from LHS to RHS.

- ‘+ quantity’ becomes ‘-‘ quantity’
- ‘-‘ quantity’ becomes ‘+’ quantity’
- ‘×’ quantity’ becomes ‘÷’ quantity’
- ‘÷’ quantity’ becomes ‘×’ quantity’.

→ Open sentence: A mathematical sentence whose truth value can’t be determined is called as open sentence.

Example: The age of GOPI is more than 12 years.

→ Equation: An open sentence containing an equality (=) symbol is called an equation.

Example: The age of GOPI =12 years.

An equation involving only one variable whose highest power is 1 is known as a simple equation.

Example: 7 + x = 15

a + 3 = 8

8 – y = 3

→ Solution of a simple equation: The value of variable for which the equation becomes

true or equal on both sides is called the solution or root of the simple equation.

Example: 7 + x = 15 becomes true or qqual on both sides when x = 8. Here 8 is called the solution of the simple equation 7 + x = 15.

→ Rules of simple equations:

- The equation remains unchanged if the same number is added on both sides of the equation.

Example: 7 + x = 15 is same as 10 + x = 18 (adding 3 on both sides) - The equation remains unchanged if the same number is subtracted from both sides of the equation.

Example: 7 + x = 15 is same as 4 + x = 12 (subtracting 3 from both sides) - The equation remains unchanged if both sides of the equation are multiplied by the

same positive number. ‘

Example: 7 + x – 15 is same as 14 + 2x = 30 (multiplied by 2 on both sides) - The equation remains unchanged if the both sides of the equation are divided by a non-zero positive number.

Example: 7+x = 15 is same as \(\frac{7}{2}+\frac{x}{2}=\frac{15}{2}\) (divided by 2 on both sides).

→ Transposition: The process of transferring the terms of a simple equation from one side to other is called transposition of term.

- When a term is transposed.
- It gets opposite sign.
- It means a positive quantity when transposed it gets a negative sign.
- Similarly, a negative quantity when transposed it gets a positive sign.
- Also when a term multiplying one side of a simple equation is transposed it divides the other side.
- Similarly when a term dividing one side of a simple equation is transposed it multiplies the other side.

→ Solving a real life problem:

- Read the problem carefully and separate knowns and unknowns i.e. identify what is given and what is to be found.
- Represent the unknowns by variables such as x, y, z, …….
- Translate the problem to the language of mathematical statements.
- Form the simple equations using the conditions given in the problem.
- Solve the simple equations.
- Verify the answer.