SIMPLE EQUATIONS_07CBSE
Dear Children,
Simple equation is not a new term, you are already familiar with the terms, constants and variables. Variables represents unknown quantities. We come across unknown quantities many a times. For example, suppose your friend gave you a box of chocolates on your birthday and one more friend gave you a box of chocolates. Now you have two boxes of chocolates but you do not know how many chocolates are there in these two boxes. This unknown quantity can be known only after opening the boxes, similarly, these unknown in algebra can be known only after solving the equations which we are learning in this chapter called “SIMPLE EQUATIONS”
What is Simple Equation in SIMPLE EQUATIONS_07
The statement of equality containing a variable is called an equation (A variable is an unknown quantity whose value varies and is represented by letters like x,y,z,a,b,c,p,q,r, etc. In this post SIMPLE EQUATIONS_07 we have some examples of simple equations are
4x+15=0, 4+y=9, 2z+7=0 etc.
Conversion of a statement to an equation
In order to convert a statement into an equation, we denote the unknown by some variables (x,y,z, etc.)and then form the equation according to the statement given.
Example- The sum of 4 times q and 5 times r is 65
Solution- 4q+5r=65
Conversion of an equation to a statement
When we convert a statement into an equation, we get a unique equation. However an equation cab be converted into many statements.
Example- 4q+8=13
Solutions- (a) 8 added to 4 times a number is 13
(b) 4 times a number q is 8 less than 13
(c) 13 is 8 more than 4 times a number q
(d) The sum of 4 times a number q and 8 is 13
Checking the Solution of a Simple equation in SIMPLE EQUATIONS_07
The solution of an equation means a value or a number that satisfies the equation. i.e. on replacing the variable with that number, LHS and RHS of the equation must have equal values.
For example, consider the equation x+3=9, we know that 6 is the only number which on addition to 3 gives 9 as answer. Therefore x=6 is the unique solution of the equation x+3=9.
We cannot find another solution that satisfies the same equation. This is because linear equation in one variable has a unique solution.
An equation may have more than one solution if it is non-linear or has more than one variable.
Solving of a Simple equation in SIMPLE EQUATIONS_07
The solution of a simple equation is also known as the root of an equation. The solution or root of an equation is that particular value of the variable which satisfies the equation. Recall that a linear equation in one variable has a unique solution.
Let us consider a simple equation x+3=7, by replacing the unknown variable x by number we can rewrite the equation and putting one by one some numbers we can get our solution. When we put 6 it gives us 9 , means 6 is the solution of this simple equation. But this method can not be useful for each and every type of equation, so normally we use TRANSPOSING METHOD for finding solution of a simple equation.
What is Transposing Method
The most common method used for solving simple equations is the method of transposing. The word transpose means “Changing the side of a number”. The following rules are followed in this method.
- Addition becomes Subtraction on changing the side.
- Subtraction becomes Addition on changing the side.
- Multiplication becomes Division on changing the side.
- Division becomes Multiplication on changing the side.
Some Exercises from NCERT book Class07 (New edition)
NCERT BOOK link –
https://ncert.nic.in/textbook.php?gemh1=4-13
Q4 (Exercise-4.1) Write equations for the following statements
- The sum of numbers x and 4 is 9
- 2 subtracted from y is 8
- Ten times a is 70
- The number b divided by 5 gives 6
- Three-fourth of t is 15
- Seven times m plus 7 gets you 77
- One-fourth of a number x minus 4 gives 4
- If you take away 6 from 6 times y, you get 60
- If you add 3 to one-third of z, you get 30
Answers-
- X+4=9
- Y-2=8
- 10a=70
- b/5=6
- 3t/4=15
- 7m+7=77
- x/4-4=4
- 6y-6=60
- z/3+3=30
Simple Equations- Worksheet