Arithmetic Additive Identity Associative Property Averages Brackets Closure Property Commutative Property Conversion of Measurement Units Cube Root Decimal Distributivity of Multiplication over Addition Divisibility Principles Equality Exponents Factors Fractions Fundamental Operations H.C.F / G.C.D Integers L.C.M Multiples Multiplicative Identity Multiplicative Inverse Numbers Percentages Profit and Loss Ratio and Proportion Simple Interest Square Root Unitary Method
Algebra Algebraic Equation Algebraic Expression Cartesian System Linear Equations Order Relation Polynomials Probability Standard Identities & their applications Transpose
Geometry Basic Geometrical Terms Circle Curves Angles Define Line, Line Segment and Rays NonCollinear Points Parallelogram Rectangle Rhombus Square Three dimensional object Trapezium Triangle Quadrilateral
Trigonometry Trigonometry Ratios
DataHandling Arithmetic Mean Frequency Distribution Table Graphs Median Mode Range 
Home >> Equality >> Add different number >> Add different number to the sides of equality
Explanation:When different numbers are added to the sides of equation i.e. L.H.S. and R.H.S of the equation, the equality fails to hold.
Let’s understand it with the help of following examples:
Example 1  Add 5 to L.H.S. and 4 to R.H.S. of given equation and check what happens to equality
2 + 4 = 9  3
Solution  This proceeds as :
Add 5 to L.H.S. & 4 to R.H.S. of given equation and we get;
2 + 4 + 5 = 9  3 + 4
Solve L.H.S. and we get;
L.H.S. = 2 + 4 + 5
L.H.S. = 11
Solve R.H.S. and we get
R.H.S. = 9  3 + 4
Now solve as per BODMAS rule and we get;
R.H.S. = 10
Since L.H.S. in not equals to R.H.S i.e. 11 is not equal to 10
So the given equation 2 + 4 = 9  3 fails to hold equality, when we add 5 to L.H.S. and 4 to R.H.S. of given equation and hence we get that
"When different numbers are added to the sides of equation i.e. L.H.S. and R.H.S of the equation, the equality fails to hold."
Example 2  Add 10 to L.H.S. and 5 R.H.S. of given equation and check what happens to equality
10  3 = 20  13
Solution  This proceeds as :
Add 10 to L.H.S. & 5 to R.H.S. of given equation and we get;
10 + 10  3 = 5 + 20  13
Solve L.H.S. and we get;
L.H.S. = 10 + 10  3
Now solve as per BODMAS rule and we get;
L.H.S. = 27
Solve R.H.S. and we get
R.H.S. = 5 + 20  13
Now solve as per BODMAS rule and we get;
R.H.S. = 12
Since L.H.S. in not equals to R.H.S i.e. 27 is not equal to 12
So the given equation 10  3 = 20  13 fails to hold equality, when we add 10 to L.H.S. and 5 to R.H.S. of given equation and hence we get that
"When different numbers are added to the sides of equation i.e. L.H.S. and R.H.S of the equation, the equality fails to hold."


