Algebra Play – Formula & Equation Sheet
Essential formulas and equations from Ganita Prakash Part II, tailored for Class 8 in Mathematics.
This one-pager compiles key formulas and equations from the Algebra Play chapter of Ganita Prakash Part II. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Formulas
x + 2 = y
Here, x is the original number, and y is the result after adding 2. This represents a simple algebraic operation.
2x + 4 = y
In this, 2x indicates doubling the original number x, followed by adding 4 to it. Useful for understanding basic manipulation.
(x + y)/2 = z
This formula calculates the average of two numbers x and y, resulting in z. Helpful for mean calculations.
y = 5M + 6
Here, y is a derived number based on month M. This relationship helps in number puzzles involving dates.
a + b = 60
This equation connects two unknowns a and b in a number pyramid puzzle where the top number is formed by their sum.
12 + c = a
This represents that the number a is derived by adding 12 to another unknown c in a pyramid context.
c + 8 = b
b is determined by adding 8 to another number c. This shows relationships in the structure of a number pyramid.
4a + 16 = 36
This equation helps to find the original number a in a grid trick situation based on the sum of its terms.
x = (y - 16)/4
Derived from the previous equation, it isolates x, allowing students to understand the concept of solving for variables.
E = mc²
This formula relates energy E to mass m and the speed of light c squared, illustrating the conversion of mass to energy.
Equations
x + 2 - x = 2
This demonstrates that regardless of the starting number x, the algebraic manipulation leads to the result 2.
y - 165 = 100M + D
This derives the date M and day D from a formula that records additions and manipulations based on date puzzles.
x + (x + 1) + (x + 7) + (x + 8) = 36
From the grid puzzle, this equation shows how to calculate the original number x based on the total provided.
2M + 4 = z
This equation connects M, the month, to z, illustrating how to derive results from a simple manipulation.
5M + 6 + 9 + D = 291
An equation relating the month M and day D that leads to a derived total, useful in the context of date puzzles.
20 + 2c = 60
This represents a simplification step in solving for c in the structure of the number pyramid.
c = 20
This is the conclusion derived from the previous equation, showing how to find a variable in a pyramid context.
100M + D = 126
This expresses the relationship derived from solving the date puzzle, isolating month M and day D.
a + b = 27
It expresses a relationship in number puzzles, where the relationship showcases the total from two variables.
pq × r
This expression shows a generic formula for calculating products when three different digits are chosen.
