Operations with Integers – Formula & Equation Sheet
Essential formulas and equations from Ganita Prakash II, tailored for Class 7 in Mathematics.
This one-pager compiles key formulas and equations from the Operations with Integers chapter of Ganita Prakash II. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Formulas
P = a + b
P is the final position of the coin, a is the distance moved in one direction (positive), and b is the distance moved in another direction (can be negative if going to the left). It models movement on a number line.
a + (-b) = a - b
This represents the addition of a number and its additive inverse. It highlights how subtracting a number is equivalent to adding its negative.
x + y = z
x and y are integers; z is their sum. This is a basic representation of integer addition.
x - y = z
x is an integer from which y is subtracted, resulting in z. This represents integer subtraction.
(-a) + (-b) = -(a + b)
This shows that the sum of two negative integers is the negative of the sum of their absolute values.
If a + b = c and a - b = d, then the pairs are related where a = (c + d)/2 and b = (c - d)/2.
This helps to find two integers from the sum and difference.
a + 0 = a
This is the identity property of addition—adding zero to an integer does not change its value.
a + (-a) = 0
This shows that every integer has an additive inverse that equals zero when added together.
(a + b) + c = a + (b + c)
This is the associative property of addition, demonstrating that how we group the integers does not affect their sum.
a + b = b + a
This is the commutative property of addition, emphasizing that the order of addition does not affect the result.
Equations
S = x + y
S is the sum of integers x and y. This demonstrates basic integer addition.
D = x - y
D is the difference when y is subtracted from x. This illustrates integer subtraction.
If x + y = 25 and x - y = 11, then x = 18 and y = 7.
This equation pair can be solved systemically to find two integers.
5 + (-7) = -2
This shows an example of integer addition where a negative integer results in a negative outcome.
7 - 18 = -11
This illustrates the concept of subtracting a larger integer from a smaller one, resulting in a negative number.
P = a + b + c
P is the final position after multiple strikes where each term represents the distance moved.
-5 + 10 = 5
This equation shows the result of adding negative and positive integers.
If a = 8, then a + a = 2a.
This demonstrates the concept of doubling a number using algebraic expressions.
If x = 0, then x + y = y.
This repeats the identity property, highlighting that zero does not alter other integers.
(-3) + 4 = 1
This shows the addition of a negative integer with a positive integer.
