Write a program to enter two integers and perform all arithmetic operations on them.

Exercises · Q13

Q. Write a program to enter two integers and perform all arithmetic operations on them.

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Concept understanding — Variable Difference

Variable Difference — The Intuition

Imagine you're watching two runners on a track. One runs fast, the other slow. The gap between them keeps changing — sometimes it grows, sometimes it shrinks. That changing gap is a variable difference.

Now think about a simpler case: two numbers, say 10 and 3. Their difference is 7 — fixed, constant. But what if the numbers themselves are changing? Then the difference between them changes too. That's all "variable difference" means: the difference between two quantities that are themselves varying.

Note

The word "variable" here means "changing" — not the algebraic symbol $x$ or $y$ , but the idea that the difference is not a fixed number.

The Precise Statement

Let two quantities depend on some common parameter — often time $t$ , or a variable $x$ . Call them $f(x)$ and $g(x)$ . Their difference is:

D(x) = f(x) - g(x)

Since $f$ and $g$ change with $x$ , $D$ changes too. That's a variable difference.

The key question is: how fast does this difference change? That's where calculus enters. The rate of change of the difference is simply:

D'(x) = f'(x) - g'(x)

In words: the rate at which the gap changes equals the difference of the individual rates.

\frac{d}{dx}\big(f(x) - g(x)\big) = f'(x) - g'(x)

Why This Matters

In Indian exam problems, you'll see this in two common forms:

1. Relative speed (motion problems)

Two trains leave stations at different times, moving at different speeds. The distance between them is a variable difference. Its rate of change is the difference of their speeds (if moving in the same direction) or the sum (if opposite).

2. Increasing/decreasing functions

If $f(x) > g(x)$ for all $x$ , and you want to know whether the gap widens or narrows, you check the sign of $f'(x) - g'(x)$ . Positive means the gap grows; negative means it shrinks.

Tip

Don't overthink it. Variable difference is just ordinary subtraction applied to changing quantities. The derivative of a difference is the difference of the derivatives — that's the only new idea. …

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Read two integers and apply all seven arithmetic operators:

num1 = int(input("Enter first integer: "))
num2 = int(input("Enter second integer: "))
print("Sum =", num1 + num2)
print("Difference =", num1 - num2)
print("Product =", num1 * num2)
print("Division =", num1 / num2)
print("Floor Division =", num1 // num2)
print("Modulus =", num1 % num2)
print("Exponent =", num1 ** num2)

Sample run (10 and 3):

Sum = 13
Difference = 7
Product = 30
Division = 3.3333333333333335 …

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Take two integers and print the result of every arithmetic operator (+, −, *, /, //, %, **) — for 10 and 3 the results are 13, 7, 30, 3.33…, 3, 1 and 1000.

The point of this exercise is to see all of Python's arithmetic operators side by side, especially the three division-family operators that beginners confuse: / (true division, always float), // (floor division) and % (remainder).

# All arithmetic operations on two integers
num1 = int(input("Enter first integer: "))
num2 = int(input("Enter second integer: "))

print("Sum =", num1 + num2)
print("Difference =", num1 - num2)
print("Product =", num1 * num2)
print("Division =", num1 / num2)
print("Floor Division =", num1 // num2)
print("Modulus =", num1 % num2)
print("Exponent =", num1 ** num2)

Sample run with num1 = 10, num2 = 3:

Enter first integer: 10
Enter second integer: 3
Sum = 13
Difference = 7
Product = 30
Division = 3.3333333333333335
Floor Division = 3
Modulus = 1
Exponent = 1000
``` …

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Q.Write a program to enter two integers and perform all arithmetic operations on them.

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