Hi @Pinaki_Ghosh @Tianyang.Yu @Pinaki_Ghosh !!
Let’s break down the calculations step by step to understand how the remainder is calculated in these cases.
Case 1: 28 % 10
When both dividend and divisor are positive, calculating the remainder is straightforward. For example, when you calculate 28 % 10
, the quotient is 2 and the remainder is 8. This is because:
28 = 10 * 2 + 8
Case 2: -28 % 10
Now, let’s consider the case of a negative dividend, such as -28 % 10
. In this case, the goal is to find a positive remainder that satisfies the equation:
-28 = 10 * quotient + remainder
However, because we want the remainder to be positive, we need to adjust the equation accordingly. Since the divisor is positive (10), the remainder should be positive, and the quotient might need to be decreased to make this equation work.
To find the correct quotient, we can test values until we find one that works:
- Quotient = -2, Remainder = -28 - (10 * -2) = -8 (Not positive)
- Quotient = -3, Remainder = -28 - (10 * -3) = 2 (Positive)
So, in the case of -28 % 10
, the quotient is -3, and the remainder is 2, which means:
-28 = 10 * -3 + 2
Case 3: -298 % 10
The same reasoning applies to your other example, -298 % 10
, where the quotient is -30 and the remainder is 2:
-298 = 10 * -30 + 2
Case 4: print(28 % -10)
In this case, the dividend is 28 and the divisor is -10. Similar to the previous examples, we want to find the quotient and remainder that satisfy the equation:
28 = -10 * quotient + remainder
Since the divisor is negative (-10), we want the remainder to be negative to satisfy this equation. To find the appropriate quotient, we can test values:
- Quotient = -2, Remainder = 28 - (-10 * -2) = 8 (Not negative)
- Quotient = -3, Remainder = 28 - (-10 * -3) = -2 (Negative)
So, in the case of 28 % -10
, the quotient is -3, and the remainder is -2, which means:
28 = -10 * -3 + (-2)
This demonstrates that when the right-hand operand (divisor) is negative, the remainder can also be negative.
Case 5: 34.4 % 2.5
In this case, we have a floating-point dividend (34.4) and a floating-point divisor (2.5). The modulo operation works similarly for floating-point numbers. The goal is to find the quotient and remainder that satisfy the equation:
34.4 = 2.5 * quotient + remainder
We can perform the division to find the quotient:
quotient = 34.4 / 2.5 = 13.76
Now, we need to find the remainder:
remainder = 34.4 - (2.5 * 13.76) = 34.4 - 34.4 = 0
So, in the case of 34.4 % 2.5
, the quotient is approximately 13.76, and the remainder is 0, which means:
34.4 = 2.5 * 13.76 + 0
This shows that the remainder can indeed be a floating-point value.
In summary, when dealing with a negative dividend and a positive divisor, the remainder is adjusted to be positive by finding the appropriate quotient that makes the equation work. This is why you get a positive remainder in these cases.
The modulo operation can handle both negative dividends and negative divisors, and it also works with floating-point numbers, calculating the remainder accordingly.
I hope it helps. Happy Learning