How is remainder calculated with modulo when solving fractions?

Question

As you can see, dividing 3/7 yields a fraction. But when I do 3%7 it yields 3. How could this be? I suppose I expected an output value of 4 (because it would take 4 to complete 7) or 0, (because there is no remainder at all if you use integer division such as 3//7).

>>> 3/7
0.42857142857142855
>>> 3%7
3
>>> 

Just trying to understand the depths of Python. Thanks!

Answer 1

Remember long division? Before you learned about fractions, 50 divided by 7 would be 7, remainder 1 . The remainder is the modulus. It is the numerator of the 1/7 remaining after integer division.

Answer 2

Let's use different numbers for demonstration.

42 divided by 5 gives a quotient of 8 and a remainder of 2. That means 42 // 5 == 8 and 42 % 5 == 2 .

3 divided by 7 gives a quotient of 0 and a remainder of 3. That means 3 // 7 == 0 and 3 % 7 == 3 .

In Python, // and % represent the quotient and remainder you probably learned about before you learned about fractions and real numbers. The only (possible) difference is that // floors and % matches the sign of the right-hand operand.

Answer 3

modulo returns the whole number after integer (floor) division.

>>>3//7
0 # with remainder 3
>>>3%7
3
>>>2//5
2 # with remainder 1
>>>2%5
1

Answer 4

Re-reading your question, it occurred to me you got your terms mixed up and that may have been the underlying confusion that none of us properly answered.

But when I do 3%7 it yields 3. How could this be? I suppose I expected an output value of 4 (because it would take 4 to complete 7)

So first that issue was masked when you said 4. Since 4 is greater than 3, 3 can be subtracted a second time, leaving 1. So 1 is the output of 7 % 3 .

But you asked about 3 % 7 , even though you then proceeded to explain 7 % 3 . 3 % 7 is less than 1 (because 7 > 3). So that is why the modulus is still 3. Integer division gives you 0, so 3 is left.

Take the first term (3) divided by the second term (7) using integer division (resulting in 0). Subtract that number from the first term (3) and you get 3. So: 3 % 7 = 3