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I have the same question as the previous person to which no one answered.

1. What does “floor of the result of the division” mean?

2. Please explain why -17//10 results in 1, and why -17%10 results in 3

1. The floor of a real number is the largest integer that is less than or equal to that number. For example, the floor of 2.75 is 2, 53.1 is 53, and -2.6 is -3 (the last results may look odd, but notice that -3 is less than or equal to -2.6).

By “floor of the result of the division”, we are referring to a two step process that involves evaluating the division operation to yield a number and then taking the floor of that number.

1. Let’s begin an example involving positive numbers. `7 // 3` is 2 and `7 % 3` is 1. That result can be rewritten as 2 1/3, which is equivalent to the fraction 7 over 3.

Next, you asked why `-17 // 10` results in `1`. However, the result of evaluating that expression is `-2`.

Let’s look at floating point division first: `-17 / 10` evaluates to `-1.7`.

Now, let’s look at the integer division: `-17 // 10` evaluates to `-2`. (Following the rule for floor, -2 is the largest integer that is less than or equal to -1.7.)

And the modulo: `-17 % 10` evaluates to 3. This is the remainder of the integer division.

As we did before, this can be written as -2 3/10, which is equivalent to the fraction -17 / 10.

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