Question

modular and floor division for python code
due: tuesday, september 16, 2025 at 11:59 pm

• 7 % 3
• 7 // 3
• 10 % 4
• 10 // 4
• -7 % 3
• -7 // 3
• 7 % -3
• 7 // -3
• 15 % 6
• 15 // 6

posted today at 3:12 pm
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Explanation:

Step1: Recall modular operation rule

The modular operation a % b gives the remainder of a divided by b. The floor - division a // b gives the largest integer less than or equal to the quotient of a divided by b.

Step2: Calculate 7 % 3

$7\div3 = 2$ with a remainder of $1$, so $7\%3 = 1$.

Step3: Calculate 7 // 3

The quotient of $7\div3$ is approximately $2.33$, and the largest integer less than or equal to it is $2$, so $7//3 = 2$.

Step4: Calculate 10 % 4

$10\div4 = 2$ with a remainder of $2$, so $10\%4 = 2$.

Step5: Calculate 10 // 4

The quotient of $10\div4$ is $2.5$, and the largest integer less than or equal to it is $2$, so $10//4 = 2$.

Step6: Calculate -7 % 3

First, find $-7\div3=-2.33\cdots$. The remainder is such that $-7 = 3\times(- 3)+2$, so $-7\%3 = 2$.

Step7: Calculate -7 // 3

The largest integer less than or equal to $-2.33\cdots$ is $-3$, so $-7//3=-3$.

Step8: Calculate 7 % -3

First, find $7\div(-3)= - 2.33\cdots$. The remainder is such that $7=(-3)\times(-3) - 2$, so $7\%-3=-2$.

Step9: Calculate 7 // -3

The largest integer less than or equal to $-2.33\cdots$ is $-3$, so $7// - 3=-3$.

Step10: Calculate 15 % 6

$15\div6 = 2$ with a remainder of $3$, so $15\%6 = 3$.

Step11: Calculate 15 // 6

The quotient of $15\div6$ is $2.5$, and the largest integer less than or equal to it is $2$, so $15//6 = 2$.

Answer:

$7\%3 = 1$
$7//3 = 2$
$10\%4 = 2$
$10//4 = 2$
$-7\%3 = 2$
$-7//3=-3$
$7\%-3=-2$
$7// - 3=-3$
$15\%6 = 3$
$15//6 = 2$