Modulus Operations

Take a look at the console below. What do you think the % operator does?

% operator

The % performs a "modulus operation." Modulus operations give the remainder of division problems.

Below is a table that captures the same information that we were calculating in the console above:

Problem         Division answer     Division remainder   Mod answer 
0 / 4           0                   0                       0
1 / 4           0                   1                       1    
2 / 4           0                   2                       2
3 / 4           0                   3                       3
4 / 4           1                   0                       0
5 / 4           1                   1                       1
6 / 4           1                   2                       2
7 / 4           1                   3                       3
8 / 4           2                   0                       0
9 / 4           2                   1                       1
10 / 4          2                   2                       2
11 / 4          2                   3                       3
12 / 4          3                   0                       0
13 / 4          3                   1                       1
14 / 4          3                   2                       2
15 / 4          3                   3                       3
16 / 4          4                   0                       0
17 / 4          4                   1                       1

Take a look at that: the division remainder and mod answer columns are precisely the same!

mods in the real world

You might use modulus operations every day if you look at an analog clock: there, the hour hand swings from 1 to 12, even though there are 24 hours in the day. So when it's 5pm, it's the 17th hour of the day: 12 + 5 = 17 and 17 % 12 = 5

If you'd like to try another clock-math exercise to sharpen your mod skills, here's a good one.

Challenge

Fill in the "Division remainder" and "Mod answer" columns of the below table. If you like, type the mod problem into the console:

Problem         Division answer     Division remainder   Mod answer 
0 / 5           0                   ?                       ?
1 / 5           0                   ?                       ?    
2 / 5           0                   ?                       ?
3 / 5           0                   ?                       ?
4 / 5           0                   ?                       ?
5 / 5           1                   ?                       ?
6 / 5           1                   ?                       ?
7 / 5           1                   ?                       ?