How To: Numbers


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

analog clock

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                   ?                       ?