 # Unit 4 Lesson 7 Level 11 Mod Practice

I am needing help understanding the Modulo Operator
The examples given in the lesson make zero sense to me. The instructions on level 11 states: 11 divided by 2 is 5 with a remainder of 1. The answer is 1 . I am confused because 11/2 is 5.5, not 5.1. And, how does 2%3 equate to 2??? when I do the math 2/3 is 0.6666666.

I need a BASIC video explanation of the modulo operator, because I do not get it!

here is what I just discovered; and I will explain it this way to my students. Please let me know if I got it right or if there is a better way to explain it.

5 % 7

1. You would ask yourself, “what number can I multiply 7 by to get 5 without going over? In this case it is 0. So, 7 x 0 = 0. Now you take 0 and subtract it from 5; the answer is 5.
2. Therefore, 5 % 7 = 5

2 % 3

1. You would ask yourself, “What number can I multiply 3 by to get 2 without going over? In this case it is also 0. So, 3 x 0 = 0. Now you take 0 and subtract it from 2; the answer is 2.
2. Therefore, 2 % 3 = 2

5 % 2

1. You would ask yourself, “What number can I multiply 2 by to get 5 without going over? In this case it is 2. So, 2 x 2 = 4. Now you take 4 and subtract it from 5; the answer is 1.
2. Therefore, 5 % 2 = 1

10 % 2

1. You would ask yourself, “What number can I multiply 2 by to get 10 without going over? In this case it is 5. So, 2 x 5 = 10. Now you take 10 and subtract it from 10; the answer is 0.
2. Therefore, 10 % 2 = 0
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Hello @msmith,

You are correct in your thinking - and I think some of my students solve mod problems exactly like this. When the numbers are small, it works pretty well. When they get larger its a little harder to do in my head and I resort to division. To make the division a little clearer here are some thoughts:

I think the thing that the thing that made mod click for me when dividing, is that I’m trying to divide evenly. When I teach this to students, I tell them to remember back to a time in their lives (3rd, 4th grade maybe) when they learned to divide and did NOT know what a decimal is. When they learned this math, they simply figured out how many times A went evenly in to B, and everything leftover was just that - leftover. We did not subdivide it. It was a ‘remainder’. For example:

11 % 2:
11 evenly goes in to 2 five times. What is left over? 1.

Visually, distributing things to people is always helpful:
I have 11 dice, I have to be fair so each person gets the same number of dice. If I’m dividing between 2 people, we each get 5 dice. That would be 11/2 = 5. BUT when we talk about mod (%) we don’t actually care about 5, we care about how many dice were left over after the even distribution has occurred, that’s the one left over die. So 11 % 2 is 1.

Here’s another forum post that also explains mod through long division, and links to a khan academy video that makes the connection between mod and ‘clock arithmetic’. I hope that one of these options helps clear it up!

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11/2 is 5 and 1/2. The 1 is what you want.
5/7 is 0 and 5/7. 5.
2/3 is 0 and 2/3. 2.
5/2 is 2 and 1/2. 1
10/2 is 5 and 0/2. 0

Don’t use decimal points. Use fractions.