---
tags: mth225, dailyprep
---

# Daily Prep 1.4 -- MTH 225

## Overview

While we're on the subject of division, this lesson takes a step back into base 10 to look at the **Division Algorithm**, a central tool in arithmetic and computer science. In the process, you'll learn about the **modulus operator** which has a multitude of uses in computing and cryptography. We'll also learn how to represent negative integers using the **two's complement** method.

## Learning objectives

**Basic Learning Objectives:** *Before* our class meeting, use the Resources listed below to learn all of the following. You should be reasonably fluent with all of these tasks prior to our meeting; we will field questions on these, but they will not be retaught.

- State the Division Algorithm.
- Find the quotient and remainder when dividing one (base 10) integer into another.
- Explain how the modulus or `%` operator works.
- Find the values of `b % a` where `b` and `a` are positive integers.

**Advanced Learning Objectives:** *During and after* our class meeting, we will work on learning the following. Fluency with these is not required prior to class.

- Find the values of `b % a` where `a` is positive but `b` is negative.
- Draw conclusions about the relationship between $a$ and $b$ given information about `b % a`.
- Find the binary representation of a negative integer using two's complement.

## Resources for learning

**Video:** Watch this from [the MTH 225 playlist](https://vimeo.com/showcase/8667148) (total running time 15:26):

<div style="padding:56.25% 0 0 0;position:relative;"><iframe src="https://player.vimeo.com/video/583046507?badge=0&amp;autopause=0&amp;player_id=0&amp;app_id=58479&amp;h=ef4d7d314f" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen style="position:absolute;top:0;left:0;width:100%;height:100%;" title="Screencast 1.8: The Division Algorithm and the modulus operator"></iframe></div><script src="https://player.vimeo.com/api/player.js"></script>

<div style="padding:56.25% 0 0 0;position:relative;"><iframe src="https://player.vimeo.com/video/583067547?badge=0&amp;autopause=0&amp;player_id=0&amp;app_id=58479&amp;h=295e39feb6" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen style="position:absolute;top:0;left:0;width:100%;height:100%;" title="Screencast 1.9: Two&amp;#039;s complement representation"></iframe></div><script src="https://player.vimeo.com/api/player.js"></script>

You are free to search for and use other resources in addition to, or instead of the above, as long as you can work the exercises below.

## Exercises

Once you have watched the videos above, go to this form and complete all the non-optional items on it:

https://docs.google.com/forms/d/e/1FAIpQLScToDS0GKX5a1m347u39qRwOd-ZGBmwoKMLz0fyJXlTYYuSHw/viewform

## Submission and grading

**Submitting your work:** Your work is submitted when you submit the Google Form. You should receive an email receipt indicating that the work was submitted successfully.

**How this is graded:** The pre-class portion of the Daily Prep is graded either 0 points or 1 point, on the basis of completeness and effort. Wrong answers are not penalized. Earning a "1" requires that you:

- Turn the work in before its deadline;
- Leave no item blank or skipped, even accidentally; and
- Give a good-faith effort at a correct answer on every non-optional item.

More information can be found in the [Specifications for Satisfactory Work in MTH 225](/Cy6P0rGZQzuOM3NwZ3ZuMw) document.

When you arrive for the class meeting, you'll be put into a group of 2-3 to complete a quiz over this material, which will be graded on a 0/1 scale on the basis of correctness.