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082-Basic Arithmetic

Quotient and Remainder…When do you use it?

In arithmetic class today, we were working on some classic Quotient and Remainder problems. You know the ones…something like, “determine the quotient and remainder when you divide 425 by 17”. There are several ways to accomplish this task and, if that is your purpose in viewing this post, you can watch some worked out examples via the links below:

Example 1

Example 2

The bigger question, which was posed by a student in class today, is “why would we want to do the task” or more commonly phrased as “when are we ever going to use this?” My usual response to this question is…”well, it depends on why you asked…did you ask because you are really curious or because you are frustrated with these problems and don’t want to learn this concept?” Today I could tell that the student was sincere (at least I THINK he was!) and really wanted to know when, ever, in our daily lives on this earth would we ever need to work with the concept of Quotient and Remainder except in math class.

Since I was not satisfied with the initial response I gave him, I thought I would take some time today and try to explain/demonstrate with some other ideas.  When we are faced with the words, QUOTIENT and REMAINDER, they are big and fancy words that just represent the components of division. When we are asked to work with Quotient and Remainder, then we are asked to avoid decimals and work with only whole numbers. So, any division problem you can think of for which you only care about the whole number components is one that can be solved by finding the Quotient and Remainder.

Let’s look at some very simple but real-word examples.

Example 3: You are hosting a small party next week and are providing canned sodas for your guests to drink. Twelve people said they were coming over and at last count, you had thirty sodas in your cooler. How many sodas do you have per person?

So, you have twelve and twelve and six makes thirty sodas meaning each person can have two (the QUOTIENT) and there will be six (the REMAINDER) left over. This problem is really common sense but it applies the concept of Quotient and Remainder. It is a division problem but we don’t want to know that each person gets 2.5 sodas because that just doesn’t make practical sense. So, we stick to whole number division and use the idea of Quotient and Remainder.

Here is another example.

Example 4: You run a weekly paper route for a local company and your car can hold 500 papers at a time. Your usual route involves drop offs of 20 paper bundles (one bundle each) to 41 businesses. How many trips must you make and how many papers will you carry each time?


So, the total papers you need to deliver is found by taking 20 x 41 = 820. You have 820 papers to deliver and your car will only hold 500. So, 820/500 = 1 with remainder 320. You will make two trips and the first will hold 500 papers and the second 320. This is another Quotient and Remainder problem with 1 being the Quotient and 320 being the remainder.

Can you think of other examples in your world? If you can, then please include them in the Comments area below.


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