# The Necessity of Long Division

Do you remember learning to do long division back when you were in grade school? It was probably fourth or fifth grade when we learned to do it. It was a long and laborious process and one that, even in my day, seemed irrelevant. After all, we all had calculators and we knew that they could do it quickly and easily. With the tapping of a few buttons we could get our solution and it would be correct every time. Kids today can probably make an even better argument that division is best handled by computers or calculators. I’ve little doubt that once most of them are out of school they never do long division again.

In case you’ve forgotten, here’s a good step-by-step example of long division in operation (drawn from Wikipedia).

950 divided by 4:

1. The dividend and divisor are written in the long division tableau:



Now instead of dividing the whole dividend (950) by the divisor (4) we will simply divide each digit of the dividend by the divisor, one at a time, starting from the most significant (leftmost) digit:

2.The first number to be divided by the divisor (4) is the leftmostdigit (9) of the dividend. Ignoring any remainder, we write the integer part of the result (2) above the division bar over the leftmost digit of the dividend.

Since we ignored the remainder, though, we have not accounted for the leftmost place entirely. That is to say: 4 2 is merely 8, and the relevant digit of the dividend was 9. Thus we subtract 8 from 9, yielding the remainder 1, to tell us how much of the leftmost place remains unaccounted for.



3. We “bring down” this unaccounted-for remainder from the leftmost place (1) then bring down the next digit of the dividend (5) and place it to the right of the remainder to create a new bottom number (15).



4. Next we repeat steps 2 and 3, using the newly created bottom number (15) as the active part of the dividend, dividing it by the divisor (4) and writing the results as before above and under the next digit of the dividend.



5. We repeat step 4 until there are no digits remaining in the dividend. The number written above the bar (237) is the quotient, and the result of the last subtraction is the remainder for the entire problem (2).



The answer to the above example is expressed as 237 with remainder 2. Alternatively, one can continue the above procedure to produce a decimal answer. We continue the process by adding a decimal and zeroes as necessary to the right of the dividend, treating each zero as another digit of the dividend. Thus the next step in such a calculation would give the following:



I’m sure you remember this kind of problem and solution. You probably remember hating having to go through all the bother. You probably remember, as I do, trying to get out of it. The argument my teachers made, and the argument I’m sure teachers continue to make today, is that doing the onerous task of long division not only teaches us how to do it on our own for those rare occasions that a computer or calculator or cell phone isn’t handy, but it also teaches how division works. By going through each step we see how it works—we learn not only the solution, but we also learn the process of solving it. It isn’t fun, but neither is it meant to be. It’s an educational process.

Since the release of my book I’ve done all kinds of written and radio interviews and I’ve spoken to many people about the book face-to-face. A question that gets asked often is what I hope people will take from the book—what are one or two things that I really want people to learn. And this is where the parallel to long division comes in. If there is just one thing I want people to take away from the book it’s the categories of discernment. If Christians can read the book and begin to think in the black and white terms of discernment, I’ll be well pleased. Just knowing that discernment is an expectation for all of us is valuable knowledge and something many Christians really do not understand.

And second to that, I want people to realize that discernment is something we are responsible for as individuals. We cannot simply leave discernment to the experts. Rather, we each need to learn to discern and we each need to grow in the skill of discernment. Like using a calculator for division, we can rely on others to give us the bottom line. But like doing long division, it is far better to do the work ourselves and to ensure we understand how to discern. The theological equivalent of using a calculator may be just Googling what John Piper or John MacArthur says about a certain topic and taking that word as law. It may be asking a parent or pastor and accepting what they say without further thought. We are all prone to want to get to the final tally without going through the intervening steps.

But like the kid who cheats by using a calculator, we cheat ourselves if we do not do the difficult work of discernment. As we discern what is good and what is evil, what is right and what is wrong, we train ourselves to think as Christians and we train ourselves to really understand what discernment is. We make sure that we understand the difficult business of discernment—not only the end result but the process of getting there.

The theological equivalent of using a calculator may be just Googling what John Piper or John MacArthur says about a certain topic and taking that word as law.”

Totally guilty, here…especially since my free time has eroded with the arrival of two babies.

Thanks for the reminder, Tim! (Though your feelings toward long division leave me quite disconcerted. Who could hate long division? ;D)

Hey, I read theology blogs because I was promised there would be no math!

I think about shorts cuts in life…

I don’t take the scenic route, that is full of God’s grace and wonder and blessings. Instead, I head to the onramp to the Interstate because that’s what gets me there faster.

David, Red letter Believers Blog”Salt and Light”http://www.redletterbelievers.com

Tim, thank you for bringing this to light. I read your book a year ago, and since have studied much doctrine on my own, and have learned so much that the evangelical church has not taught in the past 40 years.

Several years ago, when Rick Warren first came out with his Promise book, I knew something about him was wrong, but if I would have read the book I would not have seen anything wrong. I received his Christmas book last week from my sister. I just read a couple of pages and could see where he is inaccurate in his teaching.

You are correct, we “cannot simply leave discernment to the experts”. We are responsible to know what God has to say, and we need to study the Bible to be able to discern what is correct.

It’s sort of like making discernment (or division) our own, isn’t it? I took your book to a new women’s study I’m leading just to hold it up and show it to them and say, see, there is teaching—here is a whole book—written about this important topic. Just to try to begin a category for it in their minds, that there is discernment and it’s something they are responsible for.

Thanks for this post, Tim, it’s helpful and I’ll share it with our group when we meet again.

I remember reading on here once that you do not homeschool. You certainly could pass for a homeschool dad/teacher/principal with this post!

Let me know when you get to calculus…I’ll need the help!

Happy New Year and all the best to you!

Yes, I think if we have a calculator, we should use it. That’s why we’re led by the Spirit. The real reason I hated the division process was that I hated division. It wasn’t a topic of interest for me. In spiritual matters, though, if we love God the way we say we do, then diving into the process to learn more about Him is something we’ll want to do. And of course, as with division, the more we do it, the easier it becomes because we start seeing the patterns over and over again.

-Marshall Jones Jr.

Oh, I wasn’t sure where you were going with this post. Teaching long division to my first seven children was always stressful. I still have three more to go… I thought maybe you were just commiserating with me for a while there. Really, though, it isn’t quite so bad now that I’VE learned it well enough. It makes it easier to explain. That’s the way it is with the rest of life. We learn it best when we have to turn around and teach it. Anyway, I wrote a home school e-mag issue on “Learn to Disern: To Know and Do What is Right and True” a couple of years ago. You can find it here: http://www.virginiaknowles.com/learntodiscern

Fallacies do not cease to be fallacies because they become fashions.” G.K. Chesterton

Men occasionally stumble over the truth, but most of them pick themselves up and hurry off as if nothing had happened.” Winston Churchill

AMEN and AMEN !As a “laymen” I have had no “formal” education in biblical languages or hermenutics or any other such thing but as I have read scripture and ask the Holy Spirit to give me wisdom and understanding I quickly learned that it was my resposibility to “do the long work” myself. I realized that as I studied to know my God and His Son it required me to realy know His word. The beauty of it is that as I studied and poored my heart into knowing Him through His word (by learning a sound hermenutic and practicing it regularly) I began to become passionate about it and He began to become my life. A wonderful Godly friend of mine once told me that in order to be prepared to preach the word of God (which he refers to as the “sweet work”) we must first do the “sweat work”. I have over the years found the sweat to be a joy.

Great article. Paul’s exhortation is to “study to show yourself approved unto God.” This is a work of discipline, like learning long division. Googling our favorite preachers, whom we love, respect and thank God for, does not “make every effort” to show that I am that “proven worker who does not need to be ashamed, teaching the message of truth accurately.” (2 Tim2:15NET).

No wonder why I appreciated your book……I loved long division problems! Thanks for making that connection. However, I admit that I often check out Piper’s, MacArthur’s, and others (including this site!) on current books, issues and trends.

The theological equivalent of using a calculator may be just Googling what John Piper or John MacArthur says about a certain topic and taking that word as law.”

This is not a swipe at MacArthur or Piper, but I’m of the opinion that there are far too many MacArthurites and Piperites in the world. My dad taught me long division when I was in the first grade and I divided the hits into the at bats for my entire baseball card collection to double check the batting averages. I found a few typos. ;)

Not to mention, MacArthur is wrong half the time!

But seriously, this is what TR folk are doing. Slavishly following the confessions without doing the exegesis.

Tim,Excellent post. You totally zinged me with the Piper/MacArthur theological calculator. I am guilty of that sometimes.

Now a big question for all here: How do you respond to the accusation that when you discern and likely point out good and bad things, people say: “That is not what Jesus wants! That breaks Jesus’ heart! You are the kind of person who creates divisions in the church and Jesus hates that!” and “Don’t you have better things to do with your time? With all the time you spend blogging and discerning you could have went out and built a house for the homeless, etc.”

Now I forget what logical fallacy that type of argument is (the one where they don’t address the true issue)…but I encounter this first and secondhand alot.

Thoughts?

I find this a rather simplistic analogy. It does not take into account the fact that there are some people who will never have the intellect, maturity, tenacity, education and so on to be able to right;y divide the word of truth. To say to them in such broad terms, your being lazy is rather lacking in wisdom and discernment. These people need the Pipers, Macarthurs, elders, teachers etc (as do we all). Yes, as much as is possible we should be Bereans when someone is teaching us.
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