Short Division Makes Math Easy

Note: This is an article that ran on my homeschooling column at Examiner around 2009 titled “Long Division Is So Last Century.”

Last week a fellow homeschooling mother told me that her sons were struggling some days with long division. I cringed and admitted we had not even started on the subject at our house. The few times I’d tried to introduce long division, it had made as much sense to my children as hieroglyphics.

Or actually less, since my kids actually like hieroglyphics.

I’m a big believer of the “wait until you can teach it in a weekend” method when it comes to everything from potty training to reading. It takes so little time for kids to master most skills if it’s introduced when they’re really ready. That said, I felt a little bashful about their lack of exposure to such a classic elementary subject.

Then another homeschooling friend reminded me of this page by Lawrence Spector of the Borough of Manhattan Community College. I’d been impressed with it, recommended it and had completely forgotten about it.

Spector says that long division “belongs in the history of mathematics” because short division is so much simpler and faster. I have to say I absolutely agree with him!

I taught my nine year-old daughter, Rhiannon, short division this morning in all of three minutes. She loved it and has been doing pages of problems ever since. She’s asked me, her father, and her sister to give her more problems to do. She’s happily mastered decimals and remainers, and best of all she enjoys it.

Here are some shots of short division in action

An example comparing traditional long division versus short division for the same math problem

9 divided by 3 is 3, with nothing left over, so 3 goes over the 9

3 goes into 7 two times (making 6), so Rhiannon wrote 2 above the 7. Since 1 is left over, she wrote a 1 before the next number (2)

3 goes into 12 four times, so she wrote a 4 next (with no remainder)

3 goes into 8 two times (making 6) so Rhiannon wrote another 2, with a remainder of 2 since 8-6 is 2, revealing the final answer
(if she didn’t want to have remainers then she could add a decimal point and a zero after it and keep going, the same as in long division)

The problem is done the same way if there is a decimal. The decimal point is just inserted in the same place above, the same as with long division.

(As a note, Rhiannon is now 23 years old and for years she used to ask me to write her pages of short division problems for fun. She never did learn long division and she loves math.)

Be sure to look through the entire math curriculum at Spector’s main site, TheMathPage. It’s impressive and incredibly useful, with complete courses in arithmetic and algebra, plus topics in calculus, trigonometry and more. And it’s all free.

Have fun!