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Secondary Magazine - Issue 33: Focus on

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 29 April 2009 by ncetm_administrator
Updated on 11 May 2009 by ncetm_administrator

Secondary Magazine Issue 33

Focus on...division

The sign for division, ÷, is called an obelus and was first used as a symbol for division in 1659 in Teutsche Algebra by Johann Rahn. Some think that John Pell, who edited the book, may have been responsible for this use of the symbol. The obelus had been used by some writers to represent subtraction and this use continues in some parts of Europe, including Norway.

The word obelus comes from the Greek word for a sharpened stick, spit, or pointed pillar. Originally, this sign was used in ancient manuscripts to mark passages which were suspected of being corrupted or spurious.

It is quite natural for young children to associate ‘making smaller with dividing because sharing things out or breaking into groups naturally uses smaller numbers. However, it can cause confusion when division is extended to other types of numbers. It is unhelpful if the teacher reinforces that locally valid generalisation, because when the notion of number is extended, it will no longer be true, and may mislead learners into making errors. Read more about this in Mathemapedia.
What happens when you divide by zero? A professor at Reading University claimed that he had the answer in 2006, though this proved to be controversial in the mathematics community! Read more from the BBC website.

To find out if a number is divisible by 7, take the last digit, double it, and subtract it from the rest of the number. If the result is divisible by 7, then the original number is divisible by 7. For example, to test if 406 is divisible by 7, consider the last digit, 6, and double it to give 12. Taking 12 from the rest of the number gives 40 – 12 = 28. Since 28 is divisible by 7, then 406 is also divisible by 7.

Conceptually, division describes two distinct but related settings. Partitioning involves taking a set of size a and forming b groups that are equal in size. The size of each group formed, c, is the quotient of a and b. Quotative division involves taking a set of size a and forming groups of size b. The number of groups of this size that can be formed, c, is the quotient of a and b.
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