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Manipulating Numbers

Image of Two Hands With Numbered Fingers Performing a MultiplicationHow do we count more rapidly?

If we have five buns and are given three more, we can add them to our total … six, seven, eight.  If the numbers are larger, however, that method becomes impractical.  For example, adding 120 in this way, even if you could add an extra two numbers per second, the exercise would take you one minute!  Larger additions would take even longer.

To overcome this problem, people rapidly learned to use calculating tools … fingers, sticks, and pebbles in order to calculate.  In fact, our word calculate comes from the Latin word calculus (meaning small pebble) because that is what citizens of the Roman Empire used at one stage for adding figures.  Later, the abacus was invented and used extensively in many parts of the world.  In time, many other calculating tools were created as well … Napier’s Bones, Genaille-Lucas Rulers, logarithms, and mechanical and electronic calculating devices (and others).

People also tried to calculate mentally or using marks on paper.  These methods were more abstract and often required learning ‘tables’ of common calculations.  For example, memorising 5 + 3 = 8 would make the exercise of adding the buns very much more rapid!

Eventually, algorithms (strategies or methods) were developed for rapid calculation using all four operations (and more).  You will learn about a variety of those (mental and paper-based) algorithms here.

Adding and Subtracting Integers (Whole Numbers)

Powers, Indices, Roots, Radicals and Surds

Thank you for this video. In a perfect world you would have been my trigonometry teacher in 1967.
Timothy Thomas (on a CCM YouTube video about How to Understand and Memorise the Four Trigonometric Identities)

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