Tag Archives: number line

Fraction subtraction construction

So, you want to do a fraction subtraction. Here’s how, as a geometrical construction. You will need a piece of paper and a ruler.

Draw three number lines through a common point, which is the zero. Pick a nice point on the middle line to be the 1, say 6 inches away from the zero. Label the other two number lines 1,2,3,4,5,6,7 at equally spaced points, scale completely immaterial.

Now do what is shown in the picture below. (the pairs of lines are parallel)

Image

Now measure the distance with the ruler, and divide by 6 (if you put the 1 at the 6 inch point).

Bingo!

A simpler version of this (2 number lines) can be used to locate the point on the number line corresponding to any (relatively simple) fraction.

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Number lines, or lines with numbers on them

Image

It sure is a number line, and it works perfectly well with the whole or natural numbers.

The question is “How did the number line become straight, with equally spaced numbers, when the ideas of length and measurement have not yet been developed?”.  This is the math version of the “what came first, the chicken or the egg?” question.

And, with zero not there no-one can take my last cupcake.

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