Hamilton's Math To Build On - copyright 1993

Fractions of the Ruler

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* Fractions of the Ruler

This practice should help in your understanding of why measuring fractions are based on the number two. We will start by showing how to divide a line into equal parts.
First: Draw a 6 inch straight line. Be very precise when measuring this line.

Second: Set your compass for a distance a little longer than one half of the length of that line (greater than 3 inches).

To set a compass means to adjust the radius of the compass to a certain measurement. A compass is set by placing the compass ruler on the sharp metal point side at zero and pulling the pencil point side out to the needed distance. (In this case it doesn't really matter how much past the halfway point you set the radius, just stay on the paper.)
Third: Place the metal end point of the compass on one of the end points of the line. Draw an arc (part of a circle, not a whole) through the line. Imagine where the center point of the line would be if it was placed directly above and below the horizontal line. Extend the arc so that it passes beyond where you imagine these points to be.

Fourth: Do not change the compass setting and mark the horizontal line from the other end point using the same method as above.

Fifth: Draw a straight line between the two points where the arcs cross.

There are now two line segments.

You accomplished two things with this action:

One : You divided the line exactly in half. See for yourself. Measure each side from the enter point to the end point. Each segment should measure exactly three inches.

Two : You created two lines that are perpendicular to each other.

You will study perpendicular lines soon, but what is significant now is that the line has been divided into equal segments. (Part of a line is called a segment of a line).

Since you know that the above action with a compass divides a straight line in half, let's repeat the same action on each of the two line segments just created.

First: Set the compass for a little more than one half of the distance between an end point and the center point (greater than 1.5 inches). Mark arcs through the line (as you did above) from each end point of each line segment.

Second: Draw a straight line between the points where the arcs cross.

Each of the two segments has now been divided in half. The whole line has been divided into four equal parts or quarters. Measure the length of each segment. They should measure one and a half inches long.

If you again divide each of these line segments into equal parts, the line will be divided into eight equal parts (eighths) and each line segment will be three quarters of an inch in length.

The next division will divide the whole line into sixteen equal parts.

Each line segment should measure three eighths of an inch.

Can you see why the English or customary measuring system divides inches into 2, 4, 8, 16, or more?

On to Perpendicular Lines

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17 September 1995
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