Distance Measuring - Drafting 1

BASIC DISTANCE MEASURING

The imperial system is the system of measurement used in America. This is what we will be using here at Workshop Houston.

The main units of distance in the Imperial system that we will use are inches and feet.

The Imperial system divides inches into fractions of inches. So when you do not have exactly one inch, you use a fraction to express the exact distance like “4 and 3/4 inches”.

Inches on a ruler are usually divided into 16 equal pieces.

Fractions

Fractions represent parts of a whole. In this case, they are parts of an inch.

The bottom number of a fraction – the denominator – is the number of equal parts the inch was divided into.

The top number of the fraction – the numerator – is the number parts you have. For example, 4 and ¾ inches means we have 4 whole inches and 3 of 4 equal pieces of the next inch.

The figure below shows an inch divided into 16 pieces. If it’s divided into 16 pieces, why do some fractions not have 16 as the denominator? Good question. Find out why on the next page.

Simplifying Fractions

Sometimes the same amount can be expressed by more than one fraction. Even though the numbers in the fraction change, the amount stays the same. For example:

In the first circle, we have 1 piece out of 4 total, or ¼. In the second, we have 2 pieces out of 8 total, or 2/8. The amount we have has not changed, so we can say that 2/8 is the same as ¼.

When we simplify fractions, we want to make the top number (the numerator) as small as possible. To do that we need to evenly divide the top number, but whatever we divide it by, has to divide into the bottom number, too.

So to simplify 2/8 to ¼, we divide both numbers by 2. Divide by the biggest number that goes into both the numerator and denominator.

Let’s do one using an inch. In the image below, we have an inch divided into 16 pieces. Count them to the end of the gray line and we have 12 of them, for a fraction of 12/16.

Now simplify:

Copy this image and label it on the next page:

Hint: Note how the lines are different lengths, and the denominators of the fractions on each length. 

TO DO: Complete the ruler worksheet.