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.
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.