Adding and Subtracting
Lengths
Frequently, you will need to add two
lengths that are given in fractions of an inch.
Figure 4-4 illustrates direct addition by
putting two scales together. It also shows how
to add measurements given in fractions.
Subtracting dimensions given in fractions
of an inch is another skill you will need. The
procedure, shown in Figure 4-5, is nearly iden-
tical to that for addition. Note that the fractions
must have common denominators before they
can be subtracted.
When the denominators of the fractions are
not the same number, the procedure shown in
Figure 4-6 must be followed. The fractions
must be converted to equal fractions having
common (the same) denominators. Each
numerator must be increased the same number
of times as its denominator to make it equal to
the original fraction.
To solve some problems involving the
subtraction of fractions, it is necessary to
Chapter 4 Mathematics for Plumbers
89
Figure 4-4. You can add two or more dimensions by laying off the lengths on a scale. However, another way,
shown above, is to add the dimensions together using mathematics.
1
1 1
2
2 2
3 4 5 6
23∕8″ + 215∕16″ = 55∕16″
23∕8″ + 215∕16″ = _______
Denominator
Fractions can be added only when the denominators
are equal. From Figure 4-1, it can be seen that
3∕8″ = 6∕16″. Therefore, the above problem can be
rewitten as:
Numerators
26∕16″ + 215∕16″ = _______
Adding fractions is acomplished by adding
numerators. The denominators remain unchanged.
6∕16″ + 15∕16″ = 21∕16″
Since the numerator is larger than the denominator,
the fraction is greater then one (sixteen 1/16s = one).
Therefore:
21∕16″ = 16∕16″ + 5∕16″ = 15∕16″
Returning to the original problem:
23∕8″ + 215∕16″ =
Step 1 26∕16″ + 215∕16″ =
Step 2 2″ + 2″ + 21∕16″ =
Step 3 2″ + 3″ + 5∕16″ = 5 5∕16″
Denominator
Numerator
In this case:
Figure 4-3. Reading 1¼16″ intervals is easier if you
count from the nearest 1¼4″ dimension and add or sub-
tract spaces.
1 2 3
1 2
1 2 3
23∕4″ + 1∕16″
= 212∕16″ + 1∕16″ = 213∕16″
21∕2″ 1∕16″
= 28∕16″ 1∕16″ = 27∕16″
11∕4″ + 1∕16″
= 14∕16″ + 1∕16″ = 15∕16″
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