Environmental Engineering Reference
In-Depth Information
9/18 = 1/2 (both were divided by 9)
17/29 = 17/29 (is already in its simplest form)
24/32 = 3/4 (both were divided by 8)
8.
Reducing even numbers:
When the starting point is not obvious, do the fol-
lowing: If the numerator and denominator are both even numbers (2, 4, 6, 8,
10, etc.) divide them both by 2, and continue dividing by 2 until a division
will no longer yield a whole number for the numerator and the denominator.
9.
Reducing odd numbers:
When the numerator and denominator are both
odd numbers (3, 5, 7, 9, 11, 13, 15, 17, etc.), attempt to divide by three, and
continue dividing by 3 until a division will no longer yield a whole number
with the number and denominator. It is obvious that some numbers such
as 5, 7, and 11 cannot be divided by 3 and may in fact be in their simplest
terms.
10.
Different denominators:
To add and/or subtract fractions with different
denominators, the denominators must be changed to a common denom-
inator (the denominators must be the same). Each fraction must then be
converted to a fraction expressing the new denominator. For example, to
add 1/8 and 2/5, begin by multiplying the denominators (8 × 5 = 40). Now
change 1/8 to a fraction with 40 as the denominator:
40/8 = 5, 5 × 1 = 5 (the numerator); new fraction is 5/40
Notice that this is the same as 1/8 except that 5/40 is not reduced to its sim-
plest terms. Change 2/5 to a fraction with 40 as the denominator:
40/5 = 8, 8 × 2 = 16 (the numerator); new fraction is 16/40
Complete the addition:
5/40 + 16/40 = 21/40
11.
Numerator larger:
Any time the numerator is larger than the denominator
the fraction should be turned into a mixed number. This is accomplished by
the following procedure:
•
Determine the number of times the denominator can be divided evenly
into the numerator. This will be the whole number portion of the mixed
number.
•
Multiply the whole number times the denominator and subtract from
the numerator. This value, the remainder, becomes the numerator of the
fraction portion of the mixed number. Consider 28/12:
28 is divisible by 12 twice, so 2 is the whole number
2 × 12 = 24
28/12 - 24/12 = 4/12
Dividing the top and bottom by 4 gives 1/3
The new mixed number is 2-1/3
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