Environmental Engineering Reference
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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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