Environmental Engineering Reference
In-Depth Information
Following are some of the principles associated with using fractions:
1. Same numerator and denominator: When the numerator and denominator
of a fraction are the same, the fraction can be reduced to 1; for example, 5/5
= 1, 33/33 = 1, 69/69 = 1, 34.5/34.5 = 1, and 12/12 = 1.
2. Whole numbers to fractions: Any whole number can be expressed as a frac-
tion by placing a “1” in the denominator; for example , 3 is the same as 3/1,
and 69 is the same as 69/1.
3. Adding fractions : Only fractions with the same denominator can be added,
and only the numerators are added. The denominator stays the same. For
example, 1/9 + 3/9 = 4/9, and 6/18 + 8/18 = 14/18.
4. Subtracting fractions: Only fractions with the same denominator can
be subtracted, and only the numerators are subtracted. The denominator
remains the same. For example, 7/9 - 4/9 = 3/9 (or 1/3), and 16/30 - 12/30
= 4/30.
5. Mixed numbers: A fraction combined with a whole number is a mixed
number, such as 4-1/3, 14-2/3, 6-5/7, 43-1/2, and 23-12/35. These numbers
are read, respectively, as four and one third; fourteen and two thirds; six
and five sevenths; forty-three and one half; and twenty-three and twelve
thirty-fifths.
6. Changing a fraction: Multiplying the numerator and the denominator by
the same number does not change the value of the fraction; for example, 1/3
is the same as (1 × 3)/(3 × 3), which is 3/9.
7. Simplest terms: Fractions should be reduced to their simplest terms. This
is accomplished by dividing the numerator and denominator by the same
number. The result of this division must leave both the numerator and the
denominator as whole numbers. For example, 2/6 is not in its simplest
terms; by dividing both by 2 we obtain 1/3. The number 2/3 cannot be
reduced any further because there is no number that can be divided evenly
into the 2 and the 3.
Example 4.1
Problem : Reduce the following to their simplest terms:
2/4
14/18
3/4
6/10
9/18
17/29
24/32
Solution:
2/4 = 1/2 (both were divided by 2)
14/18 = 7/9 (both were divided by 2)
3/4 = 3/4 (is already in its simplest form)
6/10 = 3/5 (both were divided by 2)
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