Addition
Algebra Help: Section 3.9
We have seen that entire quantities may be added when they have a common factor, to serve as the unit of addition. In like manner, fractions may be added when they have a common unit. Since the fractional unit is the reciprocal of the denominator, fractions to be added must have a common denominator.
1. What is the sum of a ÷ b and c ÷ b?
OPERATION:
a c a + c - + - = ----- b b b
ANALYSIS -
The fractions have a common unit; 1 ÷ b.
In a ÷ b this unit is taken a times.
In c ÷ b this unit is taken c times.
Therefore the sum of the fraction must be (a + c) ÷ b.
2. What is the sum of a ÷ b, c ÷ bn, and d ÷ bm?
OPERATION:
Reduce fractions to a common denominator:
a amn - = --- b bmn c cm - = --- bn bmn d dn - = --- bm bmn
Add all numerators, reusing the common denominator:
amn + cm + dn amn + cm + dn --- --- --- = ------------- bmn bmn bmn bmn
From these examples we derive the following rules.
RULES -
- Reduce the fractions to their least common denominator.
- Add the numerators, and write the result over the common denominator.
NOTES -
1. When there are mixed quantities, the entire quantities
and the fractions may be added separately: or the mixed quantities may
be reduced to fractions then added.
2. A fractional result should be reduced to its lowest terms.
Page 90-91
Page 90-91
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