Reduce a Fraction
Entire or Mixed Quantity: Section 3.4
Reduce a fraction to an entire or mixed quantity.
1. Reduce the following fraction to a mixed quantity:
ab + x ------ b
OPERATION:
ab + x
------ =
b
x
a + ---
b
ANALYSIS -
Since the value of the
fraction is the quotient of the numerator
divided by the denominator, we
perform the division indicated, and
obtain a for the entire part of the quotient, and the
fractional part follows.
x + --- b
The following sequence breaks the steps down:
ab + x ------ = b ab x -- + - 1 b lowest common denominator: ab x -- + - b b b cancels itself: a x x - + - = a + - 1 b b
RULE -
- Divide the numerator by the denominator as far as possible, for the entire part.
- Write the remainder over the denominator, and annex the fraction thus found to the entire part, with its proper sign.
NOTE - If any term be found in the numerator, whose literal part is exactly divisible by some term in the denominator, and having a greater coefficient than this term of the denominator, the reduction will be posssible; otherwise, it will be impossible.
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