Adding and Subtracting Fractions
Adding and Subtracting Fractions
Before you start adding and subtracting fractions, you should
know how to find the lowest common denominator of at least two
fractions. You need to find a common denominator in order to
express the fractions being added or subtracted in the same
proportions.
Example #1:
In the fractions  , the lowest common denominator is 15. This is the
lowest number that is a multiple of both 3 and 5.
Example #2:
Now let's add the fractions:
 Whatever we multiply the denominators by,
we must multiply the numerators by.
Example #3:
Let's subtract fractions:
Whatever we multiply the denominators by, we must multiply the
numerators by.
Example #4:
The common denominator is 8. Why isn’t it 4? 2?
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|
simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values) |
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|
finding LCM and GCF |
|
operations with complex numbers (simplifying, rationalizing complex denominators...) |
|
solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations) |
|
solving a system of two and three linear equations (including Cramer's rule) |
|
graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions) |
|
graphing general functions |
|
operations with functions (composition, inverse, range, domain...) |
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simplifying logarithms |
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arithmetic and other pre-algebra topics (ratios, proportions, measurements...) |
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