Operations with Fractions
Operations with Fractions
Multiplying and Dividing Fractions:
1. Common denominators are NOT needed.
2. Always change mixed numbers to improper fractions.
3. CANCEL (reduce) between any numerator and any denominator
if you can, but cancel only when a multiplication sign is
present: Never cancel when you have a division sign.
4. TO MULTIPLY: Multiply numerator times numerator,
denominator times denominator. Reduce answer to a mixed number in
lowest terms.
5. TO DIVIDE: Change the divide sign to a multiplication sign,
then invert the second fraction and multiply as in Step 4.
Adding and Subtracting Fractions:
1. Common (like) denominators are necessary, so change all
unlike fractions to equivalent fractions with like denominators.
To make equivalent fractions, multiply the numerator and
denominator by the same number.
2. Keep mixed numbers; DO NOT change mixed numbers into
improper fractions.
3. Add (or subtract) the numerators, put the numerator answer
over the common denominator. If any improper fractions arise in
the answer, change the improper portion to a mixed number.
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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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operations with complex numbers (simplifying, rationalizing complex denominators...) |
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solving a system of two and three linear equations (including Cramer's rule) |
|
graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions) |
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graphing general functions |
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operations with functions (composition, inverse, range, domain...) |
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simplifying logarithms |
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