5.7: Summary of Key Concepts

Addition and Subtraction of Fractions with Like Denomi­nators
To add or subtract two fractions that have the same denominators, add or subtract the numerators and place the resulting sum or difference over the common denomi­nator. Reduce, if necessary. Do not add or subtract the denominators.
\(\dfrac{1}{8} + \dfrac{5}{8} = \dfrac{1 + 5}{8} = \dfrac{6}{8} = \dfrac{3}{4}\)

Basic Rule for Adding and Subtracting Fractions
Fractions can be added or subtracted conveniently only if they have like denomina­tors.

Addition and Subtraction of Fractions with Unlike Denominators
To add or subtract fractions having unlike denominators, convert each fraction to an equivalent fraction having as denominator the LCD of the original denominators.

Addition and Subtraction of Mixed Numbers
1. To add or subtract mixed numbers, convert each mixed number to an improper fraction, then add or subtract the fractions.

Ordered Number System
Our number system is ordered because the numbers in the system can be placed in order from smaller to larger.

Inequality Symbols
> represents the phrase "greater than."
< represents the phrase "less than."

Comparing Fractions
If two fractions have the same denominators, the fraction with the larger numera­tor is the larger fraction.
\(\dfrac{5}{8} > \dfrac{3}{8}\)

Simple Fractions
A simple fraction is any fraction in which the numerator is any whole number and the denominator is any nonzero whole number.

Complex Fractions
A complex fraction is any fraction in which the numerator and/or the denominator is a fraction.

Complex fractions can be converted to simple fractions by employing the methods of adding, subtracting, multiplying, and dividing fractions.

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