Unlike denominators partition the whole into different-sized parts, so comparing their numerical values requires recognizing equivalent fractions, using a common denominator, benchmarks such as 0, 1/2, and 1, or positions on a number line. The reasoning applies to positive proper and improper fractions, including mixed numbers, and avoids the misconception that a larger denominator alone makes a fraction larger; symbolic variables, negative fractions, and more advanced generalizations are not included.
When fractions have unlike denominators, their pieces are different sizes, so compare them by rewriting them with a common denominator.
Example: Compare and .
Find a common denominator.
The least common multiple of and is .
Rewrite each fraction with denominator :
Therefore,
Remember: a larger denominator does not automatically mean a larger fraction. Rewrite the fractions so they describe the same-sized parts before comparing.
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