Simplifying a ratio means rewriting two quantities in an equivalent form by dividing both terms by their greatest common factor, preserving the same comparison and multiplicative relationship; for example, becomes . The relationship can be represented with ratio notation, fraction form, tables, or diagrams, while dividing only one term or subtracting the same number from both terms changes the ratio; the focus is on positive whole-number ratios, not more advanced algebraic or generalized real-number cases.
A ratio compares two quantities. To simplify a ratio, divide both terms by their greatest common factor (GCF).
Simplify the ratio
Find the GCF of and .
The factors they have in common are and , so the GCF is .
Divide both terms by :
Simplify:
Therefore,
The ratio stays equivalent because both terms were divided by the same number. Do not divide only one term or subtract the same number from both terms, because that changes the comparison.
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