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.
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Detailed Explanation: Simplify ratios
A ratio compares two quantities. To simplify a ratio, divide both terms by their greatest common factor (GCF).
Example
Simplify the ratio
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Find the GCF of and .
The factors they have in common are and , so the GCF is .
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Divide both terms by :
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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.
Learn by doing: Simplify ratios
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Practice:
Ratios - Calculate Item Ratio from Values (From Image)
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Download/Modify Free Grade 7 'Simplify ratios' Worksheet
Print this free 'Simplify ratios' worksheet to practice this skill away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Ratios - Calculate Item Ratio from Values (From Image)
- Ratios - Calculate Item Ratio from Values
- Ratios - Simplified Ratios
- Ratios - Calculate Total Ratio from Values (From Image)
- Ratios - Calculate Total Ratio from Values
- Division - Power of Ten Equivalent - Whole Numbers
Units Teaching This Skill
These adaptive units introduce, teach, or reinforce this skill (Simplify ratios) through scaffolded problems that grow in difficulty as concepts are understood.