Simplifying a ratio means dividing both terms by the same common factor, often their greatest common factor, to produce an equivalent ratio in lowest terms while preserving the multiplicative relationship between the quantities. The understanding applies primarily to ratios of whole-number quantities, including forms such as and , and supports comparing equivalent ratios and solving proportions; dividing only one term changes the relationship rather than simplifying it.
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Detailed Explanation: Simplify ratios
To simplify a ratio, divide both terms by the same common factor. Using the greatest common factor (GCF) usually gives the ratio in lowest terms.
Example: Simplify .
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Find the GCF of and .
The greatest common factor is . -
Divide both terms by :
- Simplify:
So, the simplified ratio is:
The ratio stays equivalent because both terms were divided by the same number. Dividing only one term would change the relationship.
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 8 '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 - Simplified Ratios
- Ratios - Calculate Total Ratio from Values (From Image)
- Ratios - Calculate Item Ratio from Values
- Ratios - Equivalent, Expanding Recipes with Integer Multiples - Whole Numbers
- Ratios - Equivalent, Shrinking Recipes with Integer Multiples - Whole Numbers
- Fractions - Equivalent, Find Denominator - 1 digit with Equation
- Fractions - Equivalent, Find Fraction - 1 digit with Equation Graphic
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.