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Simplify ratios

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 a:ba:b and a/ba/b, and supports comparing equivalent ratios and solving proportions; dividing only one term changes the relationship rather than simplifying it.

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 (18:24)(18:24).

  1. Find the GCF of (18)(18) and (24)(24).
    The greatest common factor is 66.

  2. Divide both terms by 66:

18:24=(18÷6):(24÷6)18:24=(18\div 6):(24\div 6)
  1. Simplify:
18:24=3:418:24=3:4

So, the simplified ratio is:

3:4\boxed{3:4}

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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Ratios - Calculate Item Ratio from Values (From Image)


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