You reduce ratios to determine if they are proportional by expressing them as fractions and then simplifying them to their lowest terms. If the simplified fractions are equivalent, the ratios are proportional.
Here's a breakdown of the process:
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Express Ratios as Fractions: Write each ratio as a fraction. For example, the ratio 3:6 would be written as 3/6.
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Simplify Fractions: Reduce each fraction to its simplest form by dividing both the numerator and denominator by their greatest common factor (GCF).
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Compare Simplified Fractions: If the simplified fractions are the same, the original ratios are proportional. If they are different, the ratios are not proportional.
Example 1: Proportional Ratios
Let's say you have the ratios 4:8 and 1:2.
- Fraction Form: 4/8 and 1/2
- Simplify: 4/8 simplifies to 1/2 (dividing both 4 and 8 by 4). 1/2 is already in its simplest form.
- Compare: Since 1/2 = 1/2, the ratios 4:8 and 1:2 are proportional.
Example 2: Non-Proportional Ratios
Consider the ratios 2:3 and 4:5.
- Fraction Form: 2/3 and 4/5
- Simplify: 2/3 and 4/5 are already in their simplest forms.
- Compare: 2/3 ≠ 4/5, so the ratios 2:3 and 4:5 are not proportional.
In essence, reducing ratios to their simplest fractional forms allows for a direct comparison to determine if they represent the same relationship, thereby indicating proportionality.
