To compare the ratios \(3:8\) and \(4:12\), we can simplify each ratio.
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Simplifying \(3:8\):
- This ratio is already in its simplest form.
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Simplifying \(4:12\):
- Divide both numbers by their greatest common divisor (which is 4): \[ 4 \div 4 = 1 \quad \text{and} \quad 12 \div 4 = 3 \]
- So, \(4:12\) simplifies to \(1:3\).
Now, we can express these ratios as fractions to compare them:
- The ratio \(3:8\) can be represented as the fraction \(\frac{3}{8}\).
- The ratio \(4:12\) can be represented as the fraction \(\frac{1}{3}\).
Next, we need to compare \(\frac{3}{8}\) and \(\frac{1}{3}\). To do this, we can find a common denominator:
- The least common multiple of 8 and 3 is 24.
Now convert both fractions:
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Convert \(\frac{3}{8}\) to a fraction with a denominator of 24: \[ \frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24} \]
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Convert \(\frac{1}{3}\) to a fraction with a denominator of 24: \[ \frac{1}{3} = \frac{1 \times 8}{3 \times 8} = \frac{8}{24} \]
Now we compare \(\frac{9}{24}\) and \(\frac{8}{24}\):
- Since \(9 > 8\), it follows that \(\frac{9}{24} > \frac{8}{24}\).
Therefore, \(3:8\) is greater than \(4:12\).
In conclusion: Of the ratios \(3:8\) and \(4:12\), the ratio \(3:8\) is greater.