To determine if the ratios \( \frac{8}{24} \) and \( \frac{10}{30} \) are equivalent, we can either simplify the fractions or use the method of cross products.
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Simplifying the fractions:
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For \( \frac{8}{24} \), we can divide both the numerator and denominator by 8: \[ \frac{8 \div 8}{24 \div 8} = \frac{1}{3} \]
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For \( \frac{10}{30} \), we can divide both the numerator and denominator by 10: \[ \frac{10 \div 10}{30 \div 10} = \frac{1}{3} \]
Since both fractions simplify to \( \frac{1}{3} \), they are equivalent.
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Cross products:
- The cross products of the two fractions are calculated as follows: \[ 8 \times 30 = 240 \] \[ 10 \times 24 = 240 \] Since the cross products are equal (both are 240), this also indicates the ratios are equivalent.
Given these two methods, the correct response is: Yes, because cross products are equal.