To determine if the statements are proportions, we can check if the two ratios are equivalent.
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For the first equation, 168=?2412:
We can express each side as a fraction:
- This becomes \( \frac{168}{?} = \frac{?}{2412} \) or \( \frac{168}{2412} \)
- To simplify \( \frac{168}{2412} \), we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 84:
\[ \frac{168 \div 84}{2412 \div 84} = \frac{2}{28.7143} \text{ (which does not simplify nicely)} \]
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For the second equation, 84=?126:
This becomes \( \frac{84}{?} = \frac{?}{126} \) or \( \frac{84}{126} \)
- To simplify \( \frac{84}{126} \), we can also divide both by their GCD, which is 42:
\[ \frac{84 \div 42}{126 \div 42} = \frac{2}{3} \]
Now we will evaluate each statement provided in your options to see if they are valid:
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Response: "Neither is a proportion." - This assumes that both equations are not equivalent proportions.
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Response: "84=126 only." - This assumes only the second equation is valid, but we need to evaluate both.
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Response: "Start Fraction 8 over 4 End Fraction equals Start Fraction 12 over 6 End Fraction only." - Particularly checks these two fractions.
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Response: "168=2412 only." - This considers the first equation valid.
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Response: "168=2412, 84=126." - This considers both equations valid.
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Response: "Start Fraction 16 over 8 End Fraction equals Start Fraction 24 over 12 End Fraction." and "Start Fraction 8 over 4 End Fraction equals Start Fraction 12 over 6 End Fraction." - This would mean fractions are equal, thus proportions are true.
To conclude, both equations must be evaluated based on their structure, and you can see that neither proportion is equal to an element.
The correct response based on simple evaluations would ultimately lean towards "Neither is a proportion."
2 answers