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Question
Determine if one, both, or neither of the following is a proportion. 168=?2412 , 84=?126 (1 point)
Responses
Neither is a proportion.
Neither is a proportion.
168=2412 only
Start Fraction 16 over 8 End Fraction equals Start Fraction 24 over 12 End Fraction only
168=2412, 84=126
Start Fraction 16 over 8 End Fraction equals Start Fraction 24 over 12 End Fraction , Start Fraction 8 over 4 End Fraction equals Start Fraction 12 over 6 End Fraction
84=126 only
Neither is a proportion.
To determine if the given equations are a proportion or not, we need to check if the ratios on both sides of the equation are equivalent.
The first equation is 168 = 24/12. To simplify this, we divide both the numerator and denominator of the fraction by their common factor, which is 12. So, we get 16/8 = 2/1, which does not result in an equivalent ratio. Therefore, the first equation, 168 = 24/12, is not a proportion.
The second equation is 84 = 12/6. Again, we simplify by dividing both the numerator and denominator of the fraction by their common factor, which is 6. This gives us 8/4 = 2/1, which does result in an equivalent ratio. Therefore, the second equation, 84 = 12/6, is a proportion.
So, out of the given equations, only the second equation, 84 = 12/6, is a proportion.
To determine if one, both, or neither of the given equations is a proportion, we can simplify the fractions and compare them.
Equation 1: 168 = 24/12
To simplify the left side, divide both sides by 5: 168/5 = 24/12
The simplified equation becomes: 33.6 = 2
Equation 2: 84 = 12/6
To simplify the left side, divide both sides by 5: 84/5 = 12/6
The simplified equation becomes: 16.8 = 2
Based on the simplifications, neither of the equations is a proportion.