Question

Alan used the expression StartFraction 5 over 9 EndFraction (F minus 32), where F is a temperature in degrees Fahrenheit, to convert a temperature from Fahrenheit to Celsius. He evaluated the expression as shown below and found that 45 degrees Fahrenheit was equivalent to –7 degrees Celsius.

StartFraction 5 over 9 EndFraction (F minus 32) = StartFraction 5 over 9 (45 minus 32) = 25 minus 32 = negative 7


What error did Alan make?

He substituted 45 for F instead of –7 and should have found the answer to be Negative 21 and two-thirds degrees Celsius.

He did not combine within the parentheses first before multiplying and should have found the answer to be 7 and StartFraction 2 over 9 EndFraction degrees Celsius.

He multiplied 45 by the fraction incorrectly and should have found the answer to be 49 degrees Celsius.

He divided 5F by 9 before subtracting 32 and should have found the answer to be 21 and StartFraction 4 over 9 EndFraction degrees Celsius.

Answer 1

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Explanation:

Answer 2

`C=(5)/(9) (F-32)` [C = Celsius F = Fahrenheit]

Alan found 45°F = -7°C, his work:

`C=(5)/(9) (F-32)=(5)/(9) (45-32)=25-32=-7`

So he distributed 5/9 into (45 - 32), but he only distributed it to 45. It would've been:

`C=(5)/(9) (45-32)=((5)/(9) )45+((5)/(9) )(-32)=25-(160)/(9) =(65)/(9)`

What error did Alan make?

#1: He substituted 45 for F instead of –7 and should have found the answer to be Negative 21 and two-thirds degrees Celsius.

This is wrong because he used 45 degrees Fahrenheit, not -7 degrees Fahrenheit.

#2: He did not combine within the parentheses first before multiplying and should have found the answer to be 7 and StartFraction 2 over 9 EndFraction degrees Celsius.

This is right because he should've combined inside the parentheses first before multiplying the fraction.

`C=(5)/(9) (45-32)=(5)/(9) (13)=(65)/(9) =7(2)/(9)`

#3: He multiplied 45 by the fraction incorrectly and should have found the answer to be 49 degrees Celsius.

This is wrong because 45 multiplied by the fraction does = 25

#4: He divided 5F by 9 before subtracting 32 and should have found the answer to be 21 and StartFraction 4 over 9 EndFraction degrees Celsius.

This is wrong because he didn't do this