Alan used the expression StartFraction 5 over 9 EndFraction (F minus 32), where F is a temperature in degrees Fahrenheit, to convert a temp

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.

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Melanie 2 weeks 2021-09-26T03:49:35+00:00 2 Answers 0

Answers ( )

  1. Emma
    0
    2021-09-26T03:50:54+00:00

    C=\frac{5}{9} (F-32)     [C = Celsius    F = Fahrenheit]

    Alan found 45°F = -7°C, his work:

    C=\frac{5}{9} (F-32)=\frac{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=\frac{5}{9} (45-32)=(\frac{5}{9} )45+(\frac{5}{9} )(-32)=25-\frac{160}{9} =\frac{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=\frac{5}{9} (45-32)=\frac{5}{9} (13)=\frac{65}{9} =7\frac{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

    0
    2021-09-26T03:51:14+00:00

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45:7+7-4:2-5:5*4+35:2 =? ( )