1001 Algebra Problems.PDF

(Marvins-Underground-K-12) #1

Set 61 (Answers begin on page 274)


Some common arithmetic and pre-algebra errors are
explored in this problem set.


945.(–3)–2 = 6


a.The answer should be –9 because (–3)–2 =
–33.
b.The answer should be ^19 because (–3)–2=
(–3)^1 (–3)= ^19 .
c.There is no error.

946.(–^23 )^0 = 1


a.The answer should be –1 because (–^23 )^0 =
–(^23 )^0 = –1.
b.The answer should be zero because you
should multiply the base and exponent.
c.There is no error.

947.0.00013 = 1.3 104


a.The statement should be 0.00013 = 1.3 104
because the decimal point must move four
places to the left in order to yield 0.00013.
b.The statement should be0.00013 = 1.3 10 –3
because there are three zeros before the deci-
mal point.
c.There is no error.

948.–4^2 = –16


a.The answer should be –8 because 4^2 = 8, and
this is then multiplied by –1.
b.The answer should be 16 because –4^2 =
(–4)(–4) = 16.
c.There is no error.


  1. a = 2, for any nonzero value ofa.
    a.This is incorrect because you cannot cancel
    members of a sum; you can cancel only fac-
    tors that are common to the numerator and
    denominator.
    b.The correct result should be 3 because aa= 1
    and a+a^2 = aa+ 2 = 1 + 2 = 3.
    c.There is no error.


950.^34 +  2 a=3+ 6 a, for any real number a.
a.You must first get a common denominator
before you add two fractions. The correct
computation is:^34 +  2 a= ^34 + ^24 a= 3+ 8 ^2 a.
b.You must first get a common denominator
before you add two fractions. The correct
computation is:^34 +  2 a= ^34 + ^24 a= 3+ 4 ^2 a.
c.There is no error.


  1. 4 is 200% of 8.
    a.There is no such quantity as “200%.” You
    cannot exceed 100%.
    b.The placement of the quantities is incorrect. A
    correct statement would be “200% of 4 is 8.”
    c.There is no error.


952.0.50% of 10 is 0.05.
a.In order to compute this percentage, you
should multiply 0.50 times 10 to get 5, not
0.05.
b.In order to compute this percentage, you
should multiply 50.0 times 10 to get 500, not
0.05.
c.There is no error.

^ + 2
a


  • COMMON ALGEBRA ERRORS–

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