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Which of the following is equal to
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12 Jul 2019, 15:43
12 Jul 2019, 15:43
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Which of the following is equal to \(\frac{\frac{ab}{c}}{\frac{cd}{a}}\) for all non-zero values of a, b, c, and d?
A. \(ac\)
B. \(bd\)
C. \(\frac{1}{bd}\)
D. \(\frac{a^2b}{c^2d}\)
E. \(\frac{ab^2}{cd^2}\)
A. \(ac\)
B. \(bd\)
C. \(\frac{1}{bd}\)
D. \(\frac{a^2b}{c^2d}\)
E. \(\frac{ab^2}{cd^2}\)
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Which of the following is equal to
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13 Jul 2019, 07:21
13 Jul 2019, 07:21
1
Carcass wrote:
Which of the following is equal to \(\frac{\frac{ab}{c}}{\frac{cd}{a}}\) for all non-zero values of a, b, c, and d?
A. \(ac\)
B. \(bd\)
C. \(\frac{1}{bd}\)
D. \(\frac{a^2b}{c^2d}\)
E. \(\frac{ab^2}{cd^2}\)
A. \(ac\)
B. \(bd\)
C. \(\frac{1}{bd}\)
D. \(\frac{a^2b}{c^2d}\)
E. \(\frac{ab^2}{cd^2}\)
APPROACH #1: Algebra
\(\frac{\frac{ab}{c}}{\frac{cd}{a}}=(\frac{ab}{c})(\frac{a}{cd})= \frac{a^2b}{c^2d}\)
Answer: D
Cheers,
Brent
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Which of the following is equal to
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13 Jul 2019, 07:30
13 Jul 2019, 07:30
Carcass wrote:
Which of the following is equal to \(\frac{\frac{ab}{c}}{\frac{cd}{a}}\) for all non-zero values of a, b, c, and d?
A. \(ac\)
B. \(bd\)
C. \(\frac{1}{bd}\)
D. \(\frac{a^2b}{c^2d}\)
E. \(\frac{ab^2}{cd^2}\)
A. \(ac\)
B. \(bd\)
C. \(\frac{1}{bd}\)
D. \(\frac{a^2b}{c^2d}\)
E. \(\frac{ab^2}{cd^2}\)
APPROACH #2: Test values
Since we want to find an expression that's EQUAL to the given fraction then, if we assign values to the variables, the correct answer will evaluate to have the SAME value as the given expression.
For example, if we let \(a=2\), \(b=5\), \(c=1\) and \(d=12\) then we get: \(\frac{\frac{ab}{c}}{\frac{cd}{a}}=\frac{\frac{(2)(5)}{1}}{\frac{(1)(12)}{2}}=\frac{10}{6}=\frac{5}{3}\)
Now, we'll plug \(a=2\), \(b=5\), \(c=1\) and \(d=12\) into each answer choice to see which one evaluates to \(\frac{5}{3}\)
A. \(ac=(2)(1)=2\). This does NOT equal \(\frac{5}{3}\). ELIMINATE A.
B. \(bd=(5)(12)=60\). This does NOT equal \(\frac{5}{3}\). ELIMINATE B
C. \(\frac{1}{(5)(12)}=\frac{1}{60}\). This does NOT equal \(\frac{5}{3}\). ELIMINATE C
D. \(\frac{a^2b}{c^2d}=\frac{2^2(5)}{1^2(12)}=\frac{20}{12}=\frac{5}{3}\). PERFECT. Keep D
E. \(\frac{ab^2}{cd^2}=\frac{(2)5^2}{(1)12^2}=\frac{50}{144}\). This does NOT equal \(\frac{5}{3}\). ELIMINATE E
Answer: D
Cheers,
Brent
