(or any equivalent fraction).
One option is to punch the whole
numerator and the whole denominator into the calculator and submit each
product. If you’re very careful, that will work. However, it might be wise to
try canceling some common factors out of the fraction, to save time and to
avoid errors. It’s fine to switch to the calculator whenever the cancelations
aren’t obvious:
20.
(or any equivalent fraction).
First, turn the decimal into a sum of
two pieces, to separate the repeating portion:
7.583 = 7.58 + 0.003
Deal with each piece in turn. Like any other terminating decimal, 7.58 can be
written as a fraction with a power of 10 in the denominator:
The repeating portion is similar to 0.3 = 0.3333 … =
So 0.003 is just
, moved by a couple of decimal places: 0.003 = (0.3)(0.01)
=
.
Finally, write the original decimal as a sum of fractions, and then combine
those fractions:
Enter
unreduced, or you can reduce it to
.
21.
(A).
Both quantities are positive square roots, so just compare the
underlying numbers.
Quantity A:
= 1.33
Quantity B:
= 0.75
The square root of 1.33 (or
) is greater than the square root of 0.75 (or
).
22.
(B).
The square root of a fraction is the square root of the top over the
square root of the bottom:
Then make a common denominator:
.
23.
(or any equivalent fraction).
If a question refers to fractions of
different numbers that are
also
related by a fraction or percent, try plugging in
numbers. Since there are 40% as many men as women, some convenient
numbers are:
Men = 40
Women = 100
Women who speak Spanish =
(100) = 80
Men who speak Spanish =
(40) = 30
The group has 140 total people and 110 Spanish speakers. The answer is
(you are not required to reduce, as long as your answer is correct
and fits in the box).
24.
(D).
Cancel factors on top and bottom of each product:
Quantity A:
Quantity B:
The two quantities differ in the denominators: Quantity A has
c
2
, while
Quantity B has
c
. It cannot be determined which quantity is greater, because
for some values (e.g.,
c
= 2)
c
2
is greater than
c
, and for others (e.g.,
c
= 0.5)
c
2
is less than
c
.
25.
(C).
Multiply out Quantity A by FOILing.
Make a common denominator (2
m
) to sum these terms (also, note that this
makes Quantity A similar in form to Quantity B):
Since the quantities now have the same denominators and (
m
+ 2)
2
=
m
2
+ 4
m
+ 4, the two quantities are equal.
26.
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