All ACT Math Resources
Example Questions
Example Question #1 : Fractions
is equivalent to what percentage?
4.5%
5.5%
55%
15%
45%
55%
Divide the fraction out to get the decimal
5.5 / 10 = 0.55
To find the percentage, shift the decimal point two to the right = 55%
Example Question #1 : Fractions And Percentage
Write as a percent
To find a percent from a fraction you can either divide the number on your calculator and multiply by 100:
or you can just multiply the numerator and denominator by the same number that makes the denominator equal to 100 (because a % is just #/100):
Example Question #7 : Fractions
One half of a group of professors is made up of mathematicians, and one fourth of the remaining portion is made up of philosophers. The remaining portion is made up of sociologists. If there are professors in the room, how many are sociologists?
To begin, remember with percentages that "of" means multiplication and "is" means "equals." Now, we know that one fourth of the remaining half are philosophers. This means that he philosophers really are:
So, there are sociologists as a percentage. This is:
Therefore, of the
are sociologists, or:
are sociologists.
Example Question #1 : How To Find Percentage From A Fraction A1
Convert the following fraction into a percent.
To convert a fraction into a percent, make the denominator 100 and then the numerator will be the percent. Thus,
Example Question #1 : Fractions And Percentage
On a acre plot of land, there are
acres in which deer live. What percentage of the land does this represent? Round to the nearest hundredth.
For percentages, it is always easiest to translate into language that uses "is" and "of." "Is" means "equals" and "of" means "multiply." So, we have:
What percentage of is
? This is the same as:
Solving for , you get:
Now, as a percent, this is equal to:
Rounding to the nearest hundredth, you have .
Example Question #1 : Fractions And Percentage
is
of
, which is 35% of
. All three are positive integers. In which range does the smallest possible value of
fall?
Between 700 and 800
Between 600 and 700
Between 300 and 400
Between 500 and 600
Between 400 and 500
Between 300 and 400
is 35% of
, so
.
is
of
, so
.
Consequently,
The smallest integer can be is 240. If this happens,
Their sum is
The correct choice is that the sum is between 300 and 400.
Example Question #1391 : Act Math
is
of
and
of
; all are positive integers. Give the smallest possible value of
.
is
of
and
of
, so
,
so .
so
must be divisible by 5, so the least possible value is 5 itself.
Example Question #1392 : Act Math
is
of
. Which of the following expressions is equal to
?
None of the other responses gives a correct answer.
is
of
, so
Example Question #1393 : Act Math
.
is
of
, which is 80% of
. What percent of
is
?
The correct answer is not given among the other responses.
The correct answer is not given among the other responses.
is 80% of
, so
.
Consequently,
is
of
, so
Consequently, .
, so
is 800% of
. This is not one of the choices.
Example Question #1 : Fractions And Percentage
is
of
.
is what percent of
?
The correct answer is not given among the other responses.
is
of
, so
,
so
and
The question can be rewritten as
is what percent of
?
The answer is
All ACT Math Resources
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