Calculating Percents - SAT Math
Card 0 of 10
is 
of half of a number. What is that number?
Here it is helpful to recognize that 
is the same thing as 
. So if 
is 
of something, it is 
of that thing, meaning you can multiply 
by 
to get 
. And we know that 
then is half of the number they’re looking for, so if we multiply by 
we have the number: 
.
Here it is helpful to recognize that 
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At a manufacturing factory, 
of all widgets are found to be defective. If the plant were to produce 
widgets, how many would be defective?
At a manufacturing factory, 
There are a couple of math shortcuts that can make this question much quicker than calculating the “long way” of multiplying 
times 
without a calculator.
Option 1 is to realize that “percent” means “out of one hundred.” 
defective means that 
out of every 
are defective; since 
, the total number of widgets, is 
of 
, you can then say that 
of 
are defective -- if 
out of 
are defective, then (
of 
) out of (
of 
) would be defective. This gives you the correct answer, 
.
Option 2 is similar: you can express 
as the fraction 
, which reduces to 
. If you then know that 
out of every 
widgets is defective, and you have a total of 
widgets, which is 
times 
, you’ll have 
defective widgets.
There are a couple of math shortcuts that can make this question much quicker than calculating the “long way” of multiplying 
Option 1 is to realize that “percent” means “out of one hundred.” 
Option 2 is similar: you can express 
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What is 
increased by 
?
What is 
To increase 
by 
, you’d use the expression 
. But instead of doing the decimal multiplication, you can express 
as 
. That makes your job significantly easier, using:
Since 
equals 
, if you take 
of that you’ll just have 
. Add 
to the original 
and you have the correct answer, 
.
To increase 
Since 
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What is 
decreased by 
?
What is 
A decrease of 
is the same thing as a decrease of 
, since 
, which reduces to 
. A convenient way to handle percent decreases is to think that if 
has been taken away, then 
is left. So you can multiply 
by 
to get 
.
A decrease of 
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Tamara spent 
of her 
-hour workweek in meetings. How many hours that week was she NOT in meetings?
Tamara spent 
To calculate 
efficiently, you can first calculate 
by just moving the decimal point one place to the left. That means that 
of 
is 
(or just 
). Then to get 
, take half of what you had as 
. Since 
here is 
, then 
is half that: 
. Add those together, and you have 
. Here that means that 
is equal to 
. If she worked 
total hours and 
were in meetings, then the other 
were not in meetings.
To calculate 
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If 
of a number is 
, what is that number?
If 
A great way to perform a calculation like this is to set up a proportion. If you know that 
, you can then cross-multiply and solve for 
. (That proportion means that 
, 
out of 
, is equal to 
out of some other number.) Solving, you’d have:
Simplify the first fraction: 
Cross-multiply: 
Divide by 
to isolate 
: 
The correct answer is 
.
A great way to perform a calculation like this is to set up a proportion. If you know that 
Simplify the first fraction:
Cross-multiply:
Divide by 
The correct answer is 
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If 
of a number is 
, what is that number?
If 
A great way to set up a percent calculation like this is as a proportion:
That translates to 
(
out of 
) is equal to 
out of an unknown number.
You can then simplify the fraction 
to 
to make the calculation faster. If you then have:
You have two options. One, you can recognize that the difference between the numerators is that the second fraction is twice the second, and you can then say that the denominator must also be double, giving you 
, meaning 
.
Or you can cross-multiply and solve, giving you:
A great way to set up a percent calculation like this is as a proportion:
That translates to 
You can then simplify the fraction 
You have two options. One, you can recognize that the difference between the numerators is that the second fraction is twice the second, and you can then say that the denominator must also be double, giving you 
Or you can cross-multiply and solve, giving you:
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is 
of a number. What is that number?
A great way to calculate this type of percentage problem is by setting up a proportion:
This translates to 
(
out of 
) is equal to 
out of an unknown number. When you then cross-multiply, you’ll see that the math sets up nicely for quick calculation:
Since 
is 
, you can likely do this math in your head to find that 
, giving you the correct answer, 
.
A great way to calculate this type of percentage problem is by setting up a proportion:
This translates to 
Since 
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Keith completed a 
-kilometer race, during which he walked for 
of the distance and ran the rest. How many kilometers did he run?
Keith completed a 
If Keith walked 
of the distance, that means he ran 
of the distance. So you can calculate 
of 
. 
can be expressed as 
, which reduces to 
, making the calculation by hand much quicker. 
of 
is 
, making 
the correct answer.
If Keith walked 
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If 
is 
of 
, what is 
?
If 
One great way to set up a percent calculation like this is to follow the language of the prompt. The word “is” means equals, and “per cent” means “divided by 
,” so this prompt literally translates to the equation:
You can then reduce the fraction 
by factoring out a 
from both numerator and denominator, leaving:
Then if you multiply both sides by 
, you’re just about ready to solve:
Since 
divided by 
is 
, you can then multiply 
to get to 
, the correct answer.
One great way to set up a percent calculation like this is to follow the language of the prompt. The word “is” means equals, and “per cent” means “divided by 
You can then reduce the fraction 
Then if you multiply both sides by 
Since 
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