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Course: Digital SAT Math > Unit 11
Lesson 3: Percentages: advancedPercentages | Lesson
A guide to percentages on the digital SAT
What are percentages?
A percentage is a ratio out of that represents a part-to-whole relationship. Percent ( ) means parts per hundred.
In this lesson, we'll learn to:
- Calculate percentages using part and whole values
- Switch between equivalent forms of percentages
- Calculate percent change
You can learn anything. Let's do this!.
How do we calculate percentages?
Finding a percentage
Calculating a percent value
There are two values that are important for finding a percentage: a part and a whole. To calculate a percentage, use the following formula:
For example, say you took a quiz in math class and got out of the questions correct. We could calculate the percentage of questions you got correct as follows:
- The part is
. - The whole is
.
If we have any two of the part, the whole, and the percentage, we can solve for the missing value!
Note: be careful when identifying the part and the whole; the part won't necessarily be the smaller number!
Example: What is of ?
Finding complementary percentages
Since all parts of a whole should add up to , we can also use percentages to determine the value of any missing parts.
Example: A bag is filled with red and blue marbles. If there are marbles in the bag, and of the marbles are blue, how many red marbles are there in the bag?
Try it!
What forms can percentages take?
Converting percentages to decimals and fractions
Switching between forms of percentages
We can use equivalent forms of percentages interchangeably and choose the one(s) that best suit our purpose.
For example, is equivalent to the following:
- The ratio
, which reduces to . - The fraction
, which reduces to . - The decimal value
.
Note: a useful shortcut for converting percentages to decimals is to remove the symbol and move the decimal point places to the left.
Decimal equivalents for percentages are highly useful when making calculations. For example, if we wanted to find of value , we could simply multiply by the decimal equivalent, .
Example: What is of ?
Translating percentage word problems
You'll frequently see percentages referenced in word problems. Luckily, there's an easy way to translate these word problems into arithmetic:
- "what" means
- "is" means
- "of" means multiplied by
- "percent" means divided by
So:
In what form should I enter my answer?
Questions on the SAT may ask for "what percent" and require you to enter that value into the answer field.
In these instances, you should not enter decimal or fractional equivalents, but instead enter the percent value as an integer (without a sign). So, if the answer is , you should simply enter .
Try it!
How do we calculate percent changes?
Percentage word problems
Calculating percent change
We're often asked to calculate by what percent a quantity changes relative to an initial value: the percent discount on jeans, the percent increase in population, etc. When calculating a percent change from an initial value to a final value:
- Find the difference between the initial and final values.
- Divide the difference by the initial value.
- Convert the decimal to a percentage by multiplying the quotient by
.
Example: The price of a vacuum was reduced from to . What was the percent reduction in price?
If we have any two of the percent change, the initial value, and the final value, we can solve for the missing value! And remember: decimal equivalents for percentages are highly useful when making calculations.
Example: The price of a pair of shoes is after a discount. What is the price of the shoes before discount?
Try it!
Your turn!
Things to remember
Percent means parts per hundred.
A shortcut for converting percentages to decimals is to remove the symbol and move the decimal point left places.
When translating word problems:
- "what" means
- "is" means
- "of" means multiplied by
- "percent" means divided by
The sum of all parts of a whole is .
When calculating a percent change from an initial value to a final value:
- Find the difference between the initial and final values.
- Divide the difference by the initial value.
- Convert the resulting decimal to a percentage.
Want to join the conversation?
- Why do they teach such basic concepts with so much complexity?
I now have to come to think of Indian system of teaching math much simpler and easier to understand.(71 votes)- Rewarr, Arey bhai. They are trying to break it down man. Here we get the simple questions so that we will understand the question better. If they give us the real deal most of us will chicken out and won't do well. Hence they give simple ones and make us confident and strong with the methodology and strategy.(77 votes)
- is practising from khan academy enough for the DSAT?(18 votes)
- i thought finding for the difference is (initial-final) so why do they make it vice versa in others(6 votes)
- whether you do final-initial, or initial-final, it doesnt matter. The value doesnt change but only the signs do.
for example, 6-4 = 2
4-6 = -2
what's important is the positive value of the difference and the original amount
An example :
a banana cost 5 dollars on Monday, but on Tuesday it was for 8 dollars. Find the % change in price
here, youll get 3 or -3 as the difference, depending on the method you used. The positive value of the difference is 3 and the original value is 5
therefore, 3/5 x 100 = 60%
Thus, there was 60 % increase in the price of bananas(24 votes)
- i miss the old khan academy practice sat math(10 votes)
- What was it like?(1 vote)
- In last question why we added 4460.4 to 12,390 in last step?(4 votes)
- To find the amount in 2020 ,
basically, the amount in 2020 was the amount in 2019 plus 36 percent of that same amount in 2019
You could also do 1.36 x 12390 to make the work a bit shorter :D(13 votes)
- Why are the advanced and medium lessons the same?(1 vote)
- Because the difference between the levels is not the method for the questions but the difficulty of the questions.(15 votes)
- Why do we calculate 36% of 12390, instead of the initial 10500?(7 votes)
- Are there any questions banks available for the Digital SAT yet?(3 votes)
- Download the app Bluebook from the College Board website and you'll find practice tests there.(7 votes)
- in the guavas question why did we multiply 'X' cost of 6 guavas with 0.30(1 vote)
- $12.60 is the price-with-discount.
we want to know the price-without-discount, which he said it's X;
But X(price-without-discount) is not equal to price-with-discount, because price-with-discount is 30% less than price-without-discount.
0.30 means 30% or 30/100
So what he did is...
X(total) - 0.30 of X.
X with 30% less of it. which is the same as $12.60,
our price-with-discount.
then the rest is just the math.
X - 0.30*X = 12.60
0.70*X = 12.60
now we want to know what is the price-without-discount, which is X
So what we can do is divide de both sides by 0.70 so the X (what we want to know) is isolated
doing this we have what X is equal to.
X = 12.60/0.70 = 18(8 votes)