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.

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.

i thought finding for the difference is (initial-final) so why do they make it vice versa in others

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

In last question why we added 4460.4 to 12,390 in last step?

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

Are there any questions banks available for the Digital SAT yet?

Download the app Bluebook from the College Board website and you'll find practice tests there.

Why are the advanced and medium lessons the same?

Because the difference between the levels is not the method for the questions but the difficulty of the questions.

in the guavas question why did we multiply 'X' cost of 6 guavas with 0.30

$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

Main content

Course: Digital SAT Math > Unit 3

Lesson 3: Percentages: foundations

Percentages | Lesson

Google Classroom

A guide to percentages on the digital SAT

What are percentages?

A percentage is a ratio out of

100

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

Khan Academy video wrapper

Finding a percentSee video transcript

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:

% = \frac{part}{whole} \cdot 100

For example, say you took a quiz in math class and got

21

out of the

24

questions correct. We could calculate the percentage of questions you got correct as follows:

The part is $21$ ‍.
The whole is $24$ ‍.

\frac{21}{24} \cdot 100 = 87.5 %

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

150 %

8

Finding complementary percentages

Since all parts of a whole should add up to

100 %

, 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

25

marbles in the bag, and

56 %

of the marbles are blue, how many red marbles are there in the bag?

Try it!

Try: Identify parts and wholes

Of the juniors at South High School,

45 %

played for a school sports team. If

117

juniors played for a school sports team, how many students are in the junior class?

$45$ ‍ is the
.
$117$ ‍ is the
.
We need to solve for the
.

Try: Find complementary percentages

A group of

1,300

people took a survey in which they had to select their favorite of the four seasons (winter, spring, summer, and fall). The incomplete table below shows the results.

Season	$%$ ‍ of respondents
Winter	$16$ ‍
Spring	$22$ ‍
Summer
Fall	$28$ ‍

What percentage of respondents said summer was their favorite season? (Ignore the

%

symbol when entering your answer. For example, if the answer is

12 %

, enter

12

What number of respondents said summer was their favorite season?

What forms can percentages take?

Converting percentages to decimals and fractions

Khan Academy video wrapper

Converting percents to decimals & fractions exampleSee video transcript

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,

50 %

is equivalent to the following:

The ratio $50 : 100$ ‍, which reduces to $1 : 2$ ‍.
The fraction $\frac{50}{100}$ ‍, which reduces to $\frac{1}{2}$ ‍.
The decimal value $0.5$ ‍.

Note: a useful shortcut for converting percentages to decimals is to remove the

%

symbol and move the decimal point

2

places to the left.

Decimal equivalents for percentages are highly useful when making calculations. For example, if we wanted to find

112 %

of value

x

, we could simply multiply

x

by the decimal equivalent,

1.12

Example: What is

25 %

364

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 $x$ ‍
"is" means $=$ ‍
"of" means multiplied by
"percent" means divided by $100$ ‍

So:

36

is what percent of

60

? →

36 = \frac{x}{100} \cdot 60

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

50 %

, you should simply enter

50

Try it!

Try: switch between forms of percentages

2019

29 %

of Major League Baseball starting pitchers were left-handed.

The equivalent fraction is

The equivalent decimal is

Try: use decimal equivalents in calculations

In testing two engines, a mechanic finds that Engine A puts out

125 %

of the horsepower put out by Engine B. If Engine B puts out

120

horsepower, how many horsepower does Engine A put out?

First, we can convert

125 %

to the decimal

We can then multiply that decimal by

to find the number of horsepowers put out by Engine A.

Engine A puts out

horsepower.

How do we calculate percent changes?

Percentage word problems

Khan Academy video wrapper

Percent word problem: guavasSee video transcript

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 $100$ ‍.

% change = \frac{difference}{initial} \cdot 100

Example: The price of a vacuum was reduced from

$ 200

$ 170

. 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

$ 40

after a

20 %

discount. What is the price of the shoes before discount?

$$ 40$ ‍ is the final value.
$20$ ‍ is the $%$ ‍ change.
We're solving for the initial value ( $x$ ‍).

The price of the pair of shoes is

$ 40

after a

20 %

discount, which means

$ 40

100 % - 20 % = 80 %

of the original (initial) price.

Using

x

to represent the original price of the shoes in dollars:

80 %

x

$ 40

\begin{aligned} 80 % & = 0.8 \\ 0.8 x & = 40 \\ \frac{0.8 x}{0.8} & = \frac{40}{0.8} \\ x & = 50 \end{aligned}

The price of the shoes before discount was $$ 50$ ‍.

Try it!

Try: Identify Initial value, final value, and percent change

A customer’s monthly internet bill was

$ 63.89

. Due to a rate increase, her monthly bill is now

$ 68.86

. To the nearest tenth of a percent, by what percent did the amount of the customer’s internet bill increase?

$63.89$ ‍ is the
.
$68.86$ ‍ is the
.
We need to solve for the
.

The difference between initial and final values is

The percent change (to the nearest tenth of a percent) is

. (Ignore the

%

symbol when entering your answer. For example, if the answer is

12.4 %

, enter

12.4

Your turn!

Practice: Calculate a percentage

**Where Do People Get Most of Their News?**
Source	Percent of those surveyed
Internet/social media	$43 %$ ‍
Television	$23 %$ ‍
Newspapers	$15 %$ ‍
Radio	$11 %$ ‍
Others/none of the above	$8 %$ ‍

The table above shows a summary of

1,800

responses to a survey question. Based on the table, how many of those surveyed get most of their news from either newspapers or the radio?

Practice: USE COMPLEMENTARY PERCENTAGES

Tara has read

95 %

of the books she owns. If Tara owns

160

books, how many of her books has she NOT read?

Practice: CALCULATE PERCENT INCREASE

The price of a particular brand of headphones was

$ 7

2016

. In

2018

, the price of the same brand of headphones was

$ 10

. What is the approximate percent increase in the price of the headphones?

Practice: Calculate percent change

Year	Subscriptions sold
$2018$ ‍	$10,500$ ‍
$2019$ ‍	$12,390$ ‍

The manager of a streaming video service received the report above on the number of subscriptions sold by the service. The manager estimated that the percent increase from

2019

2020

would be double the percent increase from

2018

2019

. To the nearest integer, how many subscriptions did the manager expect would be sold in

2020

Things to remember

Percent means parts per hundred.

p % = \frac{p}{100}

A shortcut for converting percentages to decimals is to remove the

%

symbol and move the decimal point left

2

places.

When translating word problems:

"what" means $x$ ‍
"is" means $=$ ‍
"of" means multiplied by
"percent" means divided by $100$ ‍

The sum of all parts of a whole is

100 %

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.

% change = \frac{difference}{initial} \cdot 100

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rewar9207
Posted 9 months ago. Direct link to rewar9207's post “Why do they teach such ba...”
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.
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- Jiya Watson
  Posted 9 months ago. Direct link to Jiya Watson's post “Rewarr, Arey bhai. They a...”
  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.
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i thought finding for the difference is (initial-final) so why do they make it vice versa in others
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(6 votes)
Answer
- abraar
  Posted 9 months ago. Direct link to abraar's post “whether you do final-init...”
  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
  Comment on abraar's post “whether you do final-init...”
  (23 votes)
kainatss04
Posted 8 months ago. Direct link to kainatss04's post “In last question why we a...”
In last question why we added 4460.4 to 12,390 in last step?
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(4 votes)
Answer
- *Somto*
  Posted 8 months ago. Direct link to *Somto*'s post “To find the amount in *20...”
  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
  Comment on *Somto*'s post “To find the amount in *20...”
  (12 votes)
fisher.peyton
Posted 4 months ago. Direct link to fisher.peyton's post “i miss the old khan acade...”
i miss the old khan academy practice sat math
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Why are the advanced and medium lessons the same?
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(1 vote)
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- StudyBuddy
  Posted 9 months ago. Direct link to StudyBuddy's post “Because the difference be...”
  Because the difference between the levels is not the method for the questions but the difficulty of the questions.
  Comment on StudyBuddy's post “Because the difference be...”
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tara
Posted a year ago. Direct link to tara's post “Why do we calculate 36% o...”
Why do we calculate 36% of 12390, instead of the initial 10500?
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  Posted a year ago. Direct link to Dade Posh's post “Download the app Bluebook...”
  Download the app Bluebook from the College Board website and you'll find practice tests there.
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  (6 votes)
javeria.masood04
Posted a year ago. Direct link to javeria.masood04's post “in the guavas question wh...”
in the guavas question why did we multiply 'X' cost of 6 guavas with 0.30
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(1 vote)
Answer
- yankelwinbrandao
  Posted a year ago. Direct link to yankelwinbrandao's post “$12.60 is the price-with-...”
  $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
  Comment on yankelwinbrandao's post “$12.60 is the price-with-...”
  (8 votes)