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### Course: Digital SAT Math > Unit 7

Lesson 3: Percentages: medium# Percentages | Lesson

A guide to percentages on the digital SAT

## What are percentages?

A $100$ that represents a part-to-whole relationship.

**percentage**is a ratio out of**Percent (**$\mathrm{\%}$ )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 $21$ 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 .$24$

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

### Finding complementary percentages

Since all parts of a whole should add up to $100\mathrm{\%}$ , 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

### 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, $50\mathrm{\%}$ is equivalent to the following:

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

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

Decimal equivalents for percentages are highly useful when making calculations. For example, if we wanted to find $112\mathrm{\%}$ $x$ , we could simply multiply $x$ by the decimal equivalent, $1.12$ .

*of*value**Example:**What is

### 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:

### 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 $\mathrm{\%}$ sign). So, if the answer is $50\mathrm{\%}$ , you should simply enter $50$ .

*should not*enter decimal or fractional equivalents, but instead enter the percent value as an integer (without a### 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
.$100$

**Example:**The price of a vacuum was reduced from

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

### Try it!

## Your turn!

## Things to remember

Percent means parts per hundred.

A shortcut for converting percentages to decimals is to remove the $\mathrm{\%}$ 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 $100\mathrm{\%}$ .

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.(81 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(11 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(14 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.(16 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)