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## SAT (Fall 2023)

### Course: SAT (Fall 2023) > Unit 6

Lesson 5: Problem Solving and Data Analysis: lessons by skill- Ratios, rates, and proportions | Lesson
- Percents | Lesson
- Units | Lesson
- Table data | Lesson
- Scatterplots | Lesson
- Key features of graphs | Lesson
- Linear and exponential growth | Lesson
- Data inferences | Lesson
- Center, spread, and shape of distributions | Lesson
- Data collection and conclusions | Lesson

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# Percents | Lesson

## What are percentages, and how frequently do they appear on the test?

A

**percentage**is a ratio out of 100 that represents a part-to-whole relationship.**Percent (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

On your official SAT, you'll likely see

**1 to 3 questions**about percentages.**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 150, percent of 8 ?

### Finding complementary percentages

Since all parts of a whole should add up to 100, percent, 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, percent 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, 50, percent is equivalent to the following:

- The ratio 50, colon, 100, which reduces to 1, colon, 2.
- The fraction start fraction, 50, divided by, 100, end fraction, which reduces to start fraction, 1, divided by, 2, end fraction.
- The decimal value 0, point, 5.

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

*of*value x, we could simply multiply x by the decimal equivalent, 1, point, 12.**Example:**What is 25, percent of 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 equals
- "of" means
*multiplied by* - "percent" means
*divided by 100*

So:

36 is what percent of 60? → 36, equals, start fraction, x, divided by, 100, end fraction, dot, 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 percent sign). So, if the answer is 50, percent, you should simply enter 50.### 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 dollar sign, 200 to dollar sign, 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 dollar sign, 40 after a 20, percent 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 percent symbol and move the decimal point left 2 places.

When translating word problems:

- "what" means x
- "is" means equals
- "of" means
*multiplied by* - "percent" means
*divided by 100*

The sum of all parts of a whole is 100, percent.

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?

- 44% times 25 should be 11 not 12 as stated in the "Finding complementary percentages."(21 votes)
- You're correct. If you want to make sure nobody else has the same confusion, you can always tell Khan Academy about the mistake by clicking the "Report a Mistake" link when you go to ask a question.(11 votes)

- I have my SAT on 4th December. Is Khan Academy enough for practise? The books are a bit expensive. Are there other online resources?(5 votes)
- It is! Very effective and good to teach you all you need to know on what's going to be on the test and what to look forward to when taking it. Khan Academy has helped me know what to focus on and to sharpen the skills I don't do very well; skills I would've probably failed on the SAT.

I wish you luck on your SAT!(2 votes)

- is doing this for sat prep helpful?(4 votes)
- The answer to the one on subscriptions is 16,850.4. why do we round down and not up?(1 vote)
- The question has "To the nearest integer" in it, which more often than not signifies that we round as normal to the nearest whole subscription. The answer we get from doing the math is 16,850.4. To round to a place, we look at the place behind it. If it's 0-4, we round down. Else, we round up. Here, it's a 4 in the tenths place, so we round the answer down to 16, 850.(7 votes)

- Why in the very last example, the explanation says to add 12,390 to 4,460.4? I don't recall the formula states that?...(1 vote)
- The SAT absolutely loves testing familiar concepts in weird and wacky ways, so exclusively using formulas don't get you super far unless you know how to manipulate them and what everything in the formula does.

Here, we're finding the number of subscriptions sold in 2020. To do that, we have to find the percent increase from 2019 to 2020, and then use it to find the actual increase in subscribers, which we add to our existing amount to get the total subscribers in 2020.

12,390 is the number of subscribers we start out with (in 2019). We want to increase that number by 36% (based on what you've done before in the problem). To do this, we add the existing with the increased amount, which is 0.36 * 12,390. You could also think about it as multiplying 12,390 by the decimal 1.36. The 0.36 is for the increase, and the 1 added to it is the existing value. Does this make it clearer?(7 votes)

- I can't understand the last question. Can someone please explain it?(3 votes)
- how they get answers(1 vote)