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### Course: 7th grade foundations (Eureka Math/EngageNY) > Unit 4

Lesson 1: Topic A: Foundations# Percent of a whole number

Discover how to calculate percentages with a simple example: finding 30% of 6. Learn two methods, using fractions and decimals, to solve this problem. Both approaches lead to the same result, showing that 30% of 6 equals 1.8. Master these techniques for everyday calculations. Created by Sal Khan.

## Want to join the conversation?

- Here's what I did so maybe it will help you guys.

(Please don't say I'm getting this off of AI, 'cause im not, I just did some random multiplying and converting and when I put my answer is was correct every time. Im saying this because this has happened before.)*______________*

So this is one of the questions in the exercises you have to do. These question come from the "Benchmark percents" exercise.*What is 1% of 800?*(Fact! The "of" in 1%**of**800, mean "times" (x) in math, so it really translates: What is 1% x 800?)*__________*

First we convert.

1% = 1/100

Then we divide:

1 ÷ 100 = 0.01

Now we can get back to the original question; What is 1% of 800?

Multiply 0.01 by 800;

0.01 x 800 = 8!

So 1% of 800 (1% x 800) = 8!*__________________*

This question comes from the "Equivalent representations of percent problems" exercise.*_______*

Which of the following options have the same value as 62% of 45? Chose**2**answers:

a) 0.62 x 45

b) 45 ÷ 0.62

c) 62/100 x 45

d) 62 ÷ 45

e) 62 x 45*_______________*

Now this is just like the first question but asking us what equation is for the correct value of the question "Which of the following options have the same value as 62% of 45?"

So lets just solve the equation 62% of 45.

Convert:

62% = 62/100-**WAIT**you could stop right here and do 62/100 x 45 instead of converting 62/100 to a decimal.

Which option has 62/100 x 45? Option c) does. So c) is one of our answers. And we can check.

Lets finish our work.

62% = 62/100

62 ÷ 100 = 0.62

0.62 x 45 =**27.9**

Now check to see if 60/100 x 45 has the same answer as**27.9**.

62/100 x 45 = 27.9!!

So c) 62/100 x 45 is one correct answer.

Now we need one more answer since the question asks for**2**.

Lets review our options.

a) 0.62 x 45

b) 45 ÷ 0.62**c) 62/100 x 45**CORRECT

d) 62 ÷ 45

e) 62 x 45

Okay so we 4 more left now we could just enter every question into a calculator to see if it would equal 27.9. But there's a faster and better way to go about this.

Back when we were answering the question 62% of 45 there was a moment we had the number 0.62. And we were multiplying it by 45.

(0.62 x 45)

That equation is in one of our options. Which one has "0.62 x 45"? option a) does. And we don't even have to check it. We literally did it under the phrase I wrote "Lets finish our work."

0.62 x 45 does = 27.9

So our answers to the question "Which of the following options have the same value as 62% of 45" is option*c) and a).***a) 0.62 x 45**CORRECT

b) 45 ÷ 0.62**c) 62/100 x 45**CORRECT

d) 62 ÷ 45

e) 62 x 45

If you guys want be to talk about the last exercise in khan academy which is called "Finding percents". Upvote this please!(39 votes)- Also, Let's see if we can figure out what 30% of 6 is. So one way of thinking about 30%-- this literally means 30 per 100. So you could view this as 30/100 times 6 is the same thing as 30% of 6. Or you could view this as 30 hundredths times 6, so 0.30 times 6. Now we could solve both of these, and you'll see that we'll get the same answer. If you do this multiplication right over here, 30/100-- and you could view this times 6/1-- this is equal to 180/100. And let's see. We can simplify. We can divide the numerator and the denominator by 10. And then we can divide the numerator and the denominator by 2. And we will get 9/5, which is the same thing as 1 and 4/5. And then if we wanted to write this as a decimal, 4/5 is 0.8. And if you want to verify that, you could verify that 5 goes into 4-- and there's going to be a decimal. So let's throw some decimals in there. It goes into 4 zero times. So we don't have to worry about that. It goes into 40 eight times. 8 times 5 is 40. Subtract. You have no remainder, and you just have 0's left here. So 4/5 is 0.8. You've got the 1 there. This is the same thing as 1.8, which you would have gotten if you divided 5 into 9. You would've gotten 1.8. So 30% of 6 is equal to 1.8. And we can verify it doing this way as well. So if we were to multiply 0.30 times 6-- let's do that. And I could just write that literally as 0.3 times 6. Well, 3 times 6 is 18. I have only one digit behind the decimal amongst both of these numbers that I'm multiplying. I only have the 3 to the right of the decimal. So I'm only going to have one number to the right of the decimal here. So I just count one number. It's going to be 1.8. So either way you think about it or calculate it, 30% of 6 is 1.8.(3 votes)

- At0:55, how do you turn the improper fraction into a mixed number?(7 votes)
- you can turn an improper fraction to a mixed number by dividing the top number by the bottom number and that is how you do it :)(40 votes)

- I don't understand how Sal turned the fraction into a decimal. How is 4/5 related to 4 divided by 5? (At1:00)(13 votes)
- The slash in between the 4 and the 5 means division. All fractions are division sentences written in a different form. To convert a fraction to a decimal, you divide the numerator by the denominator. For 4/5, you divide 4 by 5 to get 0.8(27 votes)

- Why make these things so complex? I will just divide 6 by 100. And then multiply by 30.

6/100=0.06

0.06*30=1.8

simple as that.(12 votes)- Sal is showing different approaches that can be used for this problem. Pick one that works for you.

Note: While your method works, you do have a process error. Technically, you treated the problem as 6% * 30 when the problem is 30% * 6 = 30/100 * 6 = 0.3 * 6 = 1.8(14 votes)

- at a scale of 500 percent a measurment is 165mm. what is the actual size?(10 votes)
- The video teaches how to find a percentage of a number, here you're given the percentage and looking for the original number, so you should reverse the operation, and do division.

What is the number when multiplied by 500/100 (that's 500%) gives 165?

? x 500/100 = 165

You can divide 165 by 500/100 to find the answer, or since we're dividing by a fraction, you can just multiply by its reverse, so it becomes likes this:

165 x 100/500 = ?

(165 x 100) / 500 = 16500 / 500

16500 / 500 = 33

The original number should be 33.(12 votes)

- These comments are very old!

Not to waste your time reading this, but if i did waste your time I'm so sorry(13 votes)- I totally agree! Like, HOW?? And where are the people from these days? Trust me, you didn't waste my time. This is relatable!(3 votes)

- The video teaches how to find a percentage of a number, here you're given the percentage and looking for the original number, so you should reverse the operation, and do division.

What is the number when multiplied by 500/100 (that's 500%) gives 165?

? x 500/100 = 165

You can divide 165 by 500/100 to find the answer, or since we're dividing by a fraction, you can just multiply by its reverse, so it becomes likes this:

165 x 100/500 = ?

165 x 100 = 16500

16500 / 500 = 33

The original number should be 33.

It will help you to understand...if you could then hit a like 👍🏻👍🏻(12 votes) - this is too quick can someone explain it to me?(5 votes)
- So basically 50% of 100 is 50, and 50% of 5 is 2.5, if you get fractions and decimals then this is easy.

Here is a method to make calculating percentages easier.**Graph paper or any paper recommended**

Let's say I want to find 80% of 200, then I would write 200 x 80 (over 100)= ?. The two 0s from the 80 over 100 and 200 cancel out each other. 80 * 2= 160, so 160 is 80% of 200.

Hope this helps(11 votes)

- Can you explain it better Sal other then that Khan Academy is awsome(6 votes)
- Multiply the whole number by 100. The resulting answer is its value as a percentage. Another way is to add a decimal point after the whole number such as 4, and then move the decimal two spaces to the right, fill in each of those empty spaces with a zero, and add a percentage symbol = 400%.(7 votes)

- Sal drawing a dot instead of a multiplication symbol doesn't help my confusion...(4 votes)
- The "." is used instead of "x" since in algebra "x" is a variable and isn't used for multiplication, you will realize later in you math journey it is way better to use a "." rather than an "x"(10 votes)

## Video transcript

Let's see if we can figure
out what 30% of 6 is. So one way of thinking
about 30%-- this literally means 30 per 100. So you could view
this as 30/100 times 6 is the same thing as 30% of 6. Or you could view this
as 30 hundredths times 6, so 0.30 times 6. Now we could solve
both of these, and you'll see that we'll
get the same answer. If you do this multiplication
right over here, 30/100-- and you
could view this times 6/1-- this is equal to 180/100. And let's see. We can simplify. We can divide the numerator
and the denominator by 10. And then we can divide the
numerator and the denominator by 2. And we will get 9/5, which is
the same thing as 1 and 4/5. And then if we wanted to write
this as a decimal, 4/5 is 0.8. And if you want to
verify that, you could verify that
5 goes into 4-- and there's going
to be a decimal. So let's throw some
decimals in there. It goes into 4 zero times. So we don't have to
worry about that. It goes into 40 eight times. 8 times 5 is 40. Subtract. You have no remainder, and
you just have 0's left here. So 4/5 is 0.8. You've got the 1 there. This is the same
thing as 1.8, which you would have gotten
if you divided 5 into 9. You would've gotten 1.8. So 30% of 6 is equal to 1.8. And we can verify it
doing this way as well. So if we were to multiply
0.30 times 6-- let's do that. And I could just write that
literally as 0.3 times 6. Well, 3 times 6 is 18. I have only one digit
behind the decimal amongst both of these
numbers that I'm multiplying. I only have the 3 to the
right of the decimal. So I'm only going
to have one number to the right of
the decimal here. So I just count one number. It's going to be 1.8. So either way you think about
it or calculate it, 30% of 6 is 1.8.