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

Lesson 1: Topic A: Finding the whole

# Growing by a percentage

In this example we grow a whole number by a percentage of itself. Growing by percentage is a common skill often used when figuring how much is owed or earned with interest. Created by Sal Khan.

## Want to join the conversation?

• What is portfolio??
• Kartikeye,
In the Banking and Investment field, (which is part of Sal's life before Khan Academy), a "portfolio" means an "investment portfolio".

The "My Portfolio" to which Sal refers in the video is an "Investment Portflio" which is an abstract concept refferring to all the various investments of his money added together.

When he says "My Portfolio grows by 25%", he means the total value of all of his investments grew by 25%.

Investments means things of value which are purchased with money you saved and are purchased for the purpose of the thing becoming more valuable so that later when you need to spend your saved money, it will be worth more than you originally saved.

Investments can be a savings account in a bank, a purchase of land or a building, a purchase of a business, a purchase of part of a business which is usually in the form of a stock, a loan to someone who pays you back the money borrowed plus more in interest, a part of a loan to a government which is usually called a bond.

There is a section in Khan Academy on Finance and Capital Markets that provides some fascinating information on investments. http://www.khanacademy.org/science/core-finance
• How do we know which number is the numerator and which number is the denominator?
(1 vote)
• Haha this is going to sound silly, but I remember that the denominator is on the bottom because as I kid, I initially read the word as "DEMON"inator. I always viewed demons or monsters or whatever as staying down below in a dungeon or something, so the "denominator" always went below in a fraction. Silly, I know, but I always remembered it!
• for this problem coudn't you just say 25% =1/4 and 1/4 of 100 =25 and then do 100 - 25 = 75 .
I thought the answer was \$75.
• u forgot that it was 150 and u have to MULTIPLY it by 4 because it says 150 is 25 percent OF what. so 150 x 4 = 600
(1 vote)
• if 9/20 of females students are at a college and there are 2160 of them how many male students are there at the college?
• If you mean 9/20 of students at a college are female, then you can solve this question this way:
9/20 x=2160, xbeing the total number of students (male and female) at the college
x=4800
Then the number of male students is 11/20*4800=2640 male students
• Is there a need to remember that 25%is 1/4?
• You will use this frequently. So, it is worth memorizing.
Others that you should know: 50% = 1/2
75% = 3/4
100% = 1
• I don't get when Sal added the 1x+.25x to get 1.25x and then
1.25x=100
Why does it go from 1x+.25x to 1.25x. Isn't there two 'x'? Why do we end up with one 'x'? It seems like one of the 'x' just disappears. I'm a little confused. Can someone please explain? thank you.
• Sal adds one x with .25x (a quarter of x). So in total he has one and a quarter x's.
1x + .25x = 1.25x
'x' can stand for anything...

let x = a whole pizza
1 pizza plus a quarter of a pizza is one and a quarter pizzas

let x = 4
1*(4) + .25*(4) = 1.25*(4)
4 + 1 = 5
5 = 5

I'm going to work backwards and see if that helps too. I'm going to start with 1.25x and prove that it equals 1x + .25x
1.25x ----> (1 + .25)x
All I did was replace 1.25 with 1 + .25 because they are the same thing
(1 + .25)x ----> 1*x + .25*x ----> 1x + .25x
For the second step I just used the distributive property.
I hope this helps in some way!
• wouldn't that answer be 75 because 25 is a quarter and then you grew to 100 so that would be 75 plus 25=100
• In this case, he is actually finding that \$80 plus 25% of \$80 (which is \$20) is \$100, instead of 25% of 100, because if his portfolio was \$80 and THAT amount increases by 25%, it means that the portfolio increased by \$20. Hope this helps :)
• Couldn't you use 100% + p_% * _n (where _p_ is the percent in question, in this video 15 and n is the number, in this case 95) as the formula for finding the growth of a number? I have seen this in my math textbook. But I guess this would almost be the same as the method that Sal used, because (in this case) if 95 = 100%, then 100% + 15% * 95 = 95 + 15% * 95, right?

Parth, a.k.a. allies4ever
• He did the equation wrong .15 times 95 is 14.25?
• He immediately finds and fixes his error. So, what's the issue? His final result is 14.25.