Mastering Percents for the Digital SAT Math Exam: Complete Guide

hi everyone welcome to my channel to really need test prep today we'll be going over orochento number one percents

the goal of the otochento course is to teach students everything they need to know about the digital sat math exam

please see the link in the description to download this video's worksheet for free

let's get started okay so the first skill we're going to talk about is percent of

so what you do when you see a percent of is you change the percent to a decimal to do that you divide the percent by

100. next we change the word of to a multiplication symbol

so for example let's say we have 45 percent of 260 we divide by 100 so 45 divided by 100

and we change the of to a multiplication sign 45 divided by 100 is 0.45

and now 0.45 times 260 is 117. so you could just type the second line

or or even the first line up at the board up on Desmos but I highly recommend you know how to do this by

hand because you're gonna have to practice changing percents to decimals and up to multiplication for harder more

complex questions let's do some more examples at the board all right so the first problem we have

is sixty percent of 240. so I'm going to divide by 100 change the of to multiplication

and keep everything else the same so 60 divided by 100 you can use a calculator

to assist you especially if the numbers are really messy uh is 0.6

and let's see 0.6 times 240. is 144. so that's our answer for that one

I want to point out that once again we can do most to all of this on Desmos so let's do the second one with the

calculator helping us a little bit more so we're going to do 325 of 84. so 325 going to divide by 100.

and I'm going to change the of to multiplication so

um let's try that 325 over 100. times 84.

and I get 273. I want to point out as I said in my Desmos video on percents you could just

type in 325 percent and then of will automatically come up type in 84. however you might come across symbolic

problems we're going to do one in a minute where you might not be able to rely on that as much so I highly

recommend you remember okay divide by 100 change the of to multiplication all right let's do some more what else

do we have here okay out of 500 muffins 75 contained nuts

how many in the muffins head nuts so we're going to do this question is essentially asking us 75 percent

of 500. 75 of those 500 muffins have nuts so we're going to do 75

divided by a hundred times 500 and that should give us 375.

all right next one so this is kind of what I was talking about where you might get word problems where this one you

could just type in a Desmos but you're going to want to practice being able to do this with symbols for the test so f

of x is 30 of x so I'm going to do 30 divided by a hundred

change the of to multiplication 30 divided by 100 is 0.3

so we can rewrite this expression as 0.3 X you can imagine for a longer problem

that might be really important that you know how to do that okay I think there's one more here

so it says the width of a rectangle is eighty percent of its length so we have to do some

words to math here so the width we can call that w

is that is equals

and then 80 of its length so eighty percent of its length let's call that l

so eighty percent of L so that's 80 divided by 100 change the of to

multiplication times l so w is equal to 80 divided by 100 is 0.8

so that's one equation and they also tell us the perimeter of the rectangle is 72 feet

so um this actually isn't on the reference sheet so you might want to know this the

perimeter of a rectangle is 2L plus 2W so if the perimeter is 72 we can put 72

in for p and we have this and now we can this is now

a system of equations so what we're going to do is we're going to substitute this guy

in for w so he's going to go over there and we get 72 equals 2 L plus 2

W is 0.8 l so 2 times 0.8 you can do this on a

calculator 72 equals 2 L plus 1.60 so that should give us

2 plus 1.6 is 3.6 l and now we're going to divide both sides by 3.6

and we get the L the length is 20 feet and if you wanted to as always with any

any time you substitute if you want to go back and plug this in over here to find w why

don't we do that so 0.8 times 20. is 16. so the width is 16 feet and the length

is 20 feet and you can go back and plug that back into check 2 times 16 plus 2 times 20. I get 72. and is the width 80

of the length 0.8 times 20 I get 60. looks like we did a good job so

don't get too reliant on Desmos make sure you know how to write this out as an equation because you might have to do

that as part of a longer problem as we just did here let's move on to the next skill

okay so skill number two is fractions slash decimals two percents I don't even know if I needed to make a slide for

this but I just wanted to quickly mention this so first

um you write your fraction slash decimal then to go back to a percent you multiply it by 100 instead of

dividing by 100. so in this example we've got five red shirts out of 16 total what percent of shirts are red so

the fraction is part over a whole so 5 over 16 which if we put that in a calculator we get 0.3125

now to change it to a percent you have to remember to multiply either the fraction or the decimal by 100. since

this decimal kind of ends nicely it terminates I'll stick with the decimal so 0.3125 times 100

and I get 31.25 percent let's do a couple examples at the board

okay so for this first one we've got 28 red marbles out of a total of 400 so our fraction is going to be

28 over 400. so I'm going to put that in a calculator and since it came out nicely to 0.07 I'm

going to use that and to change it to a percent we're going to do 0.07

times 100 so we write our decimal and then we multiply it by 100.

so for this one I get seven percent R red let's keep going

all right so this table on the bottom here first off when you see a table and a problem like this you're going to want

to add like a total row if there isn't one already or at least write it down on your scratch paper

so here we're going to add all those up four plus eight plus six plus two and we get 20.

so what fraction of the shirts are red so red would be four out of a possible of

20. so we're going to do 4 over 20.

and we can write that as

4 over 20 is fine but we could write it as one-fifth which is the simplified

fraction or because the decimal comes out nicely it wouldn't be the worst thing to write the decimal we could put

it as 0.2 either of those would have been fine great okay so let's look at the next one

what percentage of shirts are green so um and why don't I do it kind of all in one

go this time so um so green so we're going to do two

out of a possible of 20. and because we want a percentage we're going to multiply by 100.

so let's see what that gives us so 2 over 20 times 100

and I get 10 percent so 10 of the shirts are green very good let's move on to the next

skill okay so skill number three is

proportions for percent problems so you might find that when you're doing like more convoluted

problems than just a percent of that knowing an equation might make it easier so

um for words to math problems you'll see what I mean by that in a minute we use the equation is over of equals

percent over 100 and for story problems we tend to use the equation part over

whole equals percent over 100. now remember we were just doing making the fraction

into a percentage that's something that they ask you to do on the SAT a lot so um I rewrote this

as percent equals part over whole times 100 just because you'll see that question a lot on the test I'll ask you

what percentage of these things are yellow or something so um maybe knowing both might save you a little bit of time

whatever works for you let's go back to the board and do a couple examples Okay so

this one these ones at the top are the first couple of these are words to math you see how there's a lot of isses and

ofs and percents so um we're going to use the equation is over of

equals percent over 100. so right away if there's a percent

I just identify that I go okay whatever is glued to the percent symbol is the percent

so on the right side I'm going to put p over 100 okay so now let's say is is next to 25

so we'll put 25 and of is next to 200 so we'll put 200 where

the of goes and now any time to solve these equations you can cross multiply

so to cross multiply we're going to do 25 times 100 and any time if you want

to use Desmos to help you you can 25 times 100 is 2500 200

times p is 200p so we're going to do 200p and now we divide both sides by 200

and we get 12.5 equals pay and if you want

you can go back and plug that back in and see if it kind of makes sense so 12.5 percent of 200 okay

so that's 0.125 times 200 and I get 25 so it seems like we did a good job great let's look at this one

43 is p percent of 129 okay all right same kind of deal always pick out the percent first

so I'm going to put p over 100 equals next to is is 43

and next to of is 129. so we can cross multiply 4300 equals 129 p and then we divide both

sides by 129. and I get P equals 33.3

I think they say five or six characters one two three four five six that should be right

now I want to point out to you guys that there's a common misconception that on the test you have to write percents

using a decimal that's not true you actually can put it in its fraction form so I'm going to

show you that right now um so let's get rid of all this rules of 4300

over 129. if I simplify that I get 100 over three so to me

um so you could write P equals 100 over three percent now that looks really weird

but it is technically correct and they've done questions like this before and you might as well just let the

calculator help you simplify right you might mess up on the rounding to five or six characters whatever the weird rule

on the SAT is but you're not going to mess up the fraction because Desmos can help you get the

fraction so don't let that confuse you you can absolutely write percents a messy

um rational percent as its fraction form you can do that looks really weird but it is right

okay let's look at this one over here 45 of X is 180 same deal I'm going to do is over of

equals percent over 100 and the first thing I'm going to do is

the percent so the percent is glued to 45. um is is next to 180.

and of is next to X so let's cross multiply so we get

180 times 100 18 000. equals 45x 45 times x divide both sides

by 45 and we should get x equals 400. I think that's right okay let's look at this guy over here

Josie sold 39 out of 120 crafts what percent did she sell okay remember guys part percent is equal to part over whole

times 100 okay so we're going to do um

39 out of a total of 120 times 100. and let's see what that gives us

we get 32.5 percent something like that not doing any of this in my head using the calculator just making sure that I

understand um the steps of what I'm doing for when I get really tricky problems

okay I think this is our last one so um whenever you see

in terms of the thing right before it you just need to get by itself

it's called a literal equation we'll have a video about that another time

so same deal is over of equals percent over 100.

and okay the percent is p next to is is 27 and next to of

is X so now we want to get X by itself so um we're gonna cross multiply so

2700 equals P percent yeah for for whatever reason they write

it like this I'm gonna write it like this 27 times 100. equals x times P so how about we just

call that PX so now to get X by itself we're going to divide both sides by P because the

opposite of multiplication is division and we get X is equal to 27 times 100

over p and I'm pretty sure that is answer Choice d

I think we did a good job there so you see like especially if you come across a hard question like this it's it just it

makes it so much easier if you just have something to look at before you start doing the question so lots of people

don't like this but I still think there's a lot of value and is over of equals percent over 100 equation it

helps a lot all right let's move on to the next skill

okay skill number four this is one of um probably the biggest takeaways from this

video so many students either forget or they just never learned how to do this and there's other ways to solve percent

problems like this but the reality is the SAT is designed for you to do it this way so you have to do it this way

so we have to find what's called a percent multiplier given a percent increase or percent decrease it the

percent multiplier is just what number you're going to multiply a value by to get

um to apply a percent change so to figure out the multiplier for a percent increase what you do is

um you do one plus the decimal so one plus percent divided by a hundred and for a decrease we do one minus the

percent divided by a hundred so one minus the decimal some keywords that are associated with the percent increase

that show up a lot on the test so percent increase percent greater

percent more now um some common like real life scenarios

where this comes up on the test and just in general sales tax so like when you go to buy something at the store they put

like a five or you know seven eight percent tax on top of it you pay extra money to

the government so that's an increase on your bill similarly if you go to a restaurant and you do a twenty percent

tip you're giving twenty percent extra for the waiter so that is also a percent increase on your bill decrease

we see the words percent decrease we see the words percent fewer percent less and this one really can

trip people up the real world scenario that you will see in the shopping problems is a discount or like a coupon

so oftentimes you'll see this worded in books and stuff using like 25 percent off

that's a 25 decrease don't confuse that with 25 of with one f two F's is a discount it means it's a

percent decrease so we'll get into how to use these in a minute

but before we do that I would make sure you have this all down in your book and then there's one other thing we got

to do which is this equation so original or your starting value times

all your percent multipliers in a row however many I have usually on the test it's just one or two

equals final original times percent multipliers equals final all right let's go ahead and do some

examples at the board okay so before we start talking about what a multiplier is let's just make

sure we can calculate them so once you have a handle on what you need to do

the calculator is incredibly helpful for figuring out the percent multiplier I went over this in my Desmos video you

can check that out but I'm going to go over it again here anyway so

one plus percent divided by 100 so for a 50 increase we're going to do one plus fifty

divided by a hundred now um

if we go to the calculator we can type it in just like that and we get 1.5 I'm telling you I'm

telling you I'm telling you do not do this in your head no matter how simple it seems because if you do it

in your head you're gonna forget how to do it you're gonna forget the mechanics of how to calculate it and you

are then going to come across harder numbers that you can't do in your head and you're going to get it wrong so

please please please don't do this in your head use the calculator even if it seems really simple just so that you

always remember how to compute it so for this one it's 1.5 all right 80 decrease we're going to do

1 minus 80 over a hundred all right let's go back over here so 1 minus 80 over 100 that's 0.2

so the multiplier for that problem would be 0.2 now these bottom ones much harder

numbers much harder to do in your head so I'm not going to do it in my head increase okay we're going to do one plus

357 over a hundred okay let's see what that is 1 plus 357

over a hundred that's four point five seven so four point five seven almost everyone

would have said 3.57 lots of people would have thought that okay let's do one more here so 0.4

percent decrease see how tricky this is to do in your head when the numbers get really small

or or really um really big sure when it's like 10 or 20 or 50 it's

not so bad but the numbers get bigger or smaller it gets really hard to do all right

so this would be 0.996 so maybe I would see that in one of the answer choices or something like that

okay great so please please please make sure that you can do that

all right what is the result of increasing okay so when we're doing all these guys

just kind of keep in mind original I'll write it again later but original times percent

multiplier equals final okay so our original value is 150 so I'm going to do 150

times what we're going to do a 190 percent increase so let's figure out what that

is so 1 plus 190 over a hundred that's 2.9 okay so we're going to do 150 times 2.9

and that should give us our final so let's see what that is I'll just do it over here 150 times 2.9

and we get 435 great very good okay let's keep going okay Susie went to buy a 60 dress a

eight percent sales tax was applied at checkout how much did she pay at the register

Okay so um the amount she paid at the registered that's the final

so we're gonna do original times the percent multipliers equals final there's

only one and the original price is the sticker price so sixty dollars

and we're going to do times the percent multipliers equals the final which is what we want to find so we

could call that X if you want so we have an eight percent sales tax that is an eight percent increase

remember we said sales tax is an increase so let's see what the multiplier is

so we're going to do one plus eight divided by 100 that's 1.08 so

1.08 and I don't need to do any algebra everything is like kind of where I want it

60 times 1.08 is 64.8 and because it's in America you know we would put you know something in the hundredths

place for sense um but that that's never something they would test you on this would probably be

a multiple choice question um great very good

um okay let's do the next one all right original times percent multipliers

equals final and the original

is they tell us is 25 dollars and we did a 30 off coupon remember we

talked about that's a decrease and we did a six percent sales tax so that would be an increase

and now watch what I do guys the order you put them in doesn't matter I'll just do both of them over here

so thirty percent off okay 1 minus Thirty over a hundred

and six percent sales tax that's an increase one plus six over a hundred so the multipliers are 0.7 and 1.06 so

watch what I do I just put them next to each other they just get multiplied one after the

other so many many people they would have tried

to like added like 30 and six or like did negative 30 plus six that is wrong do

not ever do that see what I did with the percent multipliers I found each multiplier and then put them one back to

back they are like totally separate we don't combine them or anything like that

okay now I can go over here 25 times 0.7 times 1.06 and

um you see guys it's really important that you do it like this because on a multiple choice question

they're going to write it using the percent multiplier so if you do it a different way

you're not going to be able to tell the answer as easily so please please please make sure you do

multipliers so you think it should be 18.55 at least that's what I got all right there's two more here so this

one here same deal original times percent multipliers

equals final okay so the original price it says what was the original price so

we don't know the original price so we're going to put X now for the percent multipliers we have

a 35 percent off and a seven percent sales tax so let's find both of those

so 35 off that's a decrease one minus 35 divided by a hundred and seven percent sales tax one plus

seven divided by a hundred great so we get 0.65 and 1.07 so 0.65

and see how I'm not adding them or anything I just put them right next to each other

and the final price is the amount he paid at the register fifty dollars so see how tricky that is many people

they would have put the 50 as the original price but it's not the the 50 is the final price and we

want to find the original so now you got to put your algebra cap on all right well we want to get X by

itself those guys are being multiplied opposite of multiplication is division so we're going to divide both these guys

over and I'm intentionally writing it like this because this is how the SAT will

write it in the answer choices so um this guy goes away

and we're left with x equals 50 over 0.65

times 1.07 very tricky and you better believe there would have been a trap answer where you had to

um where like if you multiplied it you get the Trap answer

so very tricky all right 0.65 1.07 okay and we round to the nearest

hundredth and we get 71.89 so it should be 71 dollars and 89 cents

so be very meticulous about writing down okay original times percent multipliers equals final what's the original what's

the percent multipliers what's the final sometimes they're not asking to find the final they're asking to find the

original okay great all right let's look at this one the

quantity is decreased by 65 percent of its value the resulting value is X okay right away

resulting value that's like another word for final right so we're going to say the final is X

the original we don't know um it wants us to find that so I I'm you could introduce a letter I'm just going

to call it original because it doesn't matter to me all right and the percent multiplier

decreased by 65 percent I feel like even if you know you could for the most part get

this one right one minus 65 divided by 100 okay so that's 0.35

so we're going to put 0.35 and and right away you can kind of see oh it's probably B right but you know on

the actual test that trap answers might be more convincing okay so to get the original by itself

um we're going to divide both sides by 0.35 and we get original

equals x over 0.35 but see like even if you don't know what to do if you know how to calculate the

multiplier on a multiple choice question like this you can you can take a pretty solid educated guess probably down to

two answers maybe even one so yeah understanding how to compute multipliers is really darn important

all right let's continue with the next skill okay so skill number five is percent

change from percent multipliers so what we just did where we took the percent change

and um found the percent multiplier now we're going to do the opposite you quite literally need to know how to do this

forwards and backwards so what you do is you take the percent multiplier you

subtract one and then multiply by 100. subtract one and then multiply by 100. I sum this up in this nice little formula

but um it's really better if you understand okay the distance from one is the change

subtract one and then to change it to a percent just to change anything to a percent you multiply it by 100.

so um let's say we have a percent multiplier of 1.3

so we're going to um do 1.3 minus 1 that gives us 0.3 0.3 times 100 is 30 it's a positive 30

percent so we're going to say the percent change is a 30 increase

let's say we had a percent multiplier of 0.75 so first we're going to do

0.75 minus 1 that gives us a negative 0.25 multiply by 100 we get Negative 25 now on the test you're never going to

write negative 25 as an answer it'll always be phrased in the question like what's the percent decrease so

um we would just say it's a positive 25 decrease hopefully that kind of makes sense it's kind of like it's kind of

like you know if you instead of saying I gained

negative three dollars you could say I lost three dollars right so you're almost always in the answer going to

phrase it using that positive so always before you lock in your answer write down oh is it an increase or a decrease

because if you got an increase when the answer the question is phrased like a decrease you probably did something

wrong right okay let's do some more practice at the Whiteboard

all right so we're just going to practice doing what we just did

um remember everybody the percent change is equal to 100 times the percent

multiplier minus one Okay so um this point 17

is just a percent multiplier so to find the percent change we're going to do

a hundred times point Seventeen minus one let's see what that gives us

so a hundred times point Seventeen minus one we get Negative 83 percent and remember guys negative percent

that's a decrease so we're going to say this is an 83 percent decrease so if this were a student produced response

you would just say 83 not negative 83. because it says the word decrease here

it already accounts for the negative so you don't need to put two negatives okay great

um let's look at the next one so 2.49 Z same kind of deal this guy is a percent multiplier

so we're going to do percent change equals 100 times 2.49

minus one percent multiplier minus one let's see what we get 100 times 2.49

that's one we get 149 percent and it is positive so we're going to call that a 149

percent increase which makes sense based on how the the problem is phrased so we would just

put 149 if it were a student produce response as our answer all right same kind of deal here

um it wants to know the percent increase from the previous year um

so um bigger than one is an increase so we don't need to do anything this is our

percent multiplier so we're going to do percent change equals

a hundred times 1.95 minus one I think I already know

that what that should give us but let's just do it at the board anyway 95 positive 95 percent

which is a percent increase and we're happy with that because the question says increase

so it seems like we did a good job all right this last one is really tricky this um has a lot we have to do for

words to math so we have B okay B

is is means equals 8 9 times C okay eight ninths times C

so maybe that would be my percent multiplier but here's the thing it wants to know about the value of C

kind of as the final right and notice how it also says greater so our our multiplier should be bigger than

one which eight ninths is not so to fix that we have to get C by itself so what we're going to do is we're going

to divide both sides by 8 9. when you divide by a fraction that's the same as multiplying by the reciprocal so we're

going to multiply both sides by nine over eight and we get

um nine over eight B these guys cancel out

equals c and if it's all right what I'm going to do is

I'm going to rewrite this just to make it a little easier to understand so B

times nine over eight equals c you see this now lines up perfectly with

what we were just talking about original times percent multiplier equals final so with C treated as the final

um that the percent multiplier is nine over eight so

that's it now we just do what we did before that was a lot of work but okay so now we're going to do the

percent change is equal to a hundred

times nine over eight minus one so let's see what that gives us

we get 12.5 so positive 12.5 percent which is

a 12.5 percent increase so for this one we would put 12.5 as our answer

so as you guys can see um really understanding this guy but then

also being very careful about your words to math and always thinking about the mechanics

of what you're doing rather than just doing it in your head makes it so that um you don't you can solve questions

more easily and you'll be less likely to fall for a trap answer okay let's go back to the board I think

we have one more skill okay last and not least everyone we have to talk about how to find the percent

change given the original and final values so we just talked about how to find it

given the multiplier now we're going to do it given the original and final values so probably the easiest way to do

this is the percent change formula the percent change formula is percent change equals new minus old divided by

old times 100 new minus old divided by old times 100 there's a very helpful mnemonic

that might help you remember it so if you just write the letters at the beginning

it spells out no like oh no so percent change equals no that might help you remember when you're taking your test

so Nu minus old divided by old times 100. let's go to the board and do a couple

examples okay so for this one uh

this one is pretty kind to us um still let's make a chart just to make

sure we're not making a mistake so I like to make a little chart and I go okay I think the old is ten

and I think the new is 13. so let's put that 10 and 13.

okay the question wants me to do greater that's an increase word right so let's see as I go from 10 to 13 is it

getting bigger 10 to 13 yeah that's bigger so I did a good job right if I had 13 on the left and 10 on the right

that would be getting smaller which would be a percent decrease so you'll probably realize that once you're done

but it's better off if you can kind of um um kind of save yourself from

making that mistake earlier just by making a little chart so just make sure as you go from old to

new that it's getting bigger or smaller depending on what kind of percent change it is increase or decrease

okay so now we're going to do percent change equals new minus old divided by old times 100 so 13 minus 10 over 10.

times 100 and guess what um I can just do this all in one go so I don't make a

mistake 13 minus 10 over 10. times 100 really quick and I get 30 percent so

this is plus 30 percent which is a 30 percent

increase so our answer for p would be 30. it's 30 P percent greater thirty percent greater

great all right let's look at this one so a lot of times they'll make these questions Harder by putting it in like a

graph or a table um so I made a little table here So based on the table the typical

maximum number of petals for flower a is p percent less okay so let's make a little chart again old

and new okay and put a little arrow from old to new

and the typical maximum number of petals for flower a is p percent less so maximum number of

petals that's here and for a okay let's make the old flower a which is five

and the new flower B which is seven ah but there's a problem with what I just did

P percent less okay five to seven is getting bigger less is a decreasing word so we're gonna swap them seven goes

on the left and five goes on the right so old seven new five it's getting smaller P percent

less good all right percent change new minus old divided by old okay so five minus

seven over seven times one hundred and we can go over here

and do that in one go five minus seven over seven times one hundred

and five or six characters man that's gonna be a huge pain um I'm just gonna just remember what I

said before and go wait a minute I can just use it as a fraction so I'm going to hit the fraction button it's

negative 200 over seven which would be an acceptable answer so it is negative 200 over seven percent

which is a decrease so we're going to write it as a 200

over seven percent decrease and I would put as my final answer 200

over 7 which is fine as long as it's like five characters or less which it is five

or six characters or less which it is very good awesome all right I think that's it for these

problems let's go back to the slides okay everyone so now we are going to be going over the

final review worksheet I have included a link to this worksheet for free in the description of the video

please also be on the lookout for a pinned comment which will contain links to other places where you can practice

these skills even more so you can get even better at it Beyond just doing the 10 or 20 problems that's on my worksheet

so please please please now would be a great time for you to download that workshe from the description and do it

yourself before watching the rest of the video okay let's get started with the

worksheet Solutions okay time for the final review so 25 of 168.

so we're going to do divide by 100. change the of to multiplication divide by a hundred

change the of to multiplication of course we could also straight up type in 25 percent and it'll put of

but like I said many times I recommend you do it the old-fashioned way so that you remember the Mechanics for when you

come across harder problems so the answer to this guy is 42. question two what is 230 percent of 54

okay so we are once again going to divide by a hundred change the of to multiplication

and let's see what we get 230 divided by a hundred times 54.

we get 124.2 all right let's look at this one thirty percent were dimes how many of

the coins were dimes okay so it basically wants us to find thirty percent

of 250. so we're going to do 30 over 100. times 250.

and let's see what that gives us 30 over 100 times 250 that gives us 75 so 75 of the

coins were dimes what fraction of the shirts are purple what percentage of the shirts are purple

okay so the fraction part over whole so 7 over 16. um that's already simplified so that

would be fine as a final answer um you could also um

leave it as a decimal especially if the decimal comes out nicely all right let's see the percentage

part over whole times 100. part over hole times 100 that's one of the things we

talked about earlier in the video so we're going to do 7 over 16. times 100

once again not going to do that in my head we get

43.75 percent very good okay for this one we're gonna do

um is over of equals percent over 100 um next to the percent is p next to

is is 45 and next two of is 160 so I'm going to put that here

now I'm going to cross multiply and we get 4500 equals 160p

now I'm going to divide both sides by 160 get P equals 28.125

okay great all right this next one is the same 60 percent

of X so we're going to do is over of so um 60 over 100

equals next to is is 315 and next to of is X so we get

60 uh 315 times 100 what is that 31 500. equals 60x cross multiply and now we

divide both sides by 60. and we get x equals 5 25. okay percent multipliers for an increase

one plus percent divided by a hundred for a decrease one minus percent divided by a hundred

so let's rapid fire all these guys increase one plus 25 over a hundred that's 1.25

decrease 1 minus 41 divided by a hundred that's 0.59 593 increase okay one

plus five ninety three over a hundred that's 6.93 increase one plus zero point three over

a hundred that's one point zero zero three and two point six percent decrease so

that's one minus 2.6 divided by a hundred which is 0.9

74 all right very good okay population of a town was 430

000. okay so see how it says the word thousand and then I'm gonna check to see

if it says in thousands in the answer it does say in thousands so I don't need to multiply by a thousand I just leave it

as is um if it didn't say in thousands you'd have

to make sure to write 430 000 at the beginning because the answer the units need to match the

answer so anyways just be careful that all right so we're going to do for a bunch of

these original um times percent multipliers equals the

final and um

we're starting with 430 and then applying a percent so um

um that's going to be our original and it says grew by 30 70 that's not one of the words we did

but um grew means to get bigger so that's our percent increasing word so let's

find the multiplier for a 70 increase 1 plus 70 over 100. it's 1.7 so we're gonna do 430 times 1.7 and

that'll give us our final which is in um 2016. so 430 times 1.7 is 731 and I don't have to put

zero zero zero because it says in thousands great

okay same kind of deal with this one so um uh the final we don't know we want to

find what is the result so we can call that X the original is 784.

and we're doing a 52 percent decrease so let's see what a 52 percent decrease is

1 minus 52 over 100 that's 0.48 so we're going to do 0.48 and I don't have to do any algebra

because X is already by itself that's nice and I get 376

.32 all right okay original

times percent multipliers equals final okay so um the original price of the video game

we don't know so we're going to put X then we have a 20 off coupon that's a decrease six percent sales tax that's an

increase let's figure out both of those so 1 minus 20 over 100 and then 1 plus because sales tax is an

increase six over 100.8 and 1.06 all right and remember we just when we have more than one we just put them next

to each other we stack them we don't like Adam or anything like that you just put them next to each other

and the final price is what he paid at the register which is forty two dollars okay and now we're going to divide both

sides by 0.8 times 1.06 and this whole guy goes away

and we get x equals 42. divided by 0.8 times 1.06 and let's see what we get so 42

divided by 0.8 1.06 and we round money to the hundredths question doesn't say but we round money

to the hundredth so this would be 49.528 so 49.53 so this would be 49 dollars

and 53 cents now when you do a question like this it might be wise to go back and plug it back into kind of the

beginning and see if you get what they told you to get 42. so why don't we do that really

quickly just to make sure we did it right so 49

and because we rounded it's going to be a little off but that's okay 53

times 0.8 times 1.06 and we do get just because we rounded we do get just about 42 dollars so that

means we did a good job stupendous all right let's keep going

all right this guy is a percent multiplier it's less than one so I bet it's asking me to find a decrease the

question is so we can do percent change equals a hundred times percent multiplier minus one

so we're going to do percent change equals 100 times 0.26 minus 1. okay let's see what that gives us so

negative 74. okay so that's negative 74 percent and we don't put the negative because we

just phrase that as a 74 percent decrease which is what they wanted us to phrase it as so the answer to this one

would just be 74. all right same thing with number 12. um we got a multiplier

and this guy is bigger than one so I bet it's asking me for an increase it is and

um we have to find the value of P so we're going to do percent change

equals a hundred times 6.82

minus one so a hundred times six point eight two minus one

that's 582 percent positive which is a 582 percent increase which is what the question wants us to put so our

final answer would just be 582. okay these guys are percent change formula so don't forget

no times 100. So based on the table the typical minimum number of petals

for flower B okay so we're looking at the minimum and

it says more okay so the bigger number should go on the right side of my table

so um flower B is four so that should go on the right

and flower a is two um okay if I go from two to four am I getting bigger yes I am

all right so percent change is 4 minus two over two times one hundred okay I think I know what that is but

let's just do it anyway so four minus two over two

times one hundred and we get a hundred so this is a hundred

positive a hundred percent change which is a one hundred percent positive is an increase

okay so now we're going to do we're looking at the lifespan so let's look at the lifespan

that's this it says P percent less okay so I bet my smaller number should be my new

so the smaller number is 10. no it's six so we're going to put six over here and 10 over here double check

as I go from 10 to 6. do I get smaller yes I do all right so let's do percent change

equals six minus ten new minus old over old times one hundred

six minus ten over ten and we get Negative 40. so this is negative 40 percent

which is a forty percent decrease less is a decreased word so we would just put 40 as the answer

okay I think we've got one or two more great a certain country had a child population of 3 35 million people the

child population was forty percent of the total population what is the total population in millions

of people okay there's a couple ways we could do this um we could do a percent of or we could

do part overhaul I'm gonna do part overhaul so

um part overhaul

equals percent divided by a hundred and

um so the part is 35

million it says in millions so we don't need to change it

the whole is the total we don't know that X and then the percent is 40

over 100. so um we're gonna do 3 500.

equals 40x divide both sides by 40. we should get 87.5 million

okay very good and you could again double check it 40 of so 0.4 times 87.5 and we get 35 so that works

all right I think this is our last one so the final price of an item okay so original

okay so the final price of an item is X okay so let's put X where final goes we want to find the original price I'll

just put original and now we got to do the percent multiplier so we have a 35 off coupon

and a seven percent sales tax so 35 off coupon that's one minus 35 divided by a hundred

and then seven percent sales tax we add because it's an increase one plus seven over a hundred

we get 0.65 and 1.07 okay right away um even if you didn't even do the problem

uh these two guys are looking to be wrong right they don't have the right multiplier so so they're probably not

the right answer okay so remember it says in terms of so the thing in front is what we want to

get by itself the original price so to get the original price by itself we're going to divide both sides by 0.65

times 1.07 this guy goes away and we get original

equals x over 0.65 times 1.07 I'm not going to type that in the calculator because the SAT has a

tendency of just leaving things kind of just in its place like that and as you can see it we did do

that on this answer answer Choice C X over 0.65 times 1.07 okay very good

all right I think that's it for the review worksheet let's go back to the slides

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