Videos

Math Bootcamp

Added Oct 16, 2020 •

Copy this URL:
Embed code:	<iframe class="edlio-embed-player" type="text/html" width="640" height="360" src="//ccas.ccusd.org/apps/embed/?v=296365" frameborder="0" allowfullscreen></iframe> Change dimensions

Math Bootcamp 10/16/20: Ratio, Proportion, and Percent review

Show Transcript

are you guys welcome back to another math boot camp today we're doing a final practice review of ratios proportions and percentages so let's get right into it this is my favorite part of the reviews start off with question number one so question number one reads from a total yearly budget of $360,000 but Kimball Foundation 30000 on leasing office space what is the ratio of dollars spent on office space $2 spent another cost so they have a total budget of 360000 and they spend 30000 on leasing office space but the question is asking me what is the ratio of dollars turn on Office Space $2 spent on other costs so not so the total but I'm other cost so the first thing I need to do is I need to figure out how much they're spending on other things right so that means I need to do is traction benzonatate their total budget and subtract amount that they spend on leasing right in order to get how much do you spend on everything else 330000 is how much they spend on everything else right this is everything and this is leasing and so they want to know what is the ratio of office space to leasing well okay this is the ratio radio we need to reduce this ratio Ray and one of the things I talk about is Crossing the zeros meaning that if you have a 0 up top and a zero down below you can cross those out so we can cross out this 0.0.0 that's a right and we're down to 3 to 33 so now given that we have three 233 what number can go both into 3 and 33 in order to further reduce this ratio other than what's the largest number that can go into 3 and 33 11:11 doesn't work for 3 so we can divide both of these by 3 right so if I take this and divide 1000 by 3 can I get 1 to 11 right or as it's written we have our two dots it's a 1 to 11 ratio the letter c round make sense yes I'm just going to I'm going to recap the problem real quick so we have a total budget of $360,000 deposit for leasing space which is 30 thousand and they want to know what the ratio of leasing space to other expenses is so in order to figure out how much they're spending on everything else what I do is I could try them out there spending on leasing from the total and I give me my 330,000 that I create my ratio and all I do from there is I just reduced so I crossed out all my zeros and I had 3 to 33 and I reduced by divide that by 3 giving me a 1 to 11 ratio okay let's check out number to a worker can assemble 5 Motors in 2 hours which the Expressions below can be used to find how long it would take the worker to assemble 50 Motors okay so they can do in 2 hours write this is a Motors Caesar hours so we want to know how long it would take them to solve for 50 Motors right how much time you don't know how many hours will put axe the right so we do is we cross multiply and we divided by the other number right 2 * 50 divided by 5 we can be a in this case right it's all we're doing is we're setting up a proportion and the reason why I put the five up top is is the 5:00 comes first the talking about 5 Motors in 2 hours so when I ride my what to write my number then I put the five first five motors for 2 hours and then to talk about 50 Motors over here I read in the same location because the motors come first and the hours are down below once I have that setup I cross multiply and divide by the other number yes I think is Steve because if you leave a you multiply into by 5 to you not just multiply 2 by 50 divided into it it would be like this 2/1 * 50 if you were to put in fraction form so you multiplying the 2 * 250 which is 101 times at 5 which is 5 and then 100 / 5 which is 20 you said keep the same it keeps the same proportion 522 or 5220 Museum in proportion go down to question number 3 so question number three reads Frank owns a discount music store the table below shows how much Frank pays for certain merchandise items to find his selling price Frankie each price by 35% to find his selling price Frank increases each price by 35% what is the selling price of a poster increases by 35% the basics and what is 5.60 increased by 35% so figure that out so one way of doing it the quick way of doing it is going into your calculator because there's two ways right one way is finding out what 35% is and then adding it on to Five Point 60 or you can do it in one step by doing this in your calculator going by points 16 * 1.35 the reason why is it so that it includes the original price of 60 plus the 35% increase instead of doing five point the other option would be to do this but it's two steps other options to go 5.60 * 35 figure out what that is and then add that about to 5.60 do you save yourself one step by going with the first option if I choose the first one how do I get that one on 35 you put the one so that it includes the 5.60 is 5.60 * 1 is going to be the 5.60 135 is included to represent the increase Eagle 5.60 * 1.35 we got 7.56 which is Bering which is be and the reason we type 35 is because we're converting the percentage into a decimal and in order to do that we just move the decimal place over two spots to the left when we convert nevus car is now worth $12 this is 60% of what she paid for it this is 60% of what she paid for it how much did she pay for the car a problem like this 100 over here the parts goes up top the total goes down below the percentage goes over here 60% goes on top of the 100 my part is 12000 and I need to figure out what the total was right 12000 is 60% of what that's what they're asking is so in order to solve that cross multiply and divide by the number of top Saiga 12 thousand * 100 divided by 60 and I get $20 question number 5 reads at a shop the ratio of Union to non-union workers 7 to 3 if there are 18 non-union workers at the shop how many union workers are there so the ratio problem right so the ratio of Union is 7 to 3 so meaning 7 comes first because it's mentioned purse so seven comes first and three girls here so seven represents so Union house for you for Union and I'll put in you for not Union non-union so if there are 18 non-union workers at how many union workers are there so this 18 where does it go does it go up top or down below down below down below us with the rest of the non-union workers and now I'm waiting for this over here so I cross multiply and divide by the remaining number I go to my calculator I go 7 * 18 is me 126 and I do 3 which is in 42 question number 6 Reed's Camila earned $954 in commission on on 15900 in sales what is her rate of commission 100 they're the percentage of top this is my part is my total I cross-multiply 9 / the other number Tigo 954 * 100 is me 95400 and I divide that by 15900 6 she has a very low Commision 26%. Such a big sale maybe a little bummed out question 7 reads John spent the following amounts of time building a workbench drawing the plans 2 hours cutting the wood hour-and-a-half assembling the workbench 2 hours sanding and sealing two and a half what is the ratio of time spent cutting wood to the total time spent on the project okay so cutting wood is one and a half hours. and as a decimal it would be 1.5 does to the total time so the total time means I need to add up everything right so that means I need to go to my calculator I just do a calculator just to be safe you go to 1.5 + 2 + 3.5 + 12 should be beside Wilmington 1.5 + 2 + 3.5 9 that's why I have you guys so but none of those are an option to write 1.5 / 9 isn't enough so I'm going to see if I can simplify my fraction or my ratio by dividing both sides by 1.5 so 1.5 / itself is just one right Tigo 9 / 1.5 I get six so it's a ratio of 1 to 6 so we're looking at a graph that reads Ford County farm land usage okay so it's about a farm what percentage what percent of Ford County Farmland is used for growing of grains vegetables or fruits I need to know two pieces of information here I need to know the total which is given to me right it's on its 40,000 Acres and then I I need to find 9 migraines vegetables or fruit to vegetables fruits and grains are right here settings I need the address up together right so I go + 9200 + 14400 so so then we go and we set up our problem represents goes up here my part is 14400 my total is 40000 and I cross multiply and divide so I go to my calculator 14400 x 100 is mean one million four hundred forty and I divide that by 40000 I got 36 36% all right now we got a little story first so it's one Dairy Farmer in Ford county is considering selling her Farm to developers will converted from a dairy farm tours if this happens the amount of Farmland devoted to dairy in Ford County will decrease by 20% how many how many acres of Farmland was Will Ford counting Benz then have is a Farmland farmer decides to sell his big story so let's see what's up important so we need a hundred percent and that's how much land the Dairy Farmer has write 20 mm it's going to decrease by 20% so we need to find out either with 20% of it is and then subtracted from the total or if it's decreases by 20% Then what percent will be remaining if 20% is decrease than what percent do we have remaining 80% right what's the 80% like me saying it's like me saying I'm going to give you 20% but say I have the land and I tell you I'm going to give you 20% of the land how much am I keeping we could either do 20% - 10% of the land - what I'm giving you or I can just find out what 80% is the amount that I'm keeping right I guess it's 100% of the land if it's decreasing by 20 is the other 80% so I'm putting 80% so that I don't need to do the subtraction after I'm saving myself one step that's what I'm doing. We can do the 20 you can find out what 20% is 10 subtracted from 22000 which will be 1776 let me see it sometimes sometimes there are mistakes in the book and sometimes I make mistakes too soon sometime soon 17000 is it an extra zero 17600 that was a very long story we didn't need any of this worried this is all we need decrease by 20% how many acres of Farmland will the Beaufort County have this highlighted part is all we needed that's all we needed questionable oven a drawing of a company logo is 4 in 5 inches long if the drawing is enlarged so that it is 12.5 in long and the original proportions remain unchanged how many inches wide world enlarged going pink okay so we have 4 in wide what's the W in 5 inch long so why why map of the four in first because it's mentioned first in the story so far in Ghostbusters and the saying get the drawing is enlarged so that it is 12.5 in long so where does my 12.5 go up top or below Bluff 12.5 so now you can go ahead and multiply Android psycho 4 * 12.5 equals 50 / 5 equals 10 boo turn 12 reads a local hospital currently has 184 male patients If the ratio of male to female patients is 423 how many shooting how many female patients are there in the hospital call Megan Ford so is 184 males If the ratio for male-to-female is 43 so 4 to 3 the 184 * 3 equals 552 + I / 4 ca-138 138 females all right question 13 a newspaper advertisement contains the following information in dollars what was the original price of the upright bike okay so first of Thai light. Bright bike upright bike is 720 it has been reduced 20% right so I put a hundred at at 7:20 I'm going to try to figure out what the original price was but if it's been reduced 20% so if 20% is the amount that you're not paying then what percent are you paying 18 x 80% so 720 is 80% of the original price does that make sense if 20% is off then you still are paying the remaining 80% meaning that 720 represents 80% of the original cost okay so if you go to the store and they're telling you regardless of the price let's say it's $100 and they say it's 20% off right 20% is the amount that you're getting off what percentage are you still paying 80% or 80% so this is the same scenario here where we don't want to figure out what 20% is because 20% would be the discount you want to figure out how much the original price so it's 7:20 doesn't represent the discount it represents how much you are paying without a disk on a 727 20 is what the discount 900 cuz we don't know what the original price is but this is the sales price the sales price at 7:20 so that's why I put 80% cuz that's the percentage that you are paying 70 $20 represents 80% of the original I'm trying to figure out the original so you cross multiply 1 / 8 CJ7 20 x 100 divided by 8900 so that was the origin of praise originally cost 908 was 20% off which was 7:20 after taking 20% off yeah in the most basic way would be like if I'm holding up this think of of each finger representing 10% right and together this is 100% if I'm not paying this 20 then what am I paying you can you can also use like this would be like a physical example of the representation oh we skip Skip One Number 10 number 10 says a serving of peanut butter contains 3 grams of saturated fat in 13 grams of unsaturated fat this amount of fat is 25% of the recommended amount of fat in a 2000 calorie diet what is the ratio of grams of saturated fat to Total fat in a serving of peanut butter wow they give you a lot of information that you don't need essentially confusing cuz they give you three grams 13g 25% 2000 calorie they're asking is this I'm going to highlight the question what is the ratio what is the ratio of grams of saturated fat to 3 2 total time so I need to add I have my 3 grams and what's this in total 3 + 30 1617 Horatio 316 that was you that's what it's like when I read it I kind of laughed cuz I was like they're giving you all this information that you don't need it's kind of like it's kind of like someone that tells a story but they say all these extra details that aren't necessary to the story and then in the end it was just a short little message right that's why sometimes it's good to get to the point Yaki purse short all right question 14 the Tigers ratio of wins to losses is 524 if the team continues winning at the same rate how many games Tigers win in a 72 Game season that's a tricky one because we need to do some calculations here so the win to loss ratio is 5 to 4 so how but they're giving you the total games here right 72 games so it's so the winds is the five the losses is the four in total how many games do they play right here all right here if the if they if they win 5 in the snooze for how many games did they say 909 games right and this is total and then winds up here photo so how many total games are they going to play in the season and out of the nine games that they play how many do they win so do you see how it's not 425 we had to do a one extra step because it's wins to Total not wins to losses when multiply and divide by 9 psycho 5 * 72 equals 360 divided by 9 is 4040 a television station called 400 blows and asked the following question do you approve of the governor's new education program the table below the results of the survey undecided 16 yes 32 no 52 of the people called how many did not answer no did not answer no silly waves including These Guys these guys so is 52% said no 48% said something other than no right and so what I need to figure out is what is 48% of 400 right or hundred so I cross multiply and divide 400 * 48 is 19200 / 100 192 the price of a carton of computer paper decrease from 25 to 2 what is the percent decrease in the price so what is the amount that decrease the amount how many how much are we going from 25 to 20 so that Samantha decrease write 5 out of the original price which was 25 so let's see what you got we're going to ticket lift by we got the V because it's the difference between 25 and 20 it's amount of Catholic priests are between $25 it was down $5 to $20 putting the amount that decreased over the original price and the cross multiply so you go 500 divided by 25 20% all right but seeing 6 months ago 55 regular customers now she has 220% as many regular customers as he did six months ago how many regular customers does Andrea have now so it doesn't matter that it was 6 months ago six months it doesn't matter what matter is their business saying what is 220% of 55 plus what they were saying so it's going to increase write my new number is going to be larger than 55 Niger 121 I remember this song gave me problems let's see if one gram of fat equals 9 calories what percent of calories in a Munchies roast beef come from fat its 1 I can already feel it I didn't I didn't understand it and it's giving trouble now okay so let's break it down so they're asking about the roast beef sandwich specifically they say one gram of fat equals 9 calories what percent of Cal okay so this is that Mrs calories down here right the roast beef has 6 grams of fat I need to figure out how many calories it has so I cross multiply divided by 1 9 * 6 is 54 / 154 there's no option how do you get there 600 person I mean and then they want to know what percent 54 is out of 300 calories so 54 out of 300 is what percent cross multiply and divide 54 * 100 equals 5400 / 300 did 18 thank God we got it I read it I didn't understand it and I remembered it from last time that I taught this section yeah so let's do a little recap on down cuz I was a little bit Troublesome so the first thing we did we had to do two separate steps right the first step was figuring out how many calories came from the 6 grams of fat from the roast beef sandwich and we figured out that it's 54 calories once we figured out that it's 54 calories we need to figure out 54 is what percentage of the calories out of 300,000 for every $8 in their budget the park spent three on food if their weekly budget is 704 how much do they spend on food each okay so for every eight bucks they spent three if their budget is the budget is 704 how much are they spending cross multiply and divide 23 * 704 yeah to 6400 people at the park you're under 64 for a whole week how much is a day if you want something Travel estimates that 80% of its employees have more than 12 days of unused if 140 + 4 is have more than 12 days of unused sick leave how many employees work at the agency that's a mouthful that's funny so 80% of its employees have no more then 12 days 140 represents the 20% pure what's 20 person all the one that I have to have less than 12 Days a hundred and forty have more than 12 so it's 240 is the 20% of them and it goes up top because it's it's a it's a part out of the total we need to figure out how much the total is I would have put 90%. The 90% is what we know 20% Then I 140 so I've seen 30140 * 100 14000 / 12 700 704 please what is a mouse who honestly like what that 12 days of unused more than 12 days less than 12 days the 12 days is really relevant you don't need it I mean we don't use the number 12 in this problem at all it's just a distinguished two sets of employees when I don't understand how do you get the 20% from 1 40% less than 12 days and if 80% have Lesson 12 days and 140 have more than 12 days and 140 represents the 20% remaining 20% of employees you mean $140 hundred percent and then the 80% we don't know how much how many employees because they just 80% of the total right so we don't know what what number that is but if they say 80% have this and 140 have. 40 is the other 20% how do you know because they're telling you that look there's there's two sets of people right people who have more than 12 days and its people Lesson 12 dates right so the people that have less than 12 days there's only two groups are already right here remember one remember one is less than 12 days they are 80% of the population right so if 80% of the population is already accounted for what's the other remaining 20% the 20% they tell us is 140 if 140 have no more so that the other group why I got it how many it's it's by process of elimination it's kind of like it's like if you walk into a room and I say half the people are wearing black the other half are wearing red and I tell you and I tell all the people were wearing black to come out of the room can you know everyone inside the room is wearing red right or if I say there's 10 people in the room 8 of them are wearing black then you know that the two remaining ones are wearing red yep Oakland the first group is 80% 80% is right here so the other remaining group has to be 20% right in order to make a hundred where was not clear for me the 80% roofers the 140 people that's the way you are + 12 days to 20%. 80% we don't know what it represents we don't know how many people are 80% we just know that there's 80% the other one 40 represent the 20% do the finger so this is 100% right 80% have less than have less than lesser more than Twelve Days right and these other 20% they tell us that they're 1:40 directions is it going to be 100% - 20 with give us 280 right or the other way around whatever is missing right if it's 60% is the you know the other person is 40% and 70% the universe 30% whatever number I give you you know the difference. That's how we know that it's 20% all right but anyways you can re-watch it on the video the Gladstone theater has 900 seats at a recent show the ratio of tickets sold the unsold was 11 to 12 how many tickets were sold okay salt on salt okay so let me do a little bit of highlighting so sold represents 11 unsouled represents 12 in total how many tickets did they have 12 12 in Soledad 12 tickets so the ratio is smiling now no I'm out of out of every twelve tickets they sell 11 right out of out of every twelve tickets they sell 11 so out of all their seats how many do they fill up that's what we want to figure out so you cross multiply and then divide the trail 825-800-2825 last one right here God will put an end to the headaches 2222 Matthew puts 2200 in a savings account for 1 year and 6 months if you earn simple interest on annual rate of 8% how much will you have in the account at the end of the time. So I'll put up the formula so interest equals principal times rate times time so let's identify in different colors principal times rate times time so the principle that we're just means the amount of money the amount of cash so the principal was 2200 the rate means the percentage Pittsburgh as a percent the time Mean Time 1 year and 6 months so so hopefully the color coordination helps you identify where everything goes some my interest so what what amount is my pee two children 2200 ray x my rate so what's my rate 8% pointedly times now here's a tricky one comes my time it's 1 year and 6 months right so we know one year point and a lot of people with 2.6 cuz they see six months point six right but that's not that's not the case here now we do 6 months how many months are in a year 1206 out of 12 is 1/2 right if I have such 1.2 612 / 61 over to right what's 1/2 as a decimal 25.5 we put I can write them it's point 59.6 very tricky now that way next time you go to the bank and you and your two trying to see how much money you have in the bank so I typed in the wrong number you can correct them all your money's been going Toledo 2200 * 2.08 * 1.5 and I got 264 right so that's my interest 264 and all I need to do is add that to my original amount of 2000 200 so you get oops 4642 see migraine Easter explosion a television set that is regularly regularly priced at 410 is on sale for 20% off what is the sale price of the tub so here we go again so if you're not paying 20% what percent are you paying 80% go back two fingers if this is 100% And I'm not paying this 20 then I'm paying so you know for 10 * 80 divided by 100 28 I was trying to read what that was on a county map shown below the masquerade half an inch equals 60 miles what is the actual distance in miles between Lakeview and Riverside okay so we understand with the questions asking question stain on a map when you look at a map where you go on Google Maps will have to have a scale right cuz you're looking at it on a tiny computer and it was saying half an inch equals so many miles in this case half an inch 60 miles Finch on Me based on your computer in real life that's 60 miles in between what they're saying is that in between these two locations is two and three quarters of an inch to how many miles is that rep that's what they're asking is so we're going to do is we're going to set up our problem we have 0.5 / 60 right inches of top miles below right so now my question is how many what is 3 quarters as a decimal three quarters 17575 I think I've ever had said about 75 so so that is 2.75 inches miles and all you do is cross multiply and divide by MattyB number I-75 I'm sick equals 165 / 0.5 3:30 distance 3 Mile. 330 miles how's the video again I need to start from the beginning we can't print over many times OKC Rios bookstore music book store kept track of the number of customers who visit his Story 3 day. And the number of those who made a purchase question reads which of the following can be used to find what percent of Sundays customers did not make a purchase so what day are we looking at Sunday so always focuses focusing on is this number of custom number of customers who made a purchase so here we go again so how in the world am I going to figure out how many did not make a purchase 140 - 91 perfect thank you so I am I calculator then I go 140 - 91 I got 49 right eraser 49 over the total number of customers rights what's my total number of customers that day thunder in 40 40 you cross multiply and then divide you see right here they have they don't have 49 they have 140 - 91 140 - 91 gives us before I lost two and then we're home free a school admits nine out of every 14 students with fine at this rate how many students will be admitted if 420 + 5 we have nine out of every 14 how many is 420 + 5 they were so nice they probably figured by this point our brains needed a little bit of a break Play 70s R&B all right last one a 40-hour workweek Marcy spends 15 hours and stream telephones what is the ratio of hours spent answering telephones 2 hours doing other types of work so how am I going to figure out other types of work 40 - 15 + 2 40 - 15 which is 25 the ratio is 15 to 25 what can I divide 15 and 25 by atopica how do I get five YouTube they have the guys

Uploaded by Daniel Gomez.

Videos

Math Bootcamp

More videos from Daniel Gomez