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Added Jun 01, 2022 •

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Equivalent Ratios

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all right you guys welcome back to another math Bridge lesson So today we're talkin about equivalent ratios let's take a look at some of our objectives of equivalent ratios values and tables containing equivalent ratios and finally use tables to compare ratios the first was talk about tables open the Rachel's in the. and we learned that a ratio is only compare two different things right and here they have an example about a cake recipe containing 2 eggs for every 3 cups of flours send it you know any any which way that they have listed here to eggs to 3 cups of flour 2 to 3 or 2 over 3 so any of these options are are perfectly fine for the ratio so if we were to incorporate in a table this is what it would look like we have two columns one with the first item in the eggs and the second item cups of flowers so we would list that under each of those at titles and so let's say we wanted to make a law search eight or more than we would need to have a a ratio that could support a larger case and the numbers are going to change the numbers are going to increase but the ratio will remain the same so we'll see that in the upcoming slides so for example in this ratio they have a two to three ratio right in the next one have a 426 which is the same ratio so these two are going to be equivalent ratios and we can do is just take a calculator and divide one by the other in your realize that in a few / 2 / 3 or if you divide 4 divided by 6. The same answer going to the same decimal all right so here they go on and build that they gone and they build that a ratio right so +42-669-812-1015 12 to 18 so if we notice the numbers are increasing but the ratio is remaining consistent so this would come in handy if you wanted to you know increase the quantity or the size of the cake these are all equivalent meaning that if we were to take any of these fractions and take the numerator divided by the denominator to get the same answer as you would with any of the other factions alright so here we have a table where we have a 1 gallons is 25 MI we can expand that table by adding additional additional gallons of gas this again is ratios are equivalent if you take you to the fraction divide the numerator by denominator the same thing these are all equivalent ratios the numbers increased at the ratios remain consistent you notice the rate of change is also consistent gallons of gas always increasing by one and miles how old is increasing by 25 so let's go ahead and take a look at this table and let me know if these are yes yeah perfect so unless all of these are increasing by one and then on the right increasing by 12% okay so let's look at the left-hand column it's increasing by one what is the next number on the left going to be if they're increasing by one yes the number and left will be five and then Applebees 61st all right let's see on the left we have an increase of one on the right we go to 85 so is this equivalent ratios are these ratios equivalent Lisa no help all right so we're back to the same example income so it is a nurse what happens when you multiply the parts of the fraction in this way so across x in x the the denominator of the fraction comes in the murder of the second and vice versa and they get the same number and so this is called the cross product when you cross multiply and you get the same so they pick to completely random ratios from the table just to demonstrate that it can work with any of the races Sinatra The Cross Park Road and come in handy you can quickly determine if she ratios are equivalent or not Raider / the denominator and do the same here you can divide your fractions and see if you get the same answer or you can cross multiply and see if you get a minute alright so here we get different answers so that are fractions are not equivalent ratios all right so we do the cross product check and we seem to get the same answer so he's would indeed be this would indeed be equivalent okay so let's go ahead and we're going to go 6 * 55 week at 3:30 15 * 22 to get 330 so that checks out these are equivalent okay room do 4 * 9360 14 x 26 364 sweetie okay and now when we do ratios there can also be variables in a ratio you can be trying to find a Unknown about success here got to let us know how to find Beck's movie do his first we cross multiply * 30 and we divided by the other number so it's always across that multiplication of Curtis and then the other the third number that we didn't use that's the number we / so this case we need to go 10 * 39 / I got next so we have 10 * 3300 + 1 / 75 figure out better meow for is the missing value I can plug it in and have our route ratio all right same here we're going to cost more by the four with the 91 10 / 14 so we got 364 and I'm going to take that number 5 x 26 26 is X represents all right so now it's go to the skills check so we're going to first cross-multiply Sammy's were doing six 42 that gives us 252 we don't take that number divided by 9 and we get 28 it's always the multiplication doesn't matter where the axes located right it should be on the top left top right bottom right all we do is we always multiply two numbers that are Frost diagonal from one another right that's what you multiply the third number that we didn't use it that much that's the number that we divide our answer by okay in this example we see instructions for mixing herbicide with water to cheat Ark are the ratios on the table all right so let's see again you can do the cross multiply just take your numerator / genomics 0508 / 20 again point zero point four so I should get the same with all of the other ratios I do so if you take any of these numbers 8 / 2000 get 0.436 / 90 .4 and 38 / 95 0 point for these are all equivalent ratios here all right let me have it this table shows the number of raisins in trail mix this table show current ratio so let some let's do the division method the reason why I opted out for the day off for the division method is because we we have you know multiple areesha show more simple to just divide the reasons by 8.5 for the first row 8.5 + and 8.5 for the show all Rose check out so yes all right so if you happen to have a missing value in the table we can figure that out that's no problem so let's see here we have a beach the 20 and then here we're missing the gallons of water so you know we can just use that that equation where we have 8/20 is equal to 18 / x x across and / the other number we have to set up an equation with the choo choo fraction for 2 ratio I guess the 8/20 and 18 or acts the way that you know which where to place your numbers is the age of 18 have to be in the same row to notice to eat in the 18 are both on top 20 of the acts have to also be in the same bro order cups of herbicide don't have to be in the same location in the project meeting it will have to be numerators because 20 + x under the category of gallons of water a boat have to be in same section of the fraction meaning both in the denominator I want to set it up I miss you can cross multiply 20 * 18 and then divided by 8 360 / 8 all right so let's set up so here we have a 1:36 or 16 oz equal to X Uber let me put it like this section I set it up my dad so it's a little easier to to see where the most patients happening so this 136 is going to multiply x 230 we're going to get 4080 divide that number by 16 how to get 255 race make my selection Perfect all good spring all right now all right so we're all set for that lesson hopefully destinations made sense just to recap when we talk about equivalent ratios it doesn't mean that the numbers have to be the same numbers it just means that they have to have the same relationship and we already found out two ways of checking that right one of the ways was setting up the two ratios side by side cross multiply meaning X ignoring you should get the same answer when you do the multiplication the second way is through the use of division take your first ratio divide the numerator by the denominator and see what number you get when you do the same thing for the second ratio to get that same number if you do and those are equivalent ratios the third thing we learned was finding the missing value so for that you set up your ratio is equal to one another you cross-multiply doesn't matter where Texas located in the ratios by wherever it is you're going to cross multiply the numbers and then once you get your answer you going to divide your answer by the third number that you didn't use in the most and that's going to give you your solution for a

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