How to Solve Proportions | Math with Mr. J

welcome to math with Mr J [Music] in this video I'm going to cover how to solve a proportion I'll cover how to use relationships and cross multiplication let's start by using relationships to solve proportions now not all proportions will have a straightforward relationship where we can use this method but it is a method we can use when we do notice a relationship there are different ways to solve proportions so this is a method to keep in mind let's jump into number one where we have 10 to 2 equals 32x so X is our unknown we need to find what x equals so let's look for a relationship that uses multiplication or division horizontally so side to side between the ratios we can use this relationship to figure out the unknown X now remember whatever we do to the top term term we must due to the bottom term or vice versa whatever we do to the bottom term we must do to the top term in order to keep this equivalent and in proportion this is just like working with equivalent fractions these just happen to be ratios in fractional form and they form a proportion so let's take a look at the 10 and the 30. is there a relationship there that either uses multiplication or division well yes we know 10 times 3 10 times 3 equals Thirty so whatever we do to those top terms we can do to the bottom terms in order to figure out what x equals so 2 times 3 equals six x equals 6. now we can also go the other way and use division so you can go either way when looking for that relationship so let me rewrite the ratios down below so 10 to 2 equals 30 2x so you may have noticed that 30 divided by 3 equals 10. so we can think what divided by 3 equals 2 well 6. so X equals 6 that way as well so keep in mind that you can go from left to right or right to left looking for that relationship that uses either multiplication or division let's move on to number two where we have x 249 equals four two seven so we need to see if we have a relationship between our ratios looking horizontally so side to side let's take a look at the 49 and 7. so do we have a relationship here well yes we know that 49 divided by 7 equals seven let's use that information to figure out what x equals so what divided by 7 equals 4 well 28 divided by 7 equals four so x equals 28. now we can also go the other way and use multiplication let's take a look at what that will look like so x 249 equals 4 2 7. well we know seven times seven equals 49 so let's use that information to figure out X well 4 times 7 equals 28 so we get 28 that way as well so there you have it there's how you solve proportions using relationships now again not all proportions will have a straightforward relationship like these examples did but it is a method to keep in mind if you do notice a relationship and you can use that relationship to solve for your unknown now let's take a look at cross multiplication a method we can use for any proportion not just proportions where we notice a relationship here are our examples for cross multiplication now when solving proportions using cross multiplication we cross multiply set the cross products equal to each other and solve let's jump into number one where we have 3 to 12 equals 5 to X so X is our unknown we need to find out what x equals first we'll do three times x that gives us 3 X we can bring our equal sign straight down and then we have 12 times 5. now I'm going to use a DOT to represent multiplication that way there isn't any confusion between X's that are variables and then X's that are multiplication sides now we can do 12 times 5. so let's bring our 3x down equals well 12 times 5 that equals 60. so we have 3x equals 60. now we have a one step equation that we can solve to figure out what x equals so we need to isolate that variable of X we do that by dividing both sides by three so three x divided by 3 and 60 divided by three three x divided by 3 gives us X and then 60 divided by 3 gives us 20. x equals 20. now one more thing I do want to mention about using cross multiplication to solve proportions don't get too held up on what numbers to multiply first or which diagonal you should put on which side of the equal sign it will all work out the same either way just make sure to multiply diagonally and have the equal sign in between your cross products let's move on to number two where we have 33 to x equals six to two we'll start by cross multiplying so multiplying diagonally first we'll do 33 times two so we have 33 times 2. bring our equal sign down and then we have x times 6 which we can write as 6 x next we can do 33 times 2 that gives us 66 bring our equal sign and 6X down now we have a one step equation that we can solve in order to figure out what x equals we need to isolate that variable of X and we can do that by dividing both sides by 6. 6X divided by 6 will isolate that X and then we also need to do 66 divided by 6. 6X divided by 6 again isolates that variable so x equals and then 66 divided by 6 gives us 11. so x equals 11 and we can rewrite that as x equals 11. so there you have it there's how you solve a proportion using cross multiplication cross multiply set the cross products equal to each other and solve to recap we can look for a relationship to solve a proportion or we can use cross multiplication I hope that helped thanks so much for watching until next time peace