Determining if Two Ratios are Proportional (3 Ways) | Proportions | Math with Mr. J

[Music] welcome to math with mr j [Music] in this video i'm going to cover how to determine if two ratios are proportional i'll go through three ways we can do this i'll cover how to use simplifying cross multiplication and equivalent fractions now remember a proportion is formed by equal or equivalent ratios they represent the same comparison and relationship we'll start by using simplifying to determine if two ratios are proportional let's jump into number one where we have 10 to 15 and 8 to 12. now when it comes to checking if two ratios are proportional using simplifying all we need to do is simplify both ratios if they simplify to the same ratio they are proportional if they are different they are not proportional let's set these ratios up in fractional form and simplify we'll start with 10 215. now the greatest common factor between 10 and 15 is 5. so let's divide both of these terms by 5. so 10 divided by 5 and 15 divided by five ten divided by five is two fifteen divided by five is three the greatest common factor between two and three is one so we are in simplest form 10 to 15 simplifies to 2 to 3. now we need to simplify 8 to 12. the greatest common factor between 8 and 12 is 4 so let's divide both of these terms by 4 8 divided by 4 and 12 divided by 4. 8 divided by 4 is 2 12 divided by 4 is 3. so both of our ratios 10 to 15 and 8 to 12 simplify to 2 to 3. since they simplify to the same ratio they are proportional so we can set them up as equal to each other and write them as a proportion so 10 to 15 is equal or proportional to 8 to 12. let's move on to number 2 where we have 21 212 and 14 to 6. let's set these up in fractional form and simplify we'll start with 21 to 12. the greatest common factor between 21 and 12 is 3 so let's divide both of these terms by 3. 21 divided by 3 and 12 divided by 3. 21 divided by 3 is 7 12 divided by 3 is 4. the greatest common factor between 7 and 4 is 1 so we are in simplest form 21 to 12 simplifies to 724 now we need to simplify fourteen to six the greatest common factor between fourteen and six is two let's divide our terms by two so fourteen divided by two and six divided by two fourteen divided by two is seven six divided by two is three the greatest common factor between seven and three is 1 so we are in simplest form 14 to 6 simplifies to 723 so for number 2 our ratios of 21 to 12 and 14 to 6 did not simplify to the same ratio that means that these ratios are not proportional we can write this as 21 to 12 is not equal or not proportional to 14 to 6. so there you have it there's how you determine if ratios are proportional by simplifying simplify each ratio if the ratios simplify to the same ratio they are proportional if they don't simplify to the same ratio they are not proportional next we'll move on to using cross multiplication here are our examples for cross multiplication let's jump into number one where we have 8 2 3 and 11 2 7. now when it comes to checking if two ratios form a proportion using cross multiplication all we need to do is cross multiply and see if our cross products the numbers we get once we multiply are equal or not if they are equal then we have a proportion if they are not equal then we do not have a proportion let's start by setting our ratios up in fractional form and setting them equal to each other now they may not turn out to be equal but for now set them up as a proportion we have eight two three and eleven two seven now we can cross multiply so we multiply diagonally we'll start with eight times seven so eight times seven and then bring our equal sign straight down and now we can do three times eleven 8 times 7 is 56 3 times 11 is 33 56 is not equal to 33 so our cross products were not equal that means we do not have a proportion 8 to 3 and 11 to 7 are not proportional they do not form a proportion so we can write this out as 8. to 3 is not equal or not proportional to 11 to 7. now one more thing i do want to mention about cross multiplying these ratios 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 so if you do 3 times 11 or 11 times 3 first and then 8 times 7 or 7 times 8 that will give you the same answer 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 6 to 10 and 9 to 15. we'll start by setting these up as a proportion so 6 to 10 and then 9 to 15. now we're ready to cross multiply we'll start with 6 times 15. so six times fifteen and now we have ten times nine so ten times nine six times fifteen that equals ninety ten times nine that also equals ninety so both of our cross products are ninety that means our ratios of six to ten and nine to 15 are proportional so we can write this as 6 to 10 is equal or proportional to 9 to 15. so those ratios form a proportion so there you have it there's how you determine if ratios are proportional using cross multiplication cross multiply if the cross products are equal the ratios are proportional if the cross products are not equal the ratios are not proportional lastly we will move on to using equivalent fractions here are our examples for equivalent fractions let's jump into number one where we have six to eight and seven to twelve now when it comes to checking if two ratios are proportional using equivalent fractions we first need to write the ratios in fractional form then we find the least common multiple between the bottom terms of our ratios and rename the ratios as equivalent ratios with that new bottom term this is just like renaming fractions with a common denominator so the same exact steps we are just working with ratios we'll start by rewriting 6 to 8 and 7 to 12 in fractional form so 6 2 8 and then 7 to 12. now we need to find the least common multiple between those bottom terms 8 and 12. now when it comes to multiples think multiply or skip count for number one i'll write out some multiples of 8 and 12 as a refresher and we can look for that least common multiple we'll start with eight so i'll come to the side here and again think multiply or skip count eight times one is eight eight times two is 16 8 times 3 is 24 and 8 times 4 is 32. now multiples go on forever my suggestion write 4 or 5 for each term look for a least common multiple if you still don't have one you can always extend your lists so let's write four multiples of 12 as well and find the least common multiple between our bottom terms so 12 times 1 is 12 12 times 2 is 24 12 times 3 is 36 12 times 4 is 48 so we can look to see if we have any in common and we want the least common multiple so the smallest in value that we have in common that's going to be 24. now that we have that least common multiple we are going to rename our original ratios with that 24 as the bottom term the denominator so again we're going to rename our original ratios as equivalent ratios or equivalent fractions with 24 being the bottom number the denominator so let's come back over here and go underneath our original ratios and rename so let's start with 6 to 8. how do we get 8 to equal 24 well 8 times 3 is 24. whatever we do to the bottom we must do to the top in order to keep this equivalent so multiply 6 by 3 as well 6 times 3 is 18. 18 to 24 is equivalent to 6 to 8. so we're not changing the value of that ratio at all now let's go to 7 to 12. how do we get 12 to equal 24 well 12 times 2 is 24. whatever we do to the bottom we must do to the top in order to keep this equivalent 7 times 2 is 14. so 14 to 24 is equivalent to that 7 to 12. now 18 to 24 is not equal to 14 to 24. that means our original ratios of 6 to 8 and 7 to 12 are not proportional so we can write that as 6 to 8 is not equal or proportional to 7 to 12. let's move on to number two where we have 2 to 10 and 5 to 225 we'll start by rewriting these ratios in fractional form so 2 to 10 and 5 to 25 now we need to think of the least common multiple between 10 and 25. we're going to do this one without writing out the lists of multiples the least common multiple between 10 and 25 is 50 so we need to rename these ratios using that 50 as our bottom term the denominator so we're going to write equivalent ratios or equivalent fractions so let's come underneath our ratios and use that 50 for our bottom term the denominator we'll start with 2 to 10. so how do we get 10 to equal 50 well 10 times 5 equals 50. whatever we do to the bottom we must do to the top in order to keep this equivalent 2 times 5 is 10. 10 250 is equivalent to 2 to 10. now we need to do 5 to 25. how do we get 25 to equal 50 well 25 times 2 is 50. do the same thing to the top in order to keep this equivalent 5 times 2 is 10. 10 250 is equivalent to 5 to 25. now we have that same bottom term that same denominator for our equivalent ratios our equivalent fractions 10 250 equals 10 to 50. that means that our original ratios 2 to 10 and 5 to 25 are proportional they form a proportion so we can write that as 2 to 10 is equal or proportional to 5 to 25. so there you have it there's how to determine if ratios are proportional using equivalent fractions rewrite the ratios in fractional form then find the least common multiple between the bottom terms of the ratios that number will be the bottom term or denominator of the renamed equivalent ratios or renamed equivalent fractions if these equivalent ratios or equivalent fractions are the same then the ratios are proportional if they are different they are not proportional as a quick recap we can use simplifying cross multiplication or equivalent fractions to determine if two ratios form a proportion i hope that helped thanks so much for watching until next time peace you