Equivalent Ratios Explained | Finding Equivalent Ratios | Math with Mr. J

[Music] welcome to math with mr j [Music] in this video i'm going to cover what equivalent ratios are and how to find equivalent ratios now remember ratios compare quantities or numbers and show the relationship between them equivalent ratios are ratios that have different numbers but show the same comparison or relationship let's jump into our examples starting with number one where we have the ratio one two five let's write three equivalent ratios and go through how we do that now equivalent ratios are very similar to equivalent fractions in fact we can set these up like equivalent fractions just like equivalent fractions we are going to use multiplication or division to find equivalent ratios let's actually rewrite 1 to 5 in fractional form and go from there so 1 2 5. so 1 to 5 equals and again we're going to multiply both terms by two well one times two is two and then five times two is ten so one to five is equivalent to two to 10. now let's take a look at a visual to help us picture how these are equivalent and i'm going to use x's and o's to represent these ratios we'll start with one two five so one x two five o's one x to five o's one two three four five next we'll do two to ten so two x's two x's to ten o's one two three four five six seven eight nine ten if we take a closer look we still have one x to every five o's one x to every five o's we are showing the same comparison and relationship we just have different numbers even though we have two x's and ten o's it still represents that comparison and relationship of one x to 5 o's these ratios are equivalent and this will be the case any time we multiply or divide the terms of a ratio by the same number let's find another equivalent ratio and multiply by 5. so 1 to 5 here and let's multiply by 5. so 1 times 5 is 5 and then 5 times 5 is 25 so 1 2 5 is equivalent to 5 to 25 lastly let's do one more equivalent ratio but here we are not going to rewrite it in fractional form let's go from our original form of using the word 2. so let me rewrite it to the side here 1 2 5. so we can multiply both of these terms by a number and as long as we do it to both terms we will still get an equivalent ratio this way as well so for example let's multiply both of these terms by 20. again it's not in fractional form this time but we can still multiply both of these terms by the same number one times twenty is twenty two five times twenty is one hundred one two five is equivalent to 20 to 100 so that's another way to think through equivalent ratios other than setting them up in fractional form again just be sure to multiply or divide the terms of the ratio by the same number and you'll end up with an equivalent ratio all of these ratios are equivalent now we can also say they are proportional we have a proportion when two ratios are equal or equivalent so for number one all of our ratios are equivalent to one to five so this two to ten here five to 225 and 20 to 100. now one more thing i do want to mention before moving on to number two and that's that we only used multiplication in number one that's because we weren't able to use division the only common factor between the terms of that ratio was one so we had nothing to divide by for number two we are able to use division let's move on to number 2 where we have 12 to 8. now here we do have common factors other than 1 between our terms that we can divide by for example let's set this ratio up as a fraction and divide each term by 2. so 12 2 8. let's divide each of these terms by 2 12 divided by 2 is 6 8 divided by 2 is 4 so 12 to 8 is equivalent to 6 to 4. another common factor is 4 so we can divide both of these by 4. so let's rewrite it in fractional form 12 to 8 and divide by 4 here twelve divided by four is three eight divided by four is two so twelve to eight is also equivalent to three to two lastly let's write one more equivalent ratio and use multiplication we will go from the original form of the ratio which used a colon so let's come over to the right 12 2 8 and let's multiply both of our terms by 10. so 12 times 10 and 8 times 10. 12 times 10 is 120 2 8 times 10 is 80. so 12 to 8 is equivalent to 120 to 80. so our equivalent ratios for number two were six to four three two two and then 120 280. so there you have it there's a little bit about equivalent ratios and how to find equivalent ratios remember you can use multiplication or you can use division if there are common factors other than one between the terms of the ratio just make sure to multiply or divide the terms of the ratio by the same number and you will end up with an equivalent ratio i hope that helped thanks so much for watching until next time peace you