Simplifying Ratios Explained | How to Simplify a Ratio | Math with Mr. J

welcome to math with Mr J [Music] in this video I'm going to cover how to simplify a ratio in other words how to write a ratio in lowest terms and really this is just like simplifying fractions when we simplify a ratio we divide both terms the numbers of a ratio by their greatest common factor this will give us the smallest possible numbers and value to represent a ratio a simplified Ratio or ratio in lowest terms is still equivalent to the original ratio so we are not changing the comparison or relationship that that ratio represents we are just getting to the simplest smallest numbers in value that we possibly can to represent that ratio let's jump into number one where we have 9 to 21. now you can simplify a ratio from whatever form it is originally in so if it has a colon if it's in fractional form or using the word to I'm actually going to take our ratio and rewrite it in fractional form so it's just like simplifying a fraction so we have 9 two 21. now we need to think of common factors between 9 and 21. numbers that we can divide both 9 and 21 by well 3 is a common factor and it happens to be the greatest common factor the largest number in value that we can divide both 9 and 21 by so let's divide 9 by 3 and 21. by 3. 9 divided by 3 is 3 21 divided by 3 is 7 so we get 3 2 7. the greatest common factor between 3 and 7 is 1 so we are in simplest form 327 is our simplified ratio now like I mentioned earlier you can simplify from the original form of a ratio so however it is originally written so before moving on to number two I do want to show you that we can divide both the 9 and 21 by 3. up here as well so divide by 3 divide by 3 and we get 3 2 7 that way as well now we can also take the fractional form of our simplified ratio and rewrite it using a colon 327 or using the word two all of those ratios mean the same thing so three to seven or three two seven let's move on to number two where we have 30 to 6. I'll rewrite this ratio as a fraction as well so 30 2 6. now we need to think of common factors between 30 and 6. I'm going to start by using the greatest common factor and simplify this ratio in one step then we'll take a look at what it looks like to simplify in multiple steps so the greatest common factor between 30 and 6 is 6 so let's divide both of these by six 30 divided by 6 is 5. 6 divided by 6 is 1 the greatest common factor between five and one is one so this is our simplified ratio five to one now that is an improper fraction but we want to leave it as an improper fraction because this is a ratio a ratio Compares and shows the relationship between two quantities or numbers so again let's leave it as an improper fraction so we have those two numbers that are being compared so now we're going to go through a different path that we can simplify this ratio let me rewrite Thirty to six so we're not going to use the greatest common factor of six we're actually going to start with two two is a common factor between 30 and 6. so let's divide 30 by 2 and 6 by 2. 30 divided by two is fifteen six divided by two is three so we got fifteen two three which is different than five to one well that's because we still have other common factors other than one that we can divide 15 and 3 by here to further simplify this to further break this down well 3 is a common factor between fifteen and three so let's divide 15 by 3 and three by three fifteen divided by 3 is 5 3 divided by three is one so we ended up with five to one that way as well so keep in mind that there can be multiple paths to simplifying a ratio just like when we simplify fractions and again we can simplify from that original form let's divide by 6 up here as well so 30 divided by 6 and 6 divided by 6 that gives us five two one and again we can always rewrite our ratio in the form that we would like so for example we can take our fractional form and rewrite this using a colon so five to one or using the word two all of those ratios mean the same thing five two one now I do want to mention one more thing and that's that a ratio can be in simplest form from the start if the greatest common factor between the terms of a ratio is one then it's already in simplest form and you can't do any more simplifying so that's something to keep in mind so there you have it there's how you simplify ratios I hope that helped thanks so much for watching until next time peace