Rates and Unit Rates | Math with Mr. J

welcome to math with Mr J [Music] in this video I'm going to cover the basics of rates and unit rates I'll cover what rates and unit rates are and then how to find unit rates now rates compare and show the relationship between quantities with different units so rates are just ratios that compare and show the relationship between quantities with different units a unit rate is a specific type of rate a unit rate is a rate with a denominator of one it shows per one unit let's jump into our examples and see exactly what this means starting with number one where we have 36 miles in four days for example let's say that someone rode their bike 36 miles in four days this rate Compares and shows the relationship between the number of miles ridden and the days that it took to do so so two different units of measure miles and days we can write this rate as a fraction now order matters we have miles and then days so our fraction needs to represent that order 36 miles and in four days make sure to label and include units within rates since we are working with different units we need to be clear what those units are so this is a rate 36 miles in four days now let's find the unit rate unit rates always have a denominator of one we want per one unit in this case we want how many miles per one day let's do this by dividing our denominator by four that will give us a denominator of one representing one day so 36 miles and four days is going to equal well again we need to divide by 4 in order to get that denominator of one four divided by 4 is 1. and we need to label so this is one day whatever we do to the bottom we must do to the top so divide 36 by 4 as well 36 divided by 4 is 9. and this is Miles and that's our unit rate 9 miles per one day or nine miles per day now we can also write this as nine miles per day so our original rate was 36 miles in four days and then we found our unit rate we did that by getting our denominator to equal one we did that by dividing by four that gave us nine miles per day let's move on to number two where we have ninety six dollars in eight hours so someone makes ninety six dollars in eight hours we will write that as a rate in fractional form and then find the unit rate so let's first write that as a rate in fractional form so we have ninety six dollars in eight hours so that's our rate let's find our unit rate so how much money per one hour we can do this by dividing by eight because again we need that denominator to equal one so let's divide by eight here to give us one hour whatever we do to the bottom we must do to the top so 96 divided by 8 as well that gives us twelve dollars so our unit rate is twelve dollars per one hour or twelve dollars per hour and we can also write that as twelve dollars per hour so there you have it there's how you write rate and unit rates rates are ratios that compare two quantities with different units and then a unit rate is a specific type of rate it's a rate with a denominator of one we show per one unit I hope that helped thanks so much for watching until next time peace foreign