hey everyone today we're doing a quick review on ratios rates and unit rates as requested we'll go through the definitions of what each term is and a couple real-life examples of ratios rates and unit rates before we get started be sure to subscribe to this channel for more math videos and study tips don't forget to give this video a thumbs up for good luck let's go so what exactly is a ratio in math a ratio is a comparison of two quantities if you look at our first example which is this group of people we'll notice that there are more boys than girls so we can say the ratio of boys to girls is three boys to two girls you can write the ratio as three to two or three colon two or three over two but out loud you would just say that the ratio of boys to girls in this group is three to two you can also flip it and say the ratio of girls to boys is two to three either way you're saying the same thing that there are more boys than girls in this group if we look at another example say i'm making this fruit salad and i want to incorporate some strawberries but i like blueberries better so i want a higher ratio of blueberries to strawberries if you see here i have one two three four five six blueberries and one two three strawberries so the ratio of blueberries to strawberries is six to three which can also be written in these different ways we can also talk about simplifying the ratio just like how we simplify normal fractions if you divide both numbers by three the ratio of blueberries to strawberries simplifies to two to one this actually tells you that for every two blueberries you have one strawberry this all sounds super abstract and useless but in real life you'll hear ratios used in statistics like you have a 1 and 292 million chance of winning the powerball lottery or just in everyday life for a chocolate chip cookie recipe your ratio of flour to chocolate chips is three to two which means for every three cups of flour you use two cups of chocolate chips so then what are rates remember how a ratio is the comparison of two quantities a rate is actually a specific type of ratio a rate is also a comparison of two quantities but with different units so before we were comparing boys and girls where the units of both numbers were people or humans but with rates the units of the numbers might be different in the real world you'll often see rates as it relates to time for example you'll hear about miles per hour or kilometers per hour if you're outside of the united states and this is in the context of speed or driving or traveling let's look at if you're on a road trip from los angeles california to san francisco california the distance between these two cities is 360 miles it'll take you about six hours without traffic to get there so the rate you'll be going is 360 miles per 6 hours whenever you hear the word per this means division so you can actually write this rate as a fraction where the miles goes on top and the hours go on the bottom we'll talk about unit rates a little later and that's where we try to make the number on the bottom equal one you'll also commonly see rates that include money for example if you're at a store buying one of those huge packs of bottled water let's say it costs four dollars to buy a pack of 32 water bottles so written as a rate we have four dollars per 32 water bottles which we can also write as four dollars over 32 water bottles another real life example includes heart rate so for example if your heart rate is 60 beats per minute or 60 bpm that means that your heart actually beats 60 times every minute if your heart starts beating faster during exercise or if you're anxious your heart rate might go up to 100 or more beats per minute i mentioned earlier we're also going to talk about unit rates as a reminder a ratio is a comparison of two quantities a rate is a specific type of ratio and it's also a comparison of two quantities but with different units and now a unit rate is a specific type of rate it's also a comparison of two quantities with different units but for a unit rate its denominator equals one if we go back to our previous example of the road trip from la to san francisco our rate was miles per six hours in order to get the unit rate for that trip we need to make the denominator equal one we can do this by dividing both numbers by six 300 divided by 6 equals 60 and 6 divided by 6 equals 1 which is exactly what we wanted for our unit rate so now that our denominator equals 1 we found our unit rate often hear this said as 60 miles per hour so this is how fast you should go on average in order to reach san francisco in six hours if you drive slower at like 40 miles per hour it'll take you longer than 6 hours obviously if you drive at a higher rate or a higher speed like 75 miles per hour you will get there faster than 6 hours of course you risk getting caught by the cops and you risk your safety which is not worth it so don't speed for our second example when we were talking about rates if we wanted to figure out how much the unit rate of each water bottle is we want to make the denominator equal one we can do this by dividing the top and bottom by the denominator which is 32 i'm using a calculator here but we will get 0.125 on the top and one on the bottom so our unit rate is 0.125 or 12.5 cents per one bottle this doesn't make practical sense because you can't really have 12.5 cents but you get an idea of how cheap it is to buy water bottles in bulk technically this means you're paying 12.5 cents per bottle just compare that to the price of vending machines where you're paying at least one dollar to get one single bottle of water so now you know what a ripoff vending machines are better yet you can buy refillable water bottle and fill it for free at a water fountain i hope you all learned something in this video be sure to give it a thumbs up if it did help you out and subscribe for more math tutorials and study tips comment down below to let me know what other topics you want me to cover see you in the next video