Learn about Ratio and Unit Rates Unit rate, so the first problem states that Tom rides his bicycle 45 miles in 3 hours. What speed does he travel? So to find the speed at which Tom travels we need to write the ratio. So we’re going to look for a ratio of total miles to total hours, and we’re writing it as a fraction. So the ratio is 45 miles to 3 hours. So our ratio be our total miles, 45 and our total hours, 3. So be 45 miles/3 hours. So now we’re going to divide the numerator and by the denominator to find the rate. So here we’re going to divide the numerator by the denominator and this will give us our unit rate. So we have 45/3 and if we divide it we get 15/1. So we divide it both by 3 and we get 15/1. So that means that Tom traveled at a speed of 15 miles per hour. Let’s move on to our second problem. Here we have a gas tank and the gas tank in a small car holds 12 galloons. It can be driven 252 miles on a full tank. What is the gas car’s mileage? So now, in this problem we need to find the gas car mileage. To find the gas car mileage we need to divide the total miles by the number of galloons used. So our distance traveled is 252 miles, and then the amount of gas used is 12 galloons. So now we’re going to divide the numerator by the denominator and this will give us our unit rate. And the unit rate is the miles traveled per galloon. So our unit rate we’ll get is our miles traveled per galloon. So our mileage like we said is 252 miles to 12 galloons. So we’re going to divide our numerator by our denominator, so we’re going to take 252/12 and we’re going to divide the numerator and the denominator by 12, by the numerator. So we’re going to divide it by 12 and we get 21/1. So that means that the gas mileage is 21 miles per galloon. Thing to remember, is that when you’re talking about rate, rate compares quantities, and values having different values. So rate compares quantities and values having different units. So rate compares quantities and values having different units. So just like we compared the rates, we had miles and hour. So those are two different units. So a unit rate which we talked about, a unit rate is ratio in which the denominator is 1. So this is a unit rate. The denominator is 1. So to convert a ratio to unit rate, we divide the numerator by the denominator and the denominator by the denominator.