Learn about Rates and Ratios Rates and ratios, in this problem it states that messenger services deliver packages to businesses within town. If a messenger delivers 9 messages in 3 hours, how many messages can he deliver in 6 hours? So in this problem we’re talking about rate. A rate is a ratio that compares measurements or amounts. So here we’re talking about a rate. And rate is a ratio that compares measurements or amounts. Now, the messenger delivers messages at a rate of 9 messages every 3 hours. So we got that right here, he delivers 9 messages in 3 hours. So this is our rate. The rate of 9 messages every 3 hours. Now, to find the number of messages that he can deliver in 6 hours we need to find an equivalent ration for 9:3 with the denominator of 6. So we got the number of messages is 9 and the number of hours is 3, so messages to hours is 9:3. To find an equivalent fraction for 9/3 we multiply the numerator and the denominator by 2. So to find the equivalent fraction we’re going to multiply the numerator and the denominator by 2. So we’re going to take 9/3 and we’re going to multiply each by 2, and we get 18/6. So at the same rate the messenger can deliver 18 messages in 6 hours, so its messages to hours, so at the same rate he can deliver 18 messages in 6 hours. So here we have 18 messages in 6 hours. Now, we can also use rate to find the number of messages. So to use rate we divide the first term by the second term to find the unit rate. Again, the number of messages in the first term is 9. The number of messages in the second term is 3. So we can find the unit rate to find the number of messages. So now we’re finding the unit rate and to do that we divide the first term by the second term to find our unit rate. So it will be first term over second term which is 9/3 and then if we divide them, now we divide and we get 3 messages per hour. So note, please make note that per means for each. So when I say per it means for each. So it’s 3 messages for each hour or 3 messages per hour. All right now, what we can do is multiply the rate by 6 to find the number of messages delivered in an hour. So now we’re going to multiply our rate by 6 and that will give us the messages in 6 hours. So we’re going to multiply our rate which is 3, so this is our unit rate times 6 which would be 18. So the messenger can deliver 18 messages in an hour. Remember that a rate compares quantities. So this is something to keep in mind that rate compares quantities and values having different units. All right, so here we find the unit rate and we got our answer and here we compare the ratios and got our answer. So things to remember and to keep in mind are that a rate is a ratio that compares measurements or amounts having different units. We can use equivalent ratios to find rates. So here we used, this first part we used equivalent ratios. Now, a unit rate is a ratio in which the denominator or the denominator is 1. We divide the first term by the second term to find our unit rate.