Intro to rates
Jayda takes 3 hours to deliver 189 newspapers on her paper route. What is the rate per hour at which she delivers the newspaper? So this first sentence tells us that she delivers, or she takes, 3 hours to deliver 189 newspapers. So you have 3 hours for every 189 newspapers. That's what the first sentence told us. But we want to figure out the rate per hour, or the newspapers per hour, so we can really just flip this rate right here. So if we were to just flip it, we would have 189 newspapers for every 3 hours, which is really the same information. We're just flipping what's in the numerator and what's in the denominator. Now we want to write it in as simple as possible form, and let's see if this top number is divisible by 3. 1 plus 8 is 9, plus 9 is 18. So that is divisible by 3. So let's divide this numerator and this denominator by 3 to simplify things. So if you divide 189 by 3. Let's do it over on the side right here. 3 goes into 189. 3 goes and 18 six times. 6 times 3 is 18. Subtract. Bring down the 9. 18 minus 18 was nothing. 3 goes into 9 exactly three times. 3 times 3 is 9, no remainder. So if you divide 189 by 3, you get 63, and if you divide 3 by 3, you're going to get 1. You have to divide both the numerator and the denominator by the same number. So now we have 63 newspapers for every 1 hour. Or we could write this as 63 over 1 newspapers per hour. Or we could write this as 63, because 63 over 1 is the same thing as 63 newspapers per hour.