Sal uses ratio reasoning to convert measurement units.
- [Instructor] We're told to complete the ratio table to convert the units of measure from hours to weeks, or weeks to hours. So we see here, they've told us already that there's 168 hours for every one week. One way to think about it is the ratio of hours for every week is 168 to one, and then they calculate, well if we have 1,176 hours, how many weeks is that going to be? So pause this video and see if you can figure it out. Let's see, to go from 168 to 1,176, what do we have to multiply by? So, let's see, that looks like we might be multiplying by seven. Let me try that out. So 168 times seven is equal to... Eight times seven is 56, six times seven is 42 plus five is 47, and then one times seven plus four is indeed 1,176. So we multiplied by seven, we multiplied the number of hours by seven, so that means we're gonna have seven times as many weeks. So, one times seven is just that is seven weeks. Now, what about a situation where we have three weeks, how many hours is that going to be? Well we are multiplying our weeks by three, so we would wanna multiply our hours. We would wanna multiply our hours times three. So, 168 times three, eight times three is 24, six times three is 18, plus two is 20, and then one times three is three, plus two is five. So, that would be 504 hours. Let's do another example. So, here they tell us the double number lines show the ratio of yards to miles. So, the ratio of yards to miles. It looks like we have 3,520 yards for every two miles. For every two miles, and you see that on this double number line right over here. Then they say how may yards are in five miles? So, why don't you pause this video and try to figure it out. Well the way my brain wants to do it is, well let's just think about how many yard are in each mile. So, if the ratio's 3,520:2, how could I rewrite this ratio so it is how many yards for every one mile. So, to go from two to one, I am dividing by two, so I would wanna divide this by two as well. So, two goes into 3,520, let's see, two goes into three one time, one times two is two, you subtract, you bring down the five. Two goes into 15 seven times, seven times two is 14, subtract, we have one, bring down that two, two goes into 12 six times, six times two is 12, and we subtract, no remainder, but then we're gonna have one more zero here, cuz we bring down that zero. We say two goes into zero zero times, zero times two is zero, and we have no remainder, and so this is 1,760. So, we could put that here on our double number lines. So, if we have one mile that is 1,760 yards. Now, they're asking about five miles, so three, four, five, so we have five miles. What is the number of yards? Well if you multiply by five here, you're also going to multiply by five right over there. So, what's 1,760 times five? Well just figure it out. 1,760 times five, five times zero is zero, five times six is 30. Regroup that three cuz it's really 300s, five times seven is 35, plus three is 38, five times one is five, plus three is eight. So, there you go, 8,800 yards. Let's do a few more examples. Here, we're told there are 914.4 millimeters in a yard. There are three feet in a yard. How many millimeters are in a foot? Okay, so one way to think about it, you could say there's 914.4 millimeters per yard, or you could say 914.4 millimeters per three feet, since three feet and a yard is the same thing. So, if you wanna know per foot, you would just divide both of these by three. So, let's do that, and I'll just do it in a different color here. Three goes into 914.4, Three goes into nine three times, three times three is nine, subtract, we get a zero bring down the one, three goes into one zero times, zero times three is zero, subtract, get a one, and bring down that four, three goes into 14 four times, gonna have this decimal right over here, four times three is 12, you subtract, and then, so you get a two, bring down this four, you get a 24, and lucky for us, three goes perfectly into 24 eight times, eight times three is 24, 24 you subtract, now we have no remainder. So, we have 304.8 millimeters for every foot. Let's do one last example. So pause this video and see if you can figure it out. So, let's just write this out in words. So, it's $12 per pound of confetti. So, you could do this as $12 per 16 ounces. 16 ounces of confetti, and so if we want it per ounce. So, you could do this as a 12 to 16 ratio, but we wanna say something to one ratio. So, if you say per one ounce, well we're dividing by 16 there, so we would wanna divide by 16 as well. So, this is going to be 12 divided by 16. So, 12 divided by... Well let me write it over here. So 12 divided by 16 is the same thing as 3/4, just divide both of them by four, and so this is 0.75, or 75 cents, 75 cents per ounce, or 75 hundredths of a dollar per ounce. So, 0.75, and we're done.