Ratios and measurement

We're told to complete the ratio table to convert the units of measure from hours to weeks or weeks to hours. So we hear, 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 1.

And then they calculate, well, if we have 1176 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 1176, what do we have to multiply by? So let's see, do we? That looks like we might be multiplying by seven. Let me try that out.

So 168 times 7 is equal to. 8 times 7 is 56. 6 times 7 is 42 plus 5 is 47. And then 1 times 7 plus 4 is indeed 1176. So we multiplied by 7. We multiply the number of hours by 7. So that means we're going to have 7 times as many weeks. So 1 times 7 is just that, is 7 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 want to multiply our hours. We would want to multiply our hours times 3. So 168 times 3. 8 times 3 is 24. 6 times 3 is 18 plus 2 is 20. And then 1 times 3 is 3 plus 2 is 5. 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 3520 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 many 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 yards are in each mile. So if the ratio is 3520 to 2, well what, how could I rewrite this ratio so it is how many yards for every 1 mile?

So to go from 2 to 1, I am dividing by 2. So I would want to divide this by 2 as well. So 2 goes into 3520, let's see. Two goes into three one time. One times two is two, you subtract, you bring down the five. Two goes into fifteen seven times. Seven times 2 is 14, subtract we have 1, bring down that 2.

Two goes into 12 six times. Six times 2 is 12, and we subtract, no remainder. But then we're going to have one more zero here because we bring down that 0. We say 2 goes into 0, 0 times, 0 times 2 is 0, and we have no remainder. And so this is 1760.

So we could put that here on our double number lines. So if we have one mile, that is 1760 yards. Now they're asking about five miles, so 3, 4, 5, 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 1760 times five? We'll just figure it out. 1760 times five. Five times 0 is 0. Five times 6 is 30, regroup that 3 because it's really three hundreds. Five times 7 is 35 plus 3 is 38. Five times 1 is 5 plus 3 is 8. So there you go, eight thousand eight hundred 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 are 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 want to 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 9 three times. Three times 3 is 9, subtract we get a 0, bring down the 1.

Three goes into 1 zero times, zero times 3 is 0, subtract you get a 1, bring down that 4. Three goes into 14 four times. We're gonna have this decimal right over here. 4 times 3 is 12, you subtract, and then so you get a 2, bring down this 4, you get a 24.

And lucky for us, 3 goes perfectly into 24, 8 times. 8 times 3 is 24, you subtract and we have no remainder. So we have 304.8 millimeters for every foot.

Let's do one last example. Yuki bought a pound of confetti for 12 dollars. What is the price in dollars per ounce of confetti? There are 16 ounces in one pound. 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 view this as 12 per 16 ounces. 16 ounces of confetti. And so if we want it per ounce, so you could view this as a 12 to 16 ratio, but we want to say something to 1 ratio.

So if you say per 1 ounce, well, we're dividing by 16 there, so we would want to 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 three fourths. 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.