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# Ratios and measurement

CCSS.Math:

## Video transcript

we're told to complete the ratio table to convert the units of measure from hours to weeks or weeks to hours so we here we see here they've told us already that there's a hundred sixty eight hours for every one week one way to think about it as the ratio of hours for every week is 168 to one and then they calculate well if we have one thousand one hundred seventy six 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 seven 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 gonna have 7 times as many weeks so 1 times 7 is just that is 7 weeks now what about a situation where we have 3 weeks how many hours is that going to be well we are multiplying our weeks by 3 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 three thousand five hundred and twenty yards for every two miles for every 2 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 3,500 22 - well what 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 want to divide this by two as well so 2 goes into 2 goes into 3520 let's see 2 goes into 3 one time 1 times 2 is 2 you subtract you bring down the 5 2 goes into 15 7 times 7 times 2 is 14 subtract we have 1 bring down that 2 2 goes into 12 6 times 6 times 2 is 12 and we subtract no remainder but then we're gonna have one more 0 here because we'd 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 1,760 yards now they're asking about 5 miles so 3 4 5 so we have 5 miles what is the number of yards well if you multiply by 5 here you're also going to multiply by 5 right over there so what's 1760 times 5 let's just figure it out 1760 times 5 5 times 0 is 0 5 times 6 is 30 regroup that 3 cuz it's really 3 hundreds 5 times 7 is 35 plus 3 is 38 5 times 1 is 5 plus 3 is 8 so there you go eight thousand eight hundred yards eight thousand eight hundred yards let's do a few more examples here we're told they're nine hundred fourteen point four 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 nine hundred fourteen point four millimeters per yard or you could say fourteen point four 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 3 goes into 914 0.4 3 goes into 9 3 times 3 times 3 is 9 subtract we get a zero bring down the 1 3 goes into 1 0 times 0 times 3 is 0 subtract you get a 1 bring down that 4 3 goes into 14 4 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 20 24 24 you subtract and we have no remainder so we have 300 and 4 point 8 millimeters for every foot let's do one last example Yukie bought a pound of confetti for \$12 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 dollars 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 that let me write it over here so 12 divided by 16 is the same thing as 3/4 just divide both of them by for and so this is 0.75 or 75 cents 75 cents per ounce or seventy five hundredths of a dollar per ounce so 0.75 and we're done