OK, so for number one, it says what is the estimated product when 157 and 817 are rounded to the nearest hundred and multiplied. So the first thing we have to do is understand how to round. When we're talking about rounding to the nearest hundred, what we always do is we look one place to the right. So if one is the 100 place, we're actually going to look at the 10s place to decide if we round up or not. So zero to four, we just leave the number alone and put zeros 5 to 9, we round up. So with 157, because this 5 is in between 5:00 and 9:00, it means we're going to round that one up. So we're going to get 200. Then if we look at 8:17, we look at this one and because it was zero to four, we're going to leave it alone and we're going to get 800. Now when I multiply 200 by 800, we have to count how many zeros there are total. So there's four zeros. So I know that my answer is going to have 4 zeros at the end. And then 8 * 2 is 16, so 61 million 123 a 160,000 right there. So the next one talks about the basal metallic metabolic rate is the rate at which our bodies use calories. The BMR for a man in his 20s is about 1700 calories per day. If 204 of those calories should come from protein, about what percentage of this man's diet should be protein? So this is actually a ratio problem where we're going to have protein to total. So if we know that 204 of his calories out of his total calories, 1700 should equal what percent out of 100? So X is the portion or the protein percent out of a total percentage of 100. So here we're going to cross multiply. When I multiply 204 * 100, it basically means we're just adding zeros. So we get 204 with two more zeros at the end and that's going to equal 1700X. So now we have to divide that 20400 divided by 1700 equal X. Now the easy way is if there's zeros on top and bottom at the end, we just divide them out. So that's basically thinking of dividing top number by 100, bottom by number by 100. So now we have 204 / 17 and we think about 17 goes into 21 time with three leftover and 17 goes into 34 twice with zero leftover. So 12% would be our final answer. This next one, how much water must be added to one liter of a 5% saline solution to get a 2% saline solution. So this is a percent times amount problem. So if we have a percent, 5% point O 5, how much water must be added to one liter? So 5% * 1 liter plus 0% saline in the water. So 0% * X, There's X amount of water that we're adding is going to give us a 2% and our total now is going to be the one liter we had and the X amount we started with. When I teach this, I sometimes have students draw pictures so they can visualize what's happening. So if I have one liter that's 5% and then I'm adding to it X amount of water. Now this total is going to be 1 + X. So that's where this 1 + X comes from. Zero times anything is going to be 0. We're combining them. So we're adding the one liter of 5% with the 0% saline of water. Sometimes the same kind of problem is said where you're adding pure saline. And if that was the case, this would be 100 for 100%. So we get .05 equaling .02 + .02 X So I'm going to subtract the .02 from each side and I get .03 equaling .02 X if I divide each side by .0 two .03 / .02. So we could think about multiplying the top and bottom each by 100 and we get 3 halves equaling X or 1 1/2 liters. The next problem, it's this one, and it says a child has a temperature of 40° Celsius. What's the child's temperature in degrees Fahrenheit? This is actually a formula, and I'm not certain if they expect you to memorize it or not, but the formulas Fahrenheit equals 9 fifths Celsius plus 32. So Fahrenheit equals 9 fifths 40 + 32. 40 you could think of as 40 / 1. And then you could think about this five goes into 40 how many times? And five goes into 48 full times and five goes into five once. So this really turns into 9 * 8 / 1 * 1 + 32 or 72 + 32, so 104 degrees. The next one talks about a woman drives W at 45 mph. So rate times time equal distance. So she goes 45 miles in some amount of time equaling distance. And then how fast must she drive to catch up to her? Three hours after he started? Oh, after half an hour. So we have 45 T equal D. Now this next part is we want to know what his rate is. So X. But he's leaving 1/2 hour later, so T -, 1/2. And that's going to be the same distance because we want him to reach her at that time. So it talks about how he starts 3 hours later. So T -, 1/2 is going to equal 3. So T is going to equal 7 halves. So if we have 7 halves, we know X * 3 equals the distance which was 45 * 7 halves. So X times the three equal 45 we could think of as over 1. So this is going to be 5 carry 3/28, 3:15 halves and then we're going to divide by 3. So 315 halves divided by three or multiplied by one third. Three goes into 315, three goes into three, one time, three goes into 10 times and three goes into 15 five times. So one O 5 halves. And if we divide one O 5 halves, we can see two goes into 1052 goes into 5 twice with one leftover. So two goes into the one with a 0 decimal place. So 52.5 mph. Let's go back and do some more. So Jason is 6 times as old as Kate. In two years Jason will be twice as old as Kate is. Then how old is Jason now? I make myself a grid for this kind of problem. Here's Jason. Here's Kate. So Jason is 6 times as old as Kate. So if I let Kate be X Jason as 6X in two years, so two years later is just going to be adding two to each of them. So in two years Jason will be twice as old as Kate is then. So as Kate is then then being in the future, so Jason will be twice as old as Kate is then. So now we just distribute two X + 4 = 6 X +2. Get all the XS to one side. 4X equal two X = 2 fourths or 1/2. So they How old is Jason now? Well, Jason is an X, Jason is 6X, so 6 * 1/2 Jason is 3. A patient's hospital stay cost 1/4 as much as his visit to the emergency room. So let X be visit to ER and one fourth X is his Hospice. And then it says his home nursing cost twice as much as his Hospice, so twice as much as his Hospice. So two times the 1/4 X is home nursing. And it says if his total healthcare bill was 140,000, how much did his home nursing cost? So we'd have X + 1 fourth X + 2 * 1/4 X is actually a half X because we could think of this as 2 / 1 and 2 * 1 / 1 * 4 is 1/2. So plus 1/2 X equal 140,000. Now there are a lot of different ways to do some of these problems. You could have thought about perhaps letting home nursing be the variable and then doing the others in relationship. This just happens to be how it's written and hence I think a little easier to see. Need to get a common denominator here. So four fourth X is one whole. Here's 1/4 X and 1/2 is 2 fourths X equals that 140,000. So 4 + 1 + 2 is 7 fourths X equals the 140,000. So I'm going to divide by 7 and multiply by 4 or I'm going to think about flipping this. And the reason I looked at the dividing first is 7 went into 14140 thousand. I think I added one too many zeros, 140,000 evenly because seven goes into 14 twice and then there's four zeros left. Then if I multiply that by four, I can see that X is 8001, two 34701234. But we didn't want X, we wanted half X, so half X is going to be 40,000. The next one talks about let's go and get a new clean sheet for the last two. So at a certain school, half of all the students are female, so 1/2 X are female and 112th of them are from out of state. Half of the out of state students are also female. So 1/2 of the out of state of typically in mathematics means multiplication, but not always. So 124th X is out of state and female. So what proportion of the students would you expect to be female from out of outside the state? 124th of the entire students? The last one that you've asked for during exercise, a person's heart rate should be 60% to 90% of the difference between 2:20 and the person's age. So 220 -. 30 because according to this guideline, what should a 30 year old person's maximum heart rate be? So 00 here we've got to borrow. So 3 from 12 is 9 so 190. And we want the maximum so we don't care about the 60, we only care about the 90. So we're going to have 190 * .9 O so 009 and 9 is 81 nine and one is 9 + 8. And then there were two decimal points so 171. Hope this helps.