Problem Solving The Ralph Way :) The following is a power point that has been designed to help you work through dimensional analysis and alternative method to solving story problems. We will work with dimensional analysis first. Then we will tackle Story problems. (As a help to those in Ralph’s and Nancy’s Online Class after each problem we will show you what you would enter into the test box to show your work)

Dimensional Analysis Dimensional analysis is the scientist fancy word for converting from one unit to another. It can be scary at the beginning but we hope to easy you into it. To start let’s work with something we are all familiar with, Money. If I ask how many quarters are in two dollars?

If I ask how many quarters are in two dollars? You of course knew the answer was 8. Correct? But let us look at this as a scientist. Two dollars = $2.00 There are 4 quarters in a dollar or $1.00 = 4 quarters So $2.00 X 4 quarters => $1.00 Cancel the dollar signs so; $2.00 x 4 quarters = 8 quarters For online test $2.00 x (4qtr/$1.00)= 8 quarters

Again you know the answer is 7. But using math $140/$20 = 7 bills Try another money problem How many twenty dollar bills does it take to have $140? Again you know the answer is 7. But using math $140/$20 = 7 bills In dimensional analysis We know 1 bill = $20 So $140 x 1 bill = 7 bills $20 For online test $140 x (1bill / $20) = 7 bills

What unit are you canceling? We can use Dimensional Analysis to convert between any two similar units. Just like the money. We have broken it down to a set of questions/steps to help you. What unit are you canceling? Place that unit on the opposite side of the line. Place the other unit. Determine which unit is bigger Place a 1 in front of that unit Place conversion number in front of other unit.

And we know 1 nickel = 5 cents What unit are you canceling? Another money problem. (do not cheat, Try it through dimensional analysis) How many nickels are in 65 cents? So we are starting out with 65 cents, write 65 cents on your paper. 65 cents X = And we know 1 nickel = 5 cents What unit are you canceling? Cents, correct? Place that unit on the opposite side of the line. So 65 cents X = cents

How many nickels are in 65 cents? Place the other unit. 65 cents X nickels = cents Determine which unit is bigger Place a 1 in front of that unit So a nickel is bigger because 5 cents = 1 nickel so it gets the one. 65 cents X 1 nickels = Place conversion number in front of other unit. 5 cents

How many nickels are in 65 cents? We then cancel the units 65 cents X 1 nickels = 5 cents We want our answer in nickels so I circle it. 65 cents X 1 nickels = nickels So our units are now nickels and we can do the math by multiplying across the top and dividing across the bottom. 65 X 1 nickels / 5 = 13 And our units are Nickels so 13 nickels. For online test 65cent x (1 nickel / 5 cent) = 13 nickels

What unit are you canceling? grams, correct? We know you are thinking why do we need to do money the math way? Isn’t that making it harder? Yes and no, We are trying to teach you how to use Dimensional analysis. What we just used for money works for all conversions. Let’s look at a different conversion problem and apply the same dimensional analysis techniques. Try How many kilograms are 2056 g? So we are starting out with 2056 g, write 2056 g on your paper. 2056 g X = What unit are you canceling? grams, correct?

How many kilograms are 2056 g? Place that unit on the opposite side of the line. So 2056 g X = g Place the other unit. 2056 g X kg = Determine which unit is bigger Place a 1 in front of that unit So 1 kilogram is 1000g 2056 g X 1 kg = Place conversion number in front of other unit. 1000 g

How many kilograms are 2056 g? We then cancel the units 2056 g X 1 kg = 1000 g We want our answer in kg so I circle it. So our units are now kg and we can do the math by multiplying across the top and dividing across the bottom. 2056 X 1 kg / 1000 = 2.056 And our units are kg so 2.056 kg. For online test 2056g x (1kg /1000g) = 2.056 kg

Now that you have a feel for Dimensional Analysis, we will move on to solving story problems which includes the use of Dimensional Analysis.

Story Problem Solving We have condensed the steps down to 7 step. The next few pages are step up to show you the steps then to talk you through each of the steps similar to what would be presented in a lecture. The steps will then be used to help you solve several problems to help ingrain the process.

Problem Solving The Ralph Way :) 1. Read the whole problem 2. Read the problem carefully for facts. a. What is known b. What are you trying to find, What units is it in? c. What could be known. d. Other info.

3. Select which number to start with 4. Put units in formula 5. Cancel units, top L -> R, Bot L -> R, Using Dimensional Analysis 6. use Calculator 7 Write down answer (with units), Determine Sig. Figs., Recheck Calculations

2. Read the problem carefully for facts. 1. Read the whole problem You want to read the problem without worrying about numbers. You are doing this to work on the flow of the question and story. It is often useful to just skip the numbers or say number. 2. Read the problem carefully for facts. This time you are reading the problem to look at the numbers and the information you will need to complete the problem. a. What is known What are the numbers given in the problem. Write them down with their units.

2 b. What are you trying to find, What units is it in? This is where you are looking at what number you are solving for. I.E. Why are you even doing this problem. Try to figure out what type of number you are looking for. Make sure to include units. c. What could be known. What conversions could you look up, or do you know? I try to think about what conversions I may need to solve the problem. d. Other info. This is if there is some other piece of information you want to note like temperature or date or etc.

3. Select which number to start with 4. Put units in formula 5. Cancel units, top L -> R, Bot L -> R, Using Dimensional Analysis 6. use Calculator 7 Write down answer (with units), Determine Sig. Figs., Recheck Calculations

3. Select which number to start with This is often the hardest part. Often times you will be presented with many numbers in a problem to pick from. So which number do you pick? First ask yourself, “is there any conversions in the problem?” Like 5 dogs equal a cat, this is a ratio or a conversion. So write it as such 5 dogs , if it is not a ratio write it normal 5 mL. 1 cat The easiest number to start with is one that contains similar units to what you are solving for. If your answer needs a volume for instance pick a number that has volume in it. Even if the units do not match, you can always convert units. So if you are solving for cats you would want to start with the 5 dogs/1 cat instead of the 5ml. You should then place this number at the start of the problem. Be mindful of the units and the numbers. If you want cats on top for the answer you will need cats on top for the problem also so 1/5 4. Put units in formula Now you need to include units with your number. Always write out the units as well as the numbers they can be a great cross check of your answer later so 1 cat 5 dogs

5. Cancel units, top L -> R, Bot L -> R, Using Dimensional Analysis See the next slide for the dimensional analysis steps I always like to work very systematically when doing my canceling of units. I will work across the top row from left to right of the problem canceling units as I go. When I get an unit that I need for the answer I often circle it to tell me that I do not need to cancel it. After I have canceled all the top row units I then work from left to right across the bottom row. Some times in the solving of a problem you place a unit from your problem that does not have a conversion on the other side of the equation. You can place a one on the other side of the problem if that helps you feel better about the problem. This is because one (1) times or divided into anything does not change the numbers. Here is an example of a complex problem, (Don’t Panic this is just an example)

Dimensional Analysis which we covered earlier. What unit are you canceling? Place that unit on the opposite side of the line. Place the other unit. Determine which unit is bigger Place a 1 in front of that unit Place conversion number in front of other unit.

6. use Calculator Now that all the units are canceled you are ready to use the calculator. The easiest way to do this without brackets and to much calculator error is to use the Times (x) Key for everything above the horizontal line and use the divide key for everything below the line. You do not want to press the equals key till the very end! This is because calculators introduce rounding errors when the equal key is pressed. Another common error is when students try to times the top, write it down, then times the bottom, right it down then try to put them back in the calculator to do the divide. You have added to many steps and to many errors to get a good anwser. Using the old Example back two pages 45 x 4.5 / 1000 / 4.184 = 0.0483987 7 Write down answer (with units), Determine Sig. Figs., Recheck Calculations This is where you finish the problem off. Write down the answer, add the units, figure out the significant figures and then redo the calculator one time to make sure the answer is right Example 0.048/39 = 0.048 kg/J Now let us Try a few together

If a Recipe calls for 600. g of chocolate chips, how many pounds of chips do you need? 1. Read problem 2. read for facts a. what is known? 600.g b. what are we finding? ? in pounds c. What do we know? (from book) 1 lbs= 454g d. other info? none 3. select which number to start with? You only have 600.g 4. put units formula 600 g 1

If a Recipe calls for 600. g of chocolate chips, how many pounds of chips do you need? 5. Cancel units, top L-> R, Bot L-> R 600 g 1 lbs 1 454 g 6. use calculator 600 /454 = 7. Write down answer, 1.3215859 lbs determine sig. figs “3” 1.32 lbs recheck calculations For online test 600 g x (1lbs/454g) = 1.32158 = 1.32 lbs

You want to change oil on your car, it need 4 You want to change oil on your car, it need 4.0L, how many quarts is that? 1. Read problem 2. read for facts a. what is known? 4.0 L b. what are we finding? ? in Quarts c. What do we know? 1 qts= 0.9463529 L d. other info? none 3. Select which number to start with 4.0 L 4. Put units in formula 1

5. Cancel units, top L->R, Bot L->R You want to change oil on your car, it need 4.0L, how many quarts is that? 5. Cancel units, top L->R, Bot L->R 4.0 L 1 qts 1 0.9463529 L 6. use calculator 4.0 / 0.9463529 = 7. Write down answer 4.2267530 qts. determine sig. figs “2” 4.2 qts. recheck calculations For online test 4.0L x (1 qts/0.9463529L) = 4.2267 = 4.2 qts

A Board is 27. 0in long, It weights 1. 2kg A Board is 27.0in long, It weights 1.2kg. Can it be used to connect a 0.56m opening? 1. Read problem 2. Read for facts a. what is known? 27.0in B 1.2kg B Opening= 0.56m b. what are we finding? ? m, will it fit? or ? in is it long enough? c. What do we know? 1 in= 2.54 cm 1 m= 100cm d. other info? 3. Select which number to start with 27.0 in or 0.56 m 4. put units in formula 27.0 in or 0.56 m 1 1

A Board is 27. 0in long, It weights 1. 2kg A Board is 27.0in long, It weights 1.2kg. Can it be used to connect a 0.56m opening? 5. Cancel units, top L-> R, Bot. L->R 27.0 in 2.54 cm or 0.56 m 100cm 1 1 in 1 1 m then 27.0 in 2.54 cm 1 m or 0.56 m 100 cm 1 in 1 1 in 100 cm 1 1 m 2.54 cm 6. use calculator 7. Write down answer 0.6858 m 22.047in determine sig. figs “3” “2” 0.686 m 22 in recheck calculations Yes it Could For Online test 27.0 in x (2.54cm/1in)(1m/100cm)=0.6858=0.686 m Yes it could Or 0.56m x (100cm/1m)(1in/2.54cm) = 22.047 = 22in Yes it could

How many minutes does it take a car traveling 85 km/hr to go 42 miles How many minutes does it take a car traveling 85 km/hr to go 42 miles? How many seconds is that? First “Don’t Panic” this is a harder problem to show you how this story problem system still works on a harder problem. In Fact you may find that this system makes what looks hard easy. 1. Read problem 2. Read for facts a. what is known? 85 km/hr 42 miles b. what are we finding? ? Time, in minutes And ? time in seconds c. What do we know? 60 minutes in a hour 60 seconds in a minute 1.609 km = 1 mile d. other info?

3. Select which number to start with How many minutes does it take a car traveling 85 km/hr to go 42 miles? How many seconds is that? 3. Select which number to start with 85 km/hour has time in it so it may be a good starting point. Ask yourself then where do you want time in the final answer on the top or the bottom? Top correct. So we want hrs km Does the 85 go with hours or km? km right 4. put units in formula 1 hrs 85 km

How many minutes does it take a car traveling 85 km/hr to go 42 miles How many minutes does it take a car traveling 85 km/hr to go 42 miles? How many seconds is that? 5. Cancel units, top L-> R, Bot. L->R So we would start with hrs. where would it go top or bottom? 1 hrs 85 km hrs What are we going to? Minutes, so 1 hrs min Which is bigger it gets a 1 and how many of the smaller in the bigger? And cancel 1 hrs 60 min 85 km 1 hrs We want minutes so circle it ARE WE DONE? No, so next page

How many minutes does it take a car traveling 85 km/hr to go 42 miles How many minutes does it take a car traveling 85 km/hr to go 42 miles? How many seconds is that? 5. Cancel units, top L-> R, Bot. L->R continued The next unit we need to get rid of is? kilometers or km where does it go top or bottom? 1 hrs 60 min km 85 km 1 hrs What are we converting it to? Miles, SO 85 km 1 hrs miles Place the numbers in with Miles getting the 1 and km getting the conversion 1 hrs 60 min 1.609 km 85 km 1 hrs 1 miles Cancel the units. Are we done?

How many minutes does it take a car traveling 85 km/hr to go 42 miles How many minutes does it take a car traveling 85 km/hr to go 42 miles? How many seconds is that? 5. Cancel units, top L-> R, Bot. L->R continued 2 We still need to get rid of Miles Correct? What do we know about miles? There are 42 miles. So where are we going to put miles top or bottom? Top right? 1 hrs 60 min 1.609 km miles 85 km 1 hrs 1 miles What goes under miles? Nothing, because we are getting rid of miles so put a one there. Place the 42 in front of miles and cancel. 1 hrs 60 min 1.609 km 42 miles 85 km 1 hrs 1 miles 1 We are now ready for step 6 on the next page.

How many minutes does it take a car traveling 85 km/hr to go 42 miles How many minutes does it take a car traveling 85 km/hr to go 42 miles? How many seconds is that? 6. use calculator 1 hrs 60 min 1.609 km 42 miles 85 km 1 hrs 1 miles 1 Typed into the calculator times across top, divide across bottom 1 x 60 x 1.609 x 42 /85 /1 /1 /1 = (p.s. you can leave the ones out if you want) 7. Write down answer 47.70211765 determine sig. figs “2” 48 minutes recheck calculations For Online test (1hrs/85km)(60min/1hrs)(1.609km/1mile)(42 miles/1)= 47.702=48 minutes

How many minutes does it take a car traveling 85 km/hr to go 42 miles How many minutes does it take a car traveling 85 km/hr to go 42 miles? How many seconds is that? Are you done with this problem? No we still need to find seconds So un-circle the minutes and add one more step What are you getting rid of ? Minutes Where does it go? What goes on other side? 1 hrs 60 min 1.609 km 42 miles 60 sec 85 km 1 hrs 1 miles 1 1 min Typed into the calculator times across top, divide across bottom 60 x 1.609 x 42x60 /85 = 7. Write down answer 2862.13 determine sig. figs “2” 2.9 x 103 sec recheck calculations (1hrs/85km)(60min/1hrs)(1.609km/1mile)(42 miles/1)(60sec/1min)= 2862.13=2.9e3 sec

It is now time to see what you know? To aid you and give you more practice at solving story problems, on the next few pages, there are many examples of story problems. We would like you to try each problem on your own. Then you can click the screen and the complete formula with answers will show up so that you can check your work. Also check the Assignments for the week because there is additional worksheets to work through.

2. What is the cost of a Kg of sugar if it cost $1.37 per 5 lb bag? 1. If you have a 3498mL of a substance how many L is that? How many ML is it? 3498 mL 1L = 3.498 L 1 1000mL and 3498 mL 1ML = 3.498e-9 ML 1 1,000,000,000 (or 1e9)mL 2. What is the cost of a Kg of sugar if it cost $1.37 per 5 lb bag? $1.37 2.2 Lbs = 0.6028 => $0.60/Kg 5 Lbs 1Kg 3. You have a 10.12lb container which contains 50 apples. Each apple weights 120. g. How much will the apples weight? 50 apples 120. g = 6000 => 6.00e3 g 1 1 apple

4. If you have a car traveling at 30m/sec how many Km/hr would that be? 30 m 1 km 60 sec 60 min = 108 => 1e2 km/hr 1 sec 1000 m 1 min 1 hr 5. A New drug has a dose of 2.3mL/kg body weight. If you have a patient who weights 198lbs. How much drug should you give them? 2.3 mL 1 kg 198 lbs = 207 => 2.1e2 mL 1 kg 2.2 lbs 1 6. If you have a 12cm square box. And you have 200.mL of sand weighting 1000g, can you fit the sand in the box in one trip? 12 x 12 x 12 = 1728 cm3 => 1.7e3 cm3 = ml So 200ml will fit

7. If the temperature outside is 25oC how hot is that in oF? In K? (1.8 x 25oC)+32= 77oF 25oC + 273.15 = 298.15=> 298K 8. If you have 200.g of a substance and it takes up 45ml what is the density of the substance? Will it float on water? 200.g / 45ml = 4.44444=> 4.4g/ml Water has a density of 1.0g/ml so the substance is more dense than water so it will sink.

9. If you have a compound with the density of 4 9. If you have a compound with the density of 4.5g/ml and a mass of 75g what volume does it take up? 1ml 75g = 16.66666=> 17ml 4.5g 1 10. If you have a compound that is 6.03 ml and has a density of 0.74g/ml what is its mass? 0.74 g 6.03ml = 4.4622 => 4.5 g ml 1