Basic Math Problems Unit 1

Transcription

1 Basic Math Problems Unit 1 Name Period Using fractions: When you are using fractions in science, we need to convert them into decimals. You can do this by dividing the top number by the bottom number. ALWAYS ROUND TO THE TENTHS PLACE. Example: 5 To find the whole number equivalent take 5 and divide it by 2. 2 Your answer should be 2.5 Practice: Find the answers to the following Did you notice something about the top line and the bottom line? What do you think made this difference? Now on your own convert the following fractions into decimals. 1) 3 2) 61 3) 48 4) ) 24 6) 8 7) 73 8) ) 81 10) 15 11) 82 12) ) 53 14) 9 15) 42 16)

2 Using decimals: When you see a decimal in a fraction use it as a normal number. Just punch in the decimal in your calculator. ALWAYS ROUND TO THE TENTHS PLACE. P.S. This doesn t really happen but we are looking at the fractions as division problems. Example: 13.5 To find the whole number equivalent take 13.5 and divide it by Your answer should be ect. Practice: Find the answers to the following Now on your own find the whole number answer for the following fractions. 1) ) 1.7 3) ) ) 4 6) ) 3.9 8) ) ) ) ) ) ) 75 15) 62 16)

3 Using units: Using units is very important in science. Units tell you what the number stands for. If I tell you that you can get an A today by doing 5. Or if I would tell you in order to get a free ice cream you only need to go 20. You would probably ask me 5 what and 20 what. The reason is because I have left off the units. The same thing holds true in science problems. You can t just have a number. You need to have something that tells you what that number stands for!!! A UNIT!!!! ALWAYS ROUND TO THE TENTHS PLACE. It is important that you memorize the units that are learned in each chapter. Let s practice the unit from chapter one. Color the following units as follows: Distance = red Time = blue Speed = green Momentum = yellow 12 kg* m/s 89 s Finding the Units 5 m 24 m 18 m/s m/sn 36 m/s 32 s 9 Kg*m/s 93 min 56 m 6 inches 50 hrs 24 m/hr If you learn each chapter s units, it will make the math much easier because each equation tells you where to put the numbers if you know their units. Example: The equation s = d t The data 5 seconds 3 meters If you know the units for distance and time you will know where to put the numbers. The unit for distance is meters and the unit for time is seconds. So we put the numbers in the equation. distance Now work the fraction and you have part of time your answer! But you re not done yet. What are the units that you are left with? You have meters / seconds, put these units behind your answer. Your answer should be 0.6 m/s. If you got this Good Job!!

4 s = d Practice: Using the same equation do the following. t 1) 6 meters 15 seconds 2) 43 seconds 3 meters 3) 18 meters 9 seconds 4) 12 meters 39 seconds 5) 90 seconds 45 meters Name Period Now on your own put the right units in the right part of the equation and solve for the answer. Remember to keep the units for your answer!! ALWAYS ROUND TO THE TENTHS PLACE. Use the equation density = mass / volume The unit for mass is g, and the unit for volume is ml. 1) 15 g, 4 ml 2) 25 ml, 18 g 3) 6.8 g, 45 ml 4) 23 g, 4.8 ml 5) 32 ml, 13 g 6) 58 ml, 6.2 g 7) 8.3 g, 5 ml 8) 7.3 g, 5 ml More practice Remember to keep the units for your answer!! Use the equation acceleration =force / mass The unit for force is Kg * m/s/s, and the unit for mass is Kg. 1) 5 kg *m/s 2, 3 kg 2) 16 kg, 9 kg *m/s 2 3) 58 kg *m/s 2, 8 kg 4) 3.5 kg *m/s 2, 8 kg 5) 2 kg, 30 kg *m/s 2 6) 62 kg, 9 kg *m/s 2 7) 9 kg *m/s 2, 7.2 kg 8) 8 kg *m/s 2, 0.3 kg

5 Using Triangles: Well Done!! The next thing we are going to learn is how to rearrange equations. Sometimes we have to solve for a different variable than the one that is isolated in the original equation. For example if we have the equation: F = M * A, and we need to find the mass of an object. We need to get Mass on the left of the equation by itself. s = d Let s say you are on a trip and you want to find out how far you have gone. You already know the t equation You know the speed you have been going and you know how long you have been traveling. You have probably gone through the process of dividing or dividing each side of the equation until it is set up the way you want it. But there is an easier way!!! Using magic triangles!!! This tool will rearrange the equation for you. We just need to fill it in correctly. If the equation is set up like s = d, the number on the top of the fraction goes on the top of the t triangle. The other two variables fill in the bottom. s = d t If the equation is set up like f = m a, you put the two variables that are being multiplied by each other in the bottom of the triangle. Practice that now. f = m a Practice filling in triangles: ONCE YOU FILL IN A TRIANGLE IT NEVER CHANGES!!!! m = r df = b i c = i aq = m c

6 Using equations: Sometimes the equations that you use need to be in a different order. We will use only equations that have three to four variables. Most of them will be one number divided by another or one number multiplied by another. 1 st Step: The very first step to this process is finding what the question is asking you to solve. Use a highlighter to indicate what we are trying to solve for. In this case, it is distance or D. 2 nd Step: See if the equation is set up to solve what you need. Is that variable on the left of the equal sign, or by itself? If it is move to step 3. If not put the equation into the triangle. Because distance is on the top of the fraction, it goes in the top of the triangle. The other two symbols go on the bottom. Now cover the variable that you are solving for and write the new equation. In this case we would enter Cover D with your thumb because we are solving D for it. If the two symbols are both on the bottom you multiply them. If one is on top of the other, you use it as a fraction and T S divide them. And write the equation D = S * T Practice: Rearrange the following equations to find a given variable. Use the equation d = m v 1) Solve for Mass Mass = 2) Solve for Volume Volume = Use the equation Mass = Force / Acceleration 3) Solve for Force Force = 4) Solve for Acceleration Acceleration =

7 Use the equation Weight = Mass X Acceleration 5) Solve for Mass Mass = 6) Solve for Acceleration Acceleration = Use the equation A = B / C 7) Solve for B B = 8) Solve for C C = Use the equation Height = Potential Energy / Gravity 9) Solve for Gravity Gravity = 10) Solve for Potential Energy Potential Energy = Solving Problems: Now we are actually going to use the information you have learned to solve problems. Remember to match up the units and rearrange the equations!!! Example: Using the equation Speed = Distance/Time you want to find out how long it would take you to get to Grandma s House Bed and Breakfast in Platte S.D. You know that Platte is around 2,000 miles away and the average speed limit is 65 miles/hour. Figure out how long it would take you. 1 st step: Highlight what the question is asking you to solve, and any important information In this case, it is Time. Equation: Data: Speed = Distance/Time 2,000 miles 65 mph

8 2 nd step: See if the equation is set up to solve what you need. If it is, move to step 3. If not put the equation into the triangle, cover what you re solving for and write the new equation. In this case we would enter Cover T because we are solving D for it. And write the equation T = D / S T S 3 rd step: Substitute the variables in the equation with the numbers and units in the problem. T = D / S T = 2,000 miles/65 mph 4 th step: Check your units and check your math. Too often the only mistake a student makes is a simple math error or putting the units in the wrong place. Check these over! A good thing to do is to estimate what the answer will be before you use your calculator, if the answer is close to your estimation you probably got it right. Practice together: By using the equation density = mass / volume, we want to find out how much volume a lead cylinder has. It has a mass 540 g and a density of 2.70 g/ml. Step 1: What are you solving for? Equation: Data: Step 2: Rearrange equation Put the equation in the triangle and write it out to solve for. = / Step 3: Put in numbers so that the units follow the equation. Solve the problem. = / = / Step 4: Check your units and check your math.

9 On Your Own: Problem #1 By using the equation momentum = mass X velocity, we want to find out how much mass Mrs. Greene s Car has. She has been driving 29 m/s and is known to have a momentum of 13,181 kg*m/s. What is the mass of the car? Step 1: What are you solving for? Equation: Data: Step 2: Rearrange equation Put the equation in the triangle and write it out to solve for Mass. Mass = / Step 3: Put in numbers so that the units follow the equation. Solve the problem. = / Step 4: Check your units and check your math. Problem #2 s = d You have been traveling on an Amtrak train for 6 hours. You want to know which town is next. The t only problem is that you have been sleeping so you don t know how far you have gone. You know that the Amtrak train travels 70 m/hr on average. How can you figure out how far you have gone? Use the equation Step 1: What are you solving for? Equation: Data: Step 2: Rearrange equation = Step 3: Put in numbers so that the units follow the equation. Solve the problem. = Step 4: Check your units and check your math.

10 Problem #3 By using the equation Force = mass X acceleration, we want to find out how fast we (as a 8 th grade class) could accelerate Mr. D s car. If we all got behind it to push we would have a force of 4,590 N. His car has a mass of 510 Kg. How much will it accelerate? UNITS: Force = N or Kg * m/s 2 Mass = Kg Acceleration = m/s 2 Step 1: What are you solving for? Equation: Data: Step 2: Rearrange equation = / Step 3: Put in numbers so that the units follow the equation. Solve the problem. = / Step 4: Check your units and check your math. Problem #4 You have been traveling in a covered wagon because your car broke down. You have been traveling for 3.5 hrs. But you find out you have only gone 30 miles. By using the equation s=d/t, find out how fast you were traveling. Step 1: What are you solving for? Equation: Data: Step 2: Rearrange equation = Step 3: Put in numbers so that the units follow the equation. Solve the problem. = Step 4: Check your units and check your math.