Unit Conversions: Fractions Made Easy | Introduction & Practice

1. PHC 3.3 Unit Conversions Init fall 2009 by Daniel R. Barnes WARNING: This presentation includes images and other content taken from the world wide web without permission of the owners of that content. Do not copy or distribute this presentation. Its very existence may be illegal.

2. SWBAT . . . . . . convert quantities from one unit to another using fractions.

3. We’ll be doing most of our unit conversion work in chapter 10, but we’re going to do some now as a preview. This presentation is a supplement to the textbook. It does not address problems in the textbook directly. For answers to textbook questions, press either of the two buttons below. Push me for answers to CHATPER 3 SECTION ASSESSMENTS Push me for answers to the CHAPTER 3 end-of-chapter ASSESSMENT questions

4. PRIOR KNOWLEDGE Before you can do the problems in this lesson, you’ll need to already be familiar with SI units (a.k.a. the “metric system”). Do all of section 3.2 (reading, practice problems, section assessment) if you’re not already familiar with metric units.

5. Q1: Convert 1.2 km to m. Click this button to jump to the solution 1.2 km 1 What have we accomplished here? What happens to a number when you divide it by one? Nada. We haven’t changed our distance measurement at all. We’ve just turned it into a fraction. So why are we doing this? Trust me. When it comes to converting units, putting things into the form of fractions makes it all work out much better.

6. Q1: Convert 1.2 km to m. Click this button to jump to the solution 1.2 km 1 Now we need to think of what we’ve got and what we want to end up with. What do we have? What do we want to turn those kilometers into? How do you turn kilometers into meters? You need to get rid of the kilometers and make some meters appear. How are we going to do that? The way we do anything worth doing, with FRACTIONS.

7. Q1: Convert 1.2 km to m. Click this button to jump to the solution 1.2 km x km 1 We get rid of what we don’t want and replace it with what we do want my multiplying by a fraction. The way to get rid of the “km” on the top of the first fraction . . . Is to put “km” on the bottom of the next fraction. Why? When we’re all done building all the fractions we need, we’re going to cancel the kilometers out. Don’t cross anything out just yet, though. Don’t turn the key in the ignition until you’ve built the car.

8. Q1: Convert 1.2 km to m. Click this button to jump to the solution 1.2 km m x km 1 To get “m” to appear in our answer . . . . . . you put it on top of the second fraction. Now we’re set up to get rid of what we don’t want (km) and replace it with what we do want (m). However, you can’t just go mutiplying measurements by anything you want to just because you want your original quantity to look different. There are rules you have to follow. Thankfully, where there are rules, there are usually loopholes . . .

9. Q1: Convert 1.2 km to m. Click this button to jump to the solution 1.2 km m x km 1 You remember how we divided by one in the beginning and it was okay? Well, now we’re going to multiply by one. What happens to a number when you multiply it by one? Nothing. Therefore, you can multiply any number by one any time you want to, because it doesn’t change the value of the number. However, if you write the number “one” the right way, you can end up changing what your original number looks like. For instance, you can make “km” disappear and make “m” magically appear.

10. Q1: Convert 1.2 km to m. Click this button to jump to the solution 1.2 km m x km 1 So, if we fiddle with our second fraction until it equals one, what we’ve done here is totally legal. How do you get a fraction to equal one? You make the top equal the bottom. 1 p 2 3 27 1 year 5280 feet = = = = = = 2 365 days 3 3.14 27 1 mile

11. Q1: Convert 1.2 km to m. Click this button to jump to the solution 1.2 km 1000 m x 1 km 1 Does our second fraction equal one? Nope. Why not? A meter is not the same thing as a kilometer. Oh no! What do we do? Well, a meter may not equal a kilometer, but one thousand meters does equal one kilometer.

12. Q1: Convert 1.2 km to m. 1.2 km 1000 m x = 1200 m 1 km 1 Now, what we’ve set ourselves up to do here is just take our original number and multiply it by one. Our original 1.2 kilometers is still going to be 1.2 kilometers, since multiplying by one doesn’t change the value of a number. However, by writing “one” the right way, we’re going to change what 1.2 kilometers looks like. Kilometers cancel out kilometers and all we’re left with is . . . . . . meters, which is just what we wanted to end up with. Yay.

13. Q1: Convert 1.2 km to m. 1.2 km 1000 m x = 1200 m 1 km 1

14. Q2: How many dollars are there in 45,000,000 pennies? 45,000,000 pennies dollar 1 x = 450,000 dollars 1 100 pennies Show me the answer NOW!

15. Q2: How many dollars are there in 45,000,000 pennies? 45,000,000 pennies dollar 1 x = 450,000 dollars 1 100 pennies

16. Q3: Convert 100,000 years to days. 100,000 years 365 days x = 36,500,000 days 1 1 year Show me the answer NOW!

17. Q3: Convert 100,000 years to days. 100,000 years 365 days x = 36,500,000 days 1 1 year

18. Q4: How many milliliters are there in 40 kiloliters? 1000 1000 mL 40 kL L x x = 40,000,000 mL 1 L kL 1 1 Show me the answer NOW!

19. Q4: How many milliliters are there in 40 kiloliters? 1000 1000 mL 40 kL L x x = 40,000,000 mL 1 L kL 1 1

20. For more practice: Read pp 80 – 86, including practice problems #28 - #37. Answers are on page R83. 3.3 Section Assessment, pg 87: Questions #38 - #45. Answers not in book! Click the red button to go to Barnes’ ch 3 section assessment answers power point. Push me for answers to CH 3 SECTION ASSESSMENTS Chapter 3 Assessment, pg 96: questions #67 - #73, #83, and #84. Answers to odd #’d questions are on page R84. For all answers, click the yellow button to get a helpful pdf. Push me for answers to CH 3 end-of-chapter ASSESSMENT