# Example people out of 400 state that they like dogs. What percent is this?

 To view this video please enable JavaScript, and consider upgrading to a web browser that supports HTML5 video
Save this PDF as:

Size: px
Start display at page:

Download "Example 1 243 people out of 400 state that they like dogs. What percent is this?"

## Transcription

1 Problem Solving 1 Problem Solving In previous math courses, you ve no doubt run into the infamous word problems. Unfortunately, these problems rarely resemble the type of problems we actually encounter in everyday life. In math books, you usually are told exactly which formula or procedure to use, and are given exactly the information you need to answer the question. In real life, problem solving requires identifying an appropriate formula or procedure, and determining what information you will need (and won t need) to answer the question. In this chapter, we will review several basic but powerful algebraic ideas: percents, rates, and proportions. We will then focus on the problem solving process, and explore how to use these ideas to solve problems where we don t have perfect information. Percents In the 2004 vice-presidential debates, Edwards's claimed that US forces have suffered "90% of the coalition casualties" in Iraq. Cheney disputed this, saying that in fact Iraqi security forces and coalition allies "have taken almost 50 percent" of the casualties 1. Who is correct? How can we make sense of these numbers? Percent literally means per 100, or parts per hundred. When we write 40%, this is equivalent to the fraction 40 or the decimal Notice that 80 out of 200 and 10 out of are also 40%, since = = Example people out of 400 state that they like dogs. What percent is this? = =. This is 60.75% Notice that the percent can be found from the equivalent decimal by moving the decimal point two places to the right. Example 2 Write each as a percent: a) 1 4 b) 0.02 c) 2.35 a) 1 = 0.25 = 25% b) 0.02 = 2% c) 2.35 = 235% 4 1 David Lippman Creative Commons BY-SA

2 2 Percents If we have a part that is some percent of a whole, then part percent =, or equivalently, part = percent whole whole To do the calculations, we write the percent as a decimal. Example 3 The sales tax in a town is 9.4%. How much tax will you pay on a \$140 purchase? Here, \$140 is the whole, and we want to find 9.4% of \$140. We start by writing the percent as a decimal by moving the decimal point two places to the left (which is equivalent to dividing by 100). We can then compute: tax = = \$13.16 in tax. ( ) Example 4 In the news, you hear tuition is expected to increase by 7% next year. If tuition this year was \$1200 per quarter, what will it be next year? The tuition next year will be the current tuition plus an additional 7%, so it will be 107% of this year s tuition: \$1200(1.07) = \$1284. Alternatively, we could have first calculated 7% of \$1200: \$1200(0.07) = \$84. Notice this is not the expected tuition for next year (we could only wish). Instead, this is the expected increase, so to calculate the expected tuition, we ll need to add this change to the previous year s tuition: \$ \$84 = \$1284. Try it Now 1 A TV originally priced at \$799 is on sale for 30% off. There is then a 9.2% sales tax. Find the price after including the discount and sales tax. Example 5 The value of a car dropped from \$7400 to \$6800 over the last year. What percent decrease is this? To compute the percent change, we first need to find the dollar value change: \$6800-\$7400 = -\$600. Often we will take the absolute value of this amount, which is called the absolute change: 600 = 600.

3 Problem Solving 3 Since we are computing the decrease relative to the starting value, we compute this percent out of \$7400: 600 = = 8.1% decrease. This is called a relative change Absolute and Relative Change Given two quantities, Absolute change = ending quantity starting quantity absolute change Relative change: starting quantity Absolute change has the same units as the original quantity. Relative change gives a percent change. The starting quantity is called the base of the percent change. The base of a percent is very important. For example, while Nixon was president, it was argued that marijuana was a gateway drug, claiming that 80% of marijuana smokers went on to use harder drugs like cocaine. The problem is, this isn t true. The true claim is that 80% of harder drug users first smoked marijuana. The difference is one of base: 80% of marijuana smokers using hard drugs, vs. 80% of hard drug users having smoked marijuana. These numbers are not equivalent. As it turns out, only one in 2,400 marijuana users actually go on to use harder drugs 2. Example 6 There are about 75 QFC supermarkets in the U.S. Albertsons has about 215 stores. Compare the size of the two companies. When we make comparisons, we must ask first whether an absolute or relative comparison. The absolute difference is = 140. From this, we could say Albertsons has 140 more stores than QFC. However, if you wrote this in an article or paper, that number does not mean much. The relative difference may be more meaningful. There are two different relative changes we could calculate, depending on which store we use as the base: Using QFC as the base, =. This tells us Albertsons is 186.7% larger than QFC. Using Albertsons as the base, =. This tells us QFC is 65.1% smaller than Albertsons. 2

4 4 Notice both of these are showing percent differences. We could also calculate the size of Albertsons relative to QFC: 215 = 2.867, which tells us Albertsons is times the size 75 of QFC. Likewise, we could calculate the size of QFC relative to Albertsons: =, which tells us that QFC is 34.9% of the size of Albertsons. Example 7 Suppose a stock drops in value by 60% one week, then increases in value the next week by 75%. Is the value higher or lower than where it started? To answer this question, suppose the value started at \$100. After one week, the value dropped by 60%: \$100 - \$100(0.60) = \$100 - \$60 = \$40. In the next week, notice that base of the percent has changed to the new value, \$40. Computing the 75% increase: \$40 + \$40(0.75) = \$40 + \$30 = \$70. In the end, the stock is still \$30 lower, or \$30 = 30% lower, valued than it started. \$100 Try it Now 2 The U.S. federal debt at the end of 2001 was \$5.77 trillion, and grew to \$6.20 trillion by the end of At the end of 2005 it was \$7.91 trillion, and grew to \$8.45 trillion by the end of Calculate the absolute and relative increase for and Which year saw a larger increase in federal debt? Example 8 A Seattle Times article on high school graduation rates reported The number of schools graduating 60 percent or fewer students in four years sometimes referred to as dropout factories decreased by 17 during that time period. The number of kids attending schools with such low graduation rates was cut in half. a) Is the decrease by 17 number a useful comparison? b) Considering the last sentence, can we conclude that the number of dropout factories was originally 34? 3

5 Problem Solving 5 a) This number is hard to evaluate, since we have no basis for judging whether this is a larger or small change. If the number of dropout factories dropped from 20 to 3, that d be a very significant change, but if the number dropped from 217 to 200, that d be less of an improvement. b) The last sentence provides relative change which helps put the first sentence in perspective. We can estimate that the number of dropout factories was probably previously around 34. However, it s possible that students simply moved schools rather than the school improving, so that estimate might not be fully accurate. Example 9 In the 2004 vice-presidential debates, Edwards's claimed that US forces have suffered "90% of the coalition casualties" in Iraq. Cheney disputed this, saying that in fact Iraqi security forces and coalition allies "have taken almost 50 percent" of the casualties. Who is correct? Without more information, it is hard for us to judge who is correct, but we can easily conclude that these two percents are talking about different things, so one does not necessarily contradict the other. Edward s claim was a percent with coalition forces as the base of the percent, while Cheney s claim was a percent with both coalition and Iraqi security forces as the base of the percent. It turns out both statistics are in fact fairly accurate. Try it Now 3 In the 2012 presidential elections, one candidate argued that the president s plan will cut \$716 billion from Medicare, leading to fewer services for seniors, while the other candidate rebuts that our plan does not cut current spending and actually expands benefits for seniors, while implementing cost saving measures. Are these claims in conflict, in agreement, or not comparable because they re talking about different things? We ll wrap up our review of percents with a couple cautions. First, when talking about a change of quantities that are already measured in percents, we have to be careful in how we describe the change. Example 10 A politician s support increases from 40% of voters to 50% of voters. Describe the change. We could describe this using an absolute change: 50% 40% = 10%. Notice that since the original quantities were percents, this change also has the units of percent. In this case, it is best to describe this as an increase of 10 percentage points. In contrast, we could compute the percent change: 10% = 0.25 = 25% increase. This is the 40% relative change, and we d say the politician s support has increased by 25%.

6 6 Lastly, a caution against averaging percents. Example 11 A basketball player scores on 40% of 2-point field goal attempts, and on 30% of 3-point of field goal attempts. Find the player s overall field goal percentage. It is very tempting to average these values, and claim the overall average is 35%, but this is likely not correct, since most players make many more 2-point attempts than 3-point attempts. We don t actually have enough information to answer the question. Suppose the player attempted point field goals and point field goals. Then they made 200(0.40) = 80 2-point shots and 100(0.30) = 30 3-point shots. Overall, they made 110 shots out of 300, for a 110 = = 36.7% overall field goal percentage. 300 Proportions and Rates If you wanted to power the city of Seattle using wind power, how many windmills would you need to install? Questions like these can be answered using rates and proportions. Rates A rate is the ratio (fraction) of two quantities. A unit rate is a rate with a denominator of one. Example 12 Your car can drive 300 miles on a tank of 15 gallons. Express this as a rate. 300miles 20miles Expressed as a rate,. We can divide to find a unit rate:, which we could 15gallons 1gallon miles also write as 20, or just 20 miles per gallon. gallon Proportion Equation A proportion equation is an equation showing the equivalence of two rates or ratios. Example 13 Solve the proportion 5 x = for the unknown value x. 3 6 This proportion is asking us to find a fraction with denominator 6 that is equivalent to the fraction 5. We can solve this by multiplying both sides of the equation by 6, giving 3 5 x = 6 = 10. 3

7 Problem Solving 7 Example 14 A map scale indicates that ½ inch on the map corresponds with 3 real miles. How many 1 miles apart are two cities that are 2 inches apart on the map? 4 map inches We can set up a proportion by setting equal two rates, and introducing a real miles variable, x, to represent the unknown quantity the mile distance between the cities. 1 1 map inch 2 map inches 2 = 4 Multiply both sides by x 3miles x miles and rewriting the mixed number x = Multiply both sides by x = Multiply both sides by 2 (or divide by ½) x = = 13 miles 2 2 Many proportion problems can also be solved using dimensional analysis, the process of multiplying a quantity by rates to change the units. Example 15 Your car can drive 300 miles on a tank of 15 gallons. How far can it drive on 40 gallons? We could certainly answer this question using a proportion: 300miles x miles =. 15gallons 40gallons However, we earlier found that 300 miles on 15 gallons gives a rate of 20 miles per gallon. If we multiply the given 40 gallon quantity by this rate, the gallons unit cancels and we re left with a number of miles: 20miles 40gallons 20miles 40 gallons = = 800miles gallon 1 gallon Notice if instead we were asked how many gallons are needed to drive 50 miles? we could answer this question by inverting the 20 mile per gallon rate so that the miles unit cancels and we re left with gallons: 1gallon 50miles 1gallon 50gallons 50 miles = = = 2.5gallons 20miles 1 20miles 20

8 8 Dimensional analysis can also be used to do unit conversions. Here are some unit conversions for reference. Unit Conversions Length 1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 feet (ft) 1 mile = 5,280 feet 1000 millimeters (mm) = 1 meter (m) 100 centimeters (cm) = 1 meter 1000 meters (m) = 1 kilometer (km) 2.54 centimeters (cm) = 1 inch Weight and Mass 1 pound (lb) = 16 ounces (oz) 1 ton = 2000 pounds 1000 milligrams (mg) = 1 gram (g) 1000 grams = 1kilogram (kg) 1 kilogram = 2.2 pounds (on earth) Capacity 1 cup = 8 fluid ounces (fl oz) * 1 pint = 2 cups 1 quart = 2 pints = 4 cups 1 gallon = 4 quarts = 16 cups 1000 milliliters (ml) = 1 liter (L) * Fluid ounces are a capacity measurement for liquids. 1 fluid ounce 1 ounce (weight) for water only. Example 16 A bicycle is traveling at 15 miles per hour. How many feet will it cover in 20 seconds? To answer this question, we need to convert 20 seconds into feet. If we know the speed of the bicycle in feet per second, this question would be simpler. Since we don t, we will need to do additional unit conversions. We will need to know that 5280 ft = 1 mile. We might start by converting the 20 seconds into hours: 1minute 1hour 1 20 seconds = hour Now we can multiply by the 15 miles/hr mile 12 60seconds 60minutes miles 1 hour = mile Now we can convert to feet 1hour feet = 440feet 1mile We could have also done this entire calculation in one long set of products: 1minute 1hour 15miles 5280feet 20 seconds = 440feet 60seconds 60 minutes 1hour 1mile Try it Now 4 A 1000 foot spool of bare 12-gauge copper wire weighs 19.8 pounds. How much will 18 inches of the wire weigh, in ounces?

9 Problem Solving 9 Notice that with the miles per gallon example, if we double the miles driven, we double the gas used. Likewise, with the map distance example, if the map distance doubles, the real-life distance doubles. This is a key feature of proportional relationships, and one we must confirm before assuming two things are related proportionally. Example 17 Suppose you re tiling the floor of a 10 ft by 10 ft room, and find that 100 tiles will be needed. How many tiles will be needed to tile the floor of a 20 ft by 20 ft room? In this case, while the width the room has doubled, the area has quadrupled. Since the number of tiles needed corresponds with the area of the floor, not the width, 400 tiles will be needed. We could find this using a proportion based on the areas of the rooms: 100 tiles n tiles = ft 400ft Other quantities just don t scale proportionally at all. Example 18 Suppose a small company spends \$1000 on an advertising campaign, and gains 100 new customers from it. How many new customers should they expect if they spend \$10,000? While it is tempting to say that they will gain 1000 new customers, it is likely that additional advertising will be less effective than the initial advertising. For example, if the company is a hot tub store, there are likely only a fixed number of people interested in buying a hot tub, so there might not even be 1000 people in the town who would be potential customers. Sometimes when working with rates, proportions, and percents, the process can be made more challenging by the magnitude of the numbers involved. Sometimes, large numbers are just difficult to comprehend. Example 19 Compare the 2010 U.S. military budget of \$683.7 billion to other quantities. Here we have a very large number, about \$683,700,000,000 written out. Of course, imagining a billion dollars is very difficult, so it can help to compare it to other quantities. If that amount of money was used to pay the salaries of the 1.4 million Walmart employees in the U.S., each would earn over \$488,000. There are about 300 million people in the U.S. The military budget is about \$2,200 per person. If you were to put \$683.7 billion in \$100 bills, and count out 1 per second, it would take 216 years to finish counting it.

10 10 Example 20 Compare the electricity consumption per capita in China to the rate in Japan. To address this question, we will first need data. From the CIA 4 website we can find the electricity consumption in 2011 for China was 4,693,000,000,000 KWH (kilowatt-hours), or trillion KWH, while the consumption for Japan was 859,700,000,000, or billion KWH. To find the rate per capita (per person), we will also need the population of the two countries. From the World Bank 5, we can find the population of China is 1,344,130,000, or billion, and the population of Japan is 127,817,277, or million. Computing the consumption per capita for each country: 4,693,000,000,000 KWH China: KWH per person 1,344,130,000 people 859,700,000,000 KWH Japan: 6726 KWH per person 127,817,277 people While China uses more than 5 times the electricity of Japan overall, because the population of Japan is so much smaller, it turns out Japan uses almost twice the electricity per person compared to China. Geometry Geometric shapes, as well as area and volumes, can often be important in problem solving. Example 21 You are curious how tall a tree is, but don t have any way to climb it. Describe a method for determining the height. There are several approaches we could take. We ll use one based on triangles, which requires that it s a sunny day. Suppose the tree is casting a shadow, say 15 ft long. I can then have a friend help me measure my own shadow. Suppose I am 6 ft tall, and cast a 1.5 ft shadow. Since the triangle formed by the tree and its shadow has the same angles as the triangle formed by me and my shadow, these triangles are called similar triangles and their sides will scale proportionally. In other words, the ratio of height to width will be the same in both triangles. Using this, we can find the height of the tree, which we ll denote by h: 6ft tall hft tall = 1.5ft shadow 15ft shadow Multiplying both sides by 15, we get h = 60. The tree is about 60 ft tall. 4 https://www.cia.gov/library/publications/the-world-factbook/rankorder/2042rank.html 5

11 Problem Solving 11 It may be helpful to recall some formulas for areas and volumes of a few basic shapes. Areas Rectangle Circle, radius r Area: LW Area: πr 2 Perimeter: 2L + 2W Circumference = 2πr W radius L Volumes Rectangular Box Volume: L W H Cylinder Volume: πr 2 H r H W L H Example 22 If a 12 inch diameter pizza requires 10 ounces of dough, how much dough is needed for a 16 inch pizza? To answer this question, we need to consider how the weight of the dough will scale. The weight will be based on the volume of the dough. However, since both pizzas will be about the same thickness, the weight will scale with the area of the top of the pizza. We can find 2 the area of each pizza using the formula for area of a circle, A= π r : 2 A 12 pizza has radius 6 inches, so the area will be π 6 = about 113 square inches. 2 A 16 pizza has radius 8 inches, so the area will be π 8 = about 201 square inches. Notice that if both pizzas were 1 inch thick, the volumes would be 113 in 3 and 201 in 3 respectively, which are at the same ratio as the areas. As mentioned earlier, since the thickness is the same for both pizzas, we can safely ignore it. We can now set up a proportion to find the weight of the dough for a 16 pizza: 10ounces xounces = Multiply both sides by in 201in 10 x = 201 = about 17.8 ounces of dough for a 16 pizza. 113

14 14 2 inches 1 ream = inches per sheet ream 500 pages 5 pounds 1 ream = 0.01 pounds per sheet, or 0.16 ounces per sheet. ream 500 pages Example 26 A recipe for zucchini muffins states that it yields 12 muffins, with 250 calories per muffin. You instead decide to make mini-muffins, and the recipe yields 20 muffins. If you eat 4, how many calories will you consume? There are several possible solution pathways to answer this question. We will explore one. To answer the question of how many calories 4 mini-muffins will contain, we would want to know the number of calories in each mini-muffin. To find the calories in each mini-muffin, we could first find the total calories for the entire recipe, then divide it by the number of mini-muffins produced. To find the total calories for the recipe, we could multiply the calories per standard muffin by the number per muffin. Notice that this produces a multi-step solution pathway. It is often easier to solve a problem in small steps, rather than trying to find a way to jump directly from the given information to the solution. We can now execute our plan: 250 calories 12 muffins = 3000 calories for the whole recipe muffin 3000 calories gives 150 calories per mini-muffin 20 mini muffins 4 mini muffins 150 calories totals 600 calories consumed. mini muffin Example 27 You need to replace the boards on your deck. About how much will the materials cost? There are two approaches we could take to this problem: 1) estimate the number of boards we will need and find the cost per board, or 2) estimate the area of the deck and find the approximate cost per square foot for deck boards. We will take the latter approach. For this solution pathway, we will be able to answer the question if we know the cost per square foot for decking boards and the square footage of the deck. To find the cost per square foot for decking boards, we could compute the area of a single board, and divide it into the cost for that board. We can compute the square footage of the deck using geometric formulas. So first we need information: the dimensions of the deck, and the cost and dimensions of a single deck board. Suppose that measuring the deck, it is rectangular, measuring 16 ft by 24 ft, for a total area of 384 ft 2.

15 Problem Solving 15 From a visit to the local home store, you find that an 8 foot by 4 inch cedar deck board costs about \$7.50. The area of this board, doing the necessary conversion from inches to feet, is: 1 foot 8 feet 4 inches = ft 2. The cost per square foot is then 12 inches \$ ft 2 = \$ per ft 2. This will allow us to estimate the material cost for the whole 384 ft 2 deck 2 \$ \$384 ft = \$1080 total cost. 2 ft Of course, this cost estimate assumes that there is no waste, which is rarely the case. It is common to add at least 10% to the cost estimate to account for waste. Example 28 Is it worth buying a Hyundai Sonata hybrid instead the regular Hyundai Sonata? To make this decision, we must first decide what our basis for comparison will be. For the purposes of this example, we ll focus on fuel and purchase costs, but environmental impacts and maintenance costs are other factors a buyer might consider. It might be interesting to compare the cost of gas to run both cars for a year. To determine this, we will need to know the miles per gallon both cars get, as well as the number of miles we expect to drive in a year. From that information, we can find the number of gallons required from a year. Using the price of gas per gallon, we can find the running cost. From Hyundai s website, the 2013 Sonata will get 24 miles per gallon (mpg) in the city, and 35 mpg on the highway. The hybrid will get 35 mpg in the city, and 40 mpg on the highway. An average driver drives about 12,000 miles a year. Suppose that you expect to drive about 75% of that in the city, so 9,000 city miles a year, and 3,000 highway miles a year. We can then find the number of gallons each car would require for the year. Sonata: 1 gallon 1 gallon 9000 city miles hightway miles = gallons 24 city miles 35 highway miles Hybrid: 1 gallon 1 gallon 9000 city miles hightway miles = gallons 35 city miles 40 highway miles If gas in your area averages about \$3.50 per gallon, we can use that to find the running cost:

17 Problem Solving 17 Try it Now Answers Continued 5. The original sandbox has volume 64 ft 3. The smaller sandbox has volume 24ft 3. 48bags x bags = results in x = 18 bags ft 24ft 6. There is not enough information provided to answer the question, so we will have to make some assumptions, and look up some values. Assumptions: a) We own a car. Suppose it gets 24 miles to the gallon. We will only consider gas cost. b) We will not need to rent a car in Spokane, but will need to get a taxi from the airport to the conference hotel downtown and back. c) We can get someone to drop us off at the airport, so we don t need to consider airport parking. d) We will not consider whether we will lose money by having to take time off work to drive. Values looked up (your values may be different) a) Flight cost: \$184 b) Taxi cost: \$25 each way (estimate, according to hotel website) c) Driving distance: 280 miles each way d) Gas cost: \$3.79 a gallon Cost for flying: \$184 flight cost + \$50 in taxi fares = \$234. Cost for driving: 560 miles round trip will require 23.3 gallons of gas, costing \$ Based on these assumptions, driving is cheaper. However, our assumption that we only include gas cost may not be a good one. Tax law allows you deduct \$0.55 (in 2012) for each mile driven, a value that accounts for gas as well as a portion of the car cost, insurance, maintenance, etc. Based on this number, the cost of driving would be \$319.

18 18 Exercises 1. Out of 230 racers who started the marathon, 212 completed the race, 14 gave up, and 4 were disqualified. What percentage did not complete the marathon? 2. Patrick left an \$8 tip on a \$50 restaurant bill. What percent tip is that? 3. Ireland has a 23% VAT (value-added tax, similar to a sales tax). How much will the VAT be on a purchase of a 250 item? 4. Employees in 2012 paid 4.2% of their gross wages towards social security (FICA tax), while employers paid another 6.2%. How much will someone earning \$45,000 a year pay towards social security out of their gross wages? 5. A project on Kickstarter.com was aiming to raise \$15,000 for a precision coffee press. They ended up with 714 supporters, raising 557% of their goal. How much did they raise? 6. Another project on Kickstarter for an ipad stylus raised 1,253% of their goal, raising a total of \$313,490 from 7,511 supporters. What was their original goal? 7. The population of a town increased from 3,250 in 2008 to 4,300 in Find the absolute and relative (percent) increase. 8. The number of CDs sold in 2010 was 114 million, down from 147 million the previous year 6. Find the absolute and relative (percent) decrease. 9. A company wants to decrease their energy use by 15%. a. If their electric bill is currently \$2,200 a month, what will their bill be if they re successful? b. If their next bill is \$1,700 a month, were they successful? Why or why not? 10. A store is hoping an advertising campaign will increase their number of customers by 30%. They currently have about 80 customers a day. a. How many customers will they have if their campaign is successful? b. If they increase to 120 customers a day, were they successful? Why or why not? 11. An article reports attendance dropped 6% this year, to 300. What was the attendance before the drop? 12. An article reports sales have grown by 30% this year, to \$200 million. What were sales before the growth? 6

19 Problem Solving The Walden University had 47,456 students in 2010, while Kaplan University had 77,966 students. Complete the following statements: a. Kaplan s enrollment was % larger than Walden s. b. Walden s enrollment was % smaller than Kaplan s. c. Walden s enrollment was % of Kaplan s. 14. In the 2012 Olympics, Usain Bolt ran the 100m dash in 9.63 seconds. Jim Hines won the 1968 Olympic gold with a time of 9.95 seconds. a. Bolt s time was % faster than Hines. b. Hine time was % slower than Bolt s. c. Hine time was % of Bolt s. 15. A store has clearance items that have been marked down by 60%. They are having a sale, advertising an additional 30% off clearance items. What percent of the original price do you end up paying? 16. Which is better: having a stock that goes up 30% on Monday than drops 30% on Tuesday, or a stock that drops 30% on Monday and goes up 30% on Tuesday? In each case, what is the net percent gain or loss? 17. Are these two claims equivalent, in conflict, or not comparable because they re talking about different things? a. 16.3% of Americans are without health insurance 7 b. only 55.9% of adults receive employer provided health insurance Are these two claims equivalent, in conflict, or not comparable because they re talking about different things? a. We mark up the wholesale price by 33% to come up with the retail price b. The store has a 25% profit margin 19. Are these two claims equivalent, in conflict, or not comparable because they re talking about different things? a. Every year since 1950, the number of American children gunned down has doubled. b. The number of child gunshot deaths has doubled from 1950 to Are these two claims equivalent, in conflict, or not comparable because they re talking about different things? 9 a. 75 percent of the federal health care law s taxes would be paid by those earning less than \$120,000 a year b. 76 percent of those who would pay the penalty [health care law s taxes] for not having insurance in 2016 would earn under \$120,

20 Are these two claims equivalent, in conflict, or not comparable because they re talking about different things? a. The school levy is only a 0.1% increase of the property tax rate. b. This new levy is a 12% tax hike, raising our total rate to \$9.33 per \$1000 of value. 22. Are the values compared in this statement comparable or not comparable? Guns have murdered more Americans here at home in recent years than have died on the battlefields of Iraq and Afghanistan. In support of the two wars, more than 6,500 American soldiers have lost their lives. During the same period, however, guns have been used to murder about 100,000 people on American soil A high school currently has a 30% dropout rate. They ve been tasked to decrease that rate by 20%. Find the equivalent percentage point drop. 24. A politician s support grew from 42% by 3 percentage points to 45%. What percent (relative) change is this? 25. Marcy has a 70% average in her class going into the final exam. She says "I need to get a 100% on this final so I can raise my score to 85%." Is she correct? 26. Suppose you have one quart of water/juice mix that is 50% juice, and you add 2 quarts of juice. What percent juice is the final mix? 27. Find a unit rate: You bought 10 pounds of potatoes for \$ Find a unit rate: Joel ran 1500 meters in 4 minutes, 45 seconds. 29. Solve: 30. Solve: 2 6 =. 5 x n 16 5 = A crepe recipe calls for 2 eggs, 1 cup of flour, and 1 cup of milk. How much flour would you need if you use 5 eggs? 32. An 8ft length of 4 inch wide crown molding costs \$14. How much will it cost to buy 40ft of crown molding? 33. Four 3-megawatt wind turbines can supply enough electricity to power 3000 homes. How many turbines would be required to power 55,000 homes? 10

### Math in Society Edition 2.3

Math in Society Edition 2.3 Contents Problem Solving...................... Extension: Taxes................... David Lippman 1 30 Voting Theory........................ 35 David Lippman Weighted Voting......................

### Math in Society Edition 2.4

Math in Society Edition 2.4 Contents Problem Solving...................... Extension: Taxes................... David Lippman 1 30 Voting Theory........................ 35 David Lippman Weighted Voting......................

### Math 98 Supplement 2 LEARNING OBJECTIVE

Dimensional Analysis 1. Convert one unit of measure to another. Math 98 Supplement 2 LEARNING OBJECTIVE Often measurements are taken using different units. In order for one measurement to be compared to

### MATH FOR NURSING MEASUREMENTS. Written by: Joe Witkowski and Eileen Phillips

MATH FOR NURSING MEASUREMENTS Written by: Joe Witkowski and Eileen Phillips Section 1: Introduction Quantities have many units, which can be used to measure them. The following table gives common units

### Relationships Between Quantities

Relationships Between Quantities MODULE 1? ESSENTIAL QUESTION How do you calculate when the numbers are measurements? CALIFORNIA COMMON CORE LESSON 1.1 Precision and Significant Digits N.Q.3 LESSON 1.2

### Objective To introduce a formula to calculate the area. Family Letters. Assessment Management

Area of a Circle Objective To introduce a formula to calculate the area of a circle. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment

### Section 1.7 Dimensional Analysis

Dimensional Analysis Dimensional Analysis Many times it is necessary to convert a measurement made in one unit to an equivalent measurement in another unit. Sometimes this conversion is between two units

### Basic Garden Math. This document is organized into the following sections:

Basic Garden Math Gardening is an activity which occasionally requires the use of math, such as when you are computing how much fertilizer to use or how much compost to buy. Luckily, the math involved

### Unit Conversions. 1liter. Imagine that we want to convert this quantity in quarts to gallons. There are 4 quarts in one gallon. Show your work below:

IDS 101 Name Unit Conversions In our everyday lives we frequently have to convert from one unit of measurement to another. When we go to the store and some rope is sold as \$.50 per foot and we want 18

### 4 th Grade Summer Mathematics Review #1. Name: 1. How many sides does each polygon have? 2. What is the rule for this function machine?

. How many sides does each polygon have? th Grade Summer Mathematics Review #. What is the rule for this function machine? A. Pentagon B. Nonagon C. Octagon D. Quadrilateral. List all of the factors of

### 2) 4.6 mi to ft A) 24,288 ft B) ft C)2024 ft D) 8096 ft. 3) 78 ft to yd A) 234 yd B) 2808 yd C)26 yd D) 8.67 yd

Review questions - test 2 MULTIPLE CHOICE. Circle the letter corresponding to the correct answer. Partial credit may be earned if correct work is shown. Use dimensional analysis to convert the quantity

### Dimensional Analysis is a simple method for changing from one unit of measure to another. How many yards are in 49 ft?

HFCC Math Lab NAT 05 Dimensional Analysis Dimensional Analysis is a simple method for changing from one unit of measure to another. Can you answer these questions? How many feet are in 3.5 yards? Revised

### 11-4 Multiplying and Dividing Rational Expressions. Find each product. ANSWER: 4x ANSWER: ANSWER: ANSWER: 4(r 1)

1. 2. Find each product. 4x 8. 9. 3c 2 d 2 3. 10. 2(x + 3) Find each product. 11. 4. 4(r 1) 5. CCSS PRECISION The slowest land mammal is the three-toed sloth. It travels 0.07 mile per hour on the ground.

### MEASUREMENTS. U.S. CUSTOMARY SYSTEM OF MEASUREMENT LENGTH The standard U.S. Customary System units of length are inch, foot, yard, and mile.

MEASUREMENTS A measurement includes a number and a unit. 3 feet 7 minutes 12 gallons Standard units of measurement have been established to simplify trade and commerce. TIME Equivalences between units

### MM 6-1 MM What is the largest number you can make using 8, 4, 6 and 2? (8,642) 1. Divide 810 by 9. (90) 2. What is ?

MM 6-1 1. What is the largest number you can make using 8, 4, 6 and 2? (8,642) 2. What is 500 20? (480) 3. 6,000 2,000 400 = (3,600). 4. Start with 6 and follow me; add 7, add 2, add 4, add 3. (22) 5.

### MEASUREMENTS. U.S Distance. inch is in. foot is ft. yard is yd. mile is mi ft. = 12 in yd. = 36 in./3 ft mi. = 5,280 ft.

MEASUREMENTS U.S Distance inch is in. foot is ft. yard is yd. mile is mi. 1. 1 ft. = 12 in. 2. 1 yd. = 36 in./3 ft. 3. 1 mi. = 5,280 ft. Metric Distance millimeter is mm. centimeter is cm. meter is m.

### Area is a measure of how much space is occupied by a figure. 1cm 1cm

Area Area is a measure of how much space is occupied by a figure. Area is measured in square units. For example, one square centimeter (cm ) is 1cm wide and 1cm tall. 1cm 1cm A figure s area is the number

### TERMS. Fractions: Adding and subtracting: you need to have the same common denominator (bottom) then, you + or the numerators (top).

1 TERMS Edges: This is all the straight lines of a figure. Like the edge of a desk. Faces: This is the flat surface of a figure. Vertex: This is all the corners of a figure. Right angle: An angle at 90

### Dimensional Analysis #3

Dimensional Analysis #3 Many units of measure consist of not just one unit but are actually mixed units. The most common examples of mixed units are ratios of two different units. Many are probably familiar

### Project: Dimensional Analysis

Project: Dimensional Analysis How big do you think one of the blocks that make up the Cheops Pyramid at Giza is? This question actually came up in conversation with some friends at our house a few years

### Math Refresher. Book #2. Workers Opportunities Resources Knowledge

Math Refresher Book #2 Workers Opportunities Resources Knowledge Contents Introduction...1 Basic Math Concepts...2 1. Fractions...2 2. Decimals...11 3. Percentages...15 4. Ratios...17 Sample Questions...18

### Perimeter, Area, and Volume

Perimeter, Area, and Volume Perimeter of Common Geometric Figures The perimeter of a geometric figure is defined as the distance around the outside of the figure. Perimeter is calculated by adding all

### Applications of Multiplication of Fractions

.6 Applications of Multiplication of Fractions.6 OBJECTIVES. Solve applications involving multiplication of fractions. Use appropriate units analysis when solving applications Units Analysis When dividing

### USEFUL RELATIONSHIPS

Use the chart below for the homework problems in this section. USEFUL RELATIONSHIPS U.S. Customary 12 in. = 1 ft 3 ft = 1 yd 280 ft = 1 mi 16 oz = 1 lb 2000 lbs = 1 T 8 fl oz = 1 c 2 c = 1 pt 2 pts = 1

### One basic concept in math is that if we multiply a number by 1, the result is equal to the original number. For example,

MA 35 Lecture - Introduction to Unit Conversions Tuesday, March 24, 205. Objectives: Introduce the concept of doing algebra on units. One basic concept in math is that if we multiply a number by, the result

### Measurement/Volume and Surface Area Long-Term Memory Review Grade 7, Standard 3.0 Review 1

Review 1 1. Explain how to convert from a larger unit of measurement to a smaller unit of measurement. Include what operation(s) would be used to make the conversion. 2. What basic metric unit would be

### 18) 6 3 4 21) 1 1 2 22) 7 1 2 23) 19 1 2 25) 1 1 4. 27) 6 3 qt to cups 30) 5 1 2. 32) 3 5 gal to pints. 33) 24 1 qt to cups

Math 081 Chapter 07 Practice Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 18) 6 3 4 gal to quarts Convert as indicated. 1) 72 in. to feet 19)

### Name: School Team: X = 5 X = 25 X = 40 X = 0.09 X = 15

7th/8th grade Math Meet Name: School Team: Event : Problem Solving (no calculators) Part : Computation ( pts. each) ) / + /x + /0 = X = 5 ) 0% of 5 = x % of X = 5 ) 00 - x = ()()(4) + 6 X = 40 4) 0.6 x

### 1,892.7 ml. 4-7 Convert Between Systems. Complete. Round to the nearest hundredth if necessary in. cm SOLUTION:

Complete. Round to the nearest hundredth if necessary. 1. 5 in. cm Since 1 inch 2.54 centimeters, multiply by. So, 5 inches is approximately 12.7 centimeters. 12.7 2. 2 qt ml Since 946.35 milliliters 1

### REVIEW FOR MAT 0012 FINAL EXAM

REVIEW FOR MAT 002 FINAL EXAM Name Rewrite the following number using digits. ) Seven thousand, six A) 7006 B) 7060 C) 7600 D) 76,000 ) Answer the question. 2) What does the digit 0 mean in the number

### Lesson 21: Getting the Job Done Speed, Work, and Measurement Units

Lesson 2 6 Lesson 2: Getting the Job Done Speed, Work, and Measurement Student Outcomes Students use rates between measurements to convert measurement in one unit to measurement in another unit. They manipulate

### Handout Unit Conversions (Dimensional Analysis)

Handout Unit Conversions (Dimensional Analysis) The Metric System had its beginnings back in 670 by a mathematician called Gabriel Mouton. The modern version, (since 960) is correctly called "International

### Measurement. Customary Units of Measure

Chapter 7 Measurement There are two main systems for measuring distance, weight, and liquid capacity. The United States and parts of the former British Empire use customary, or standard, units of measure.

### Section 1.6 Systems of Measurement

Systems of Measurement Measuring Systems of numeration alone do not provide enough information to describe all the physical characteristics of objects. With numerals, we can write down how many fish we

### DIMENSIONAL ANALYSIS #2

DIMENSIONAL ANALYSIS #2 Area is measured in square units, such as square feet or square centimeters. These units can be abbreviated as ft 2 (square feet) and cm 2 (square centimeters). For example, we

### MEASUREMENT. Historical records indicate that the first units of length were based on people s hands, feet and arms. The measurements were:

MEASUREMENT Introduction: People created systems of measurement to address practical problems such as finding the distance between two places, finding the length, width or height of a building, finding

### 6.1 NUMBER SENSE 3-week sequence

Year 6 6.1 NUMBER SENSE 3-week sequence Pupils can represent and explain the multiplicative nature of the number system, understanding how to multiply and divide by 10, 100 and 1000. Pupils make appropriate

### DIMENSIONAL ANALYSIS #2

DIMENSIONAL ANALYSIS #2 Area is measured in square units, such as square feet or square centimeters. These units can be abbreviated as ft 2 (square feet) and cm 2 (square centimeters). For example, we

### Unit 5, Activity 1, Customary and Metric Vocabulary Self-Awareness

Unit 5, Activity 1, Customary and Metric Vocabulary Self-Awareness Look at the vocabulary word. Indicate your knowledge of the word using a +,, or. A plus sign (+) indicates a high degree of comfort and

### The Road to Proportional Reasoning: VOCABULARY LIST

SCALE CITY The Road to Proportional Reasoning: VOCABULARY LIST Term and Definition angle: the amount of turn between two rays that meet at a common endpoint area: the size of a two-dimensional surface

### millimeter centimeter decimeter meter dekameter hectometer kilometer 1000 (km) 100 (cm) 10 (dm) 1 (m) 0.1 (dam) 0.01 (hm) 0.

Section 2.4 Dimensional Analysis We will need to know a few equivalencies to do the problems in this section. I will give you all equivalencies from this list that you need on the test. There is no need

### Write each measurement in millimeters (mm). Round the measurement to the nearest centimeter (cm).

5-1 Write each measurement in millimeters (mm). Round the measurement to the nearest centimeter (cm). 1 2 3 4 5 6 7 8 mm 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 cm 26 27 28 29 30 31

### 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B. Whole Numbers

Whole Numbers Scope and Sequence for Primary Mathematics, U.S. Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced or specifically addressed. Understand

### Unit Conversions. Ben Logan Feb 10, 2005

Unit Conversions Ben Logan Feb 0, 2005 Abstract Conversion between different units of measurement is one of the first concepts covered at the start of a course in chemistry or physics.

### Lesson 11: Measurement and Units of Measure

LESSON 11: Units of Measure Weekly Focus: U.S. and metric Weekly Skill: conversion and application Lesson Summary: First, students will solve a problem about exercise. In Activity 1, they will practice

### Calculating Area and Volume of Ponds and Tanks

SRAC Publication No. 103 Southern Regional Aquaculture Center August 1991 Calculating Area and Volume of Ponds and Tanks Michael P. Masser and John W. Jensen* Good fish farm managers must know the area

### \$566.30. What is the monthly interest rate on the account? (Round to the nearest hundredth of a percent.) 4 = x 12. 7)

Exam Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1)What percent of 6 is 27? 1) 2)64.288 is 28.7% of what number? 2) 3)112% of what number is

### Practice 116 problems for test 1. This in addition to the quiz problems and the problems assigned on the syllabus should be studied for the test

Practice 116 problems for test 1. This in addition to the quiz problems and the problems assigned on the syllabus should be studied for the test SHORT ANSWER. Write the word or phrase that best completes

### 12-4 Volumes of Prisms and Cylinders. Find the volume of each prism.

Find the volume of each prism. 3. the oblique rectangular prism shown at the right 1. The volume V of a prism is V = Bh, where B is the area of a base and h is the height of the prism. If two solids have

### Math 208, Section 7.1 Solutions: The Meaning of Division

Math 208, Section 7.1 Solutions: The Meaning of Division 1. For each of the following story problems, write the corresponding numerical division problem, state which interpretation of division is involved

### Virginia Mathematics Checkpoint Assessment MATHEMATICS 5.8. Strand: Measurement

Virginia Mathematics Checkpoint Assessment MATHEMATICS 5.8 Strand: Measurement Standards of Learning Blueprint Summary Reporting Category Grade 5 SOL Number of Items Number & Number Sense 5.1, 5.2(a-b),

### 5.2. Nets and Solids LESSON. Vocabulary. Explore. Materials

LESSON 5.2 Nets and Solids A net is a flat figure that can be folded to form a closed, three- dimensional object. This type of object is called a geometric solid. Inv 1 Use a Net 229 Inv 2 Use Nets to

### Characteristics of the Four Main Geometrical Figures

Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.

### Third Grade Illustrated Math Dictionary Updated 9-13-10 As presented by the Math Committee of the Northwest Montana Educational Cooperative

Acute An angle less than 90 degrees An acute angle is between 1 and 89 degrees Analog Clock Clock with a face and hands This clock shows ten after ten Angle A figure formed by two line segments that end

### Dividing Decimals 4.5

4.5 Dividing Decimals 4.5 OBJECTIVES 1. Divide a decimal by a whole number 2. Divide a decimal by a decimal 3. Divide a decimal by a power of ten 4. Apply division to the solution of an application problem

### Applications of Algebraic Fractions

5.6 Applications of Algebraic Fractions 5.6 OBJECTIVES. Solve a word problem that leads to a fractional equation 2. Apply proportions to the solution of a word problem Many word problems will lead to fractional

### East Bay Municipal Utility District. Entry-Level Sample Test Items

East Bay Municipal Utility District Entry-Level Sample Test Items East Bay Municipal Utility District Sample Test Items Table of Contents Page Overview...1 Section One - Math... 2 Math Concepts... 2 Math

### SOLVING WORD PROBLEMS

SOLVING WORD PROBLEMS Word problems can be classified into different categories. Understanding each category will give be an advantage when trying to solve word problems. All problems in each category

### Grade 6 FCAT 2.0 Mathematics Sample Questions

Grade FCAT. Mathematics Sample Questions The intent of these sample test materials is to orient teachers and students to the types of questions on FCAT. tests. By using these materials, students will become

### Measurement. 2. If the perimeter of a rectangular house is 44 yards, and the length is 36 feet, what is the width of the house?

Measurement 1. What will it cost to carpet a room with indoor/outdoor carpet if the room is 10 feet wide and 12 feet long? The carpet costs 12.51 per square yard. \$166.80 \$175.90 \$184.30 \$189.90 \$192.20

### Name. # s. We found the unit rate or conversion rate. We know there are about 0.62 miles in 1 kilometer.

Homework Problems Name Team Name Team Complete? Team Did Not Agree On Questions # s Quick Look Today we learned to convert units of different measure. Because conversions rate are a type of rate, find

### Timeframe: Recommend spending a day on each system of units. It will depend on each gradelevel and how many units of measurement are being taught.

Grade Level/Course: Grades 3-5 Lesson/Unit Plan Name: Do I Reall Have to Teach Measurement? Rationale/Lesson Abstract: With measurement being a large component in Common Core, this lesson provides strategies

### Area & Volume. 1. Surface Area to Volume Ratio

1 1. Surface Area to Volume Ratio Area & Volume For most cells, passage of all materials gases, food molecules, water, waste products, etc. in and out of the cell must occur through the plasma membrane.

### T. H. Rogers School Summer Math Assignment

T. H. Rogers School Summer Math Assignment Mastery of all these skills is extremely important in order to develop a solid math foundation. I believe each year builds upon the previous year s skills in

### 3D Geometry: Chapter Questions

3D Geometry: Chapter Questions 1. What are the similarities and differences between prisms and pyramids? 2. How are polyhedrons named? 3. How do you find the cross-section of 3-Dimensional figures? 4.

### Units of Measurement: A. The Imperial System

Units of Measurement: A. The Imperial System Canada uses the metric system most of the time! However, there are still places and occasions where the imperial system of measurement is used. People often

### Lakeview Christian Academy Summer Math Packet For Students Entering Grade 7 (Pre-Algebra 1)

Lakeview Christian Academy Summer Math Packet For Students Entering Grade 7 (Pre-Algebra 1) Student s Name Summer 2016 To be completed during the month of August prior to the start of the school year.

Division with Fractions 1. Solve the following. Copyright 2013 Edmentum - All rights reserved. Volume 2. A stick of butter has a length of 8 inches, a width of 2 inches, and a height of 2 inches. What

### FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST. Mathematics Reference Sheets. Copyright Statement for this Assessment and Evaluation Services Publication

FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST Mathematics Reference Sheets Copyright Statement for this Assessment and Evaluation Services Publication Authorization for reproduction of this document is hereby

### Geometry Notes PERIMETER AND AREA

Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter

### Appendix C: Conversions and Calculations

Appendix C: Conversions and Calculations Effective application of pesticides depends on many factors. One of the more important is to correctly calculate the amount of material needed. Unless you have

### Chapter 3 Review Math 1030

Section A.1: Three Ways of Using Percentages Using percentages We can use percentages in three different ways: To express a fraction of something. For example, A total of 10, 000 newspaper employees, 2.6%

### Math Review Sheets Math 20 Basic Mathematics (Arithmetic)

Math Review Sheets Math 0 Basic Mathematics (Arithmetic) The purpose of this Review Sheet is to provide students a comprehensive review of items that are taught in Math 0 classes. It is the KCC Math Department

### To Multiply Decimals

4.3 Multiplying Decimals 4.3 OBJECTIVES 1. Multiply two or more decimals 2. Use multiplication of decimals to solve application problems 3. Multiply a decimal by a power of ten 4. Use multiplication by

### 1. Write the ratio of two numbers in simplest form 2. Write the ratio of two quantities in simplest form

5.1 Ratios 5.1 OBJECTIVES 1. Write the ratio of two numbers in simplest form. Write the ratio of two quantities in simplest form In Chapter, you saw two meanings for a fraction: 3 1. A fraction can name

### Scope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B

Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced

### Ratios (pages )

A Ratios (pages 80 8) You can compare two quantities by using a ratio. A common way to express a ratio is as a fraction in simplest form. If the two quantities you are comparing have different units of

### CH 304K Practice Problems

1 CH 304K Practice Problems Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. How many millimeters are there in 25 feet? a. 7.6 10 2 mm b.

### 2. A painted 2 x 2 x 2 cube is cut into 8 unit cubes. What fraction of the total surface area of the 8 small cubes is painted?

Black Surface Area and Volume (Note: when converting between length, volume, and mass, 1 cm 3 equals 1 ml 3, and 1 ml 3 equals 1 gram) 1. A rectangular container, 25 cm long, 18 cm wide, and 10 cm high,

### Free Pre-Algebra Lesson 3 page 1. Example: Find the perimeter of each figure. Assume measurements are in centimeters.

Free Pre-Algebra Lesson 3 page 1 Lesson 3 Perimeter and Area Enclose a flat space; say with a fence or wall. The length of the fence (how far you walk around the edge) is the perimeter, and the measure

### FCAT Math Vocabulary

FCAT Math Vocabulary The terms defined in this glossary pertain to the Sunshine State Standards in mathematics for grades 3 5 and the content assessed on FCAT in mathematics. acute angle an angle that

### NOTE: Please DO NOT write in exam booklet. Use the answer sheet for your answers.

ELECTRICIAN PRE-APPRENTICESHIP MATH ENTRANCE EXAM NOTE: Please DO NOT write in exam booklet. Use the answer sheet for your answers. NOTE: DO NOT MARK SECTION A. PLACE YOUR ANSWERS ON THE SHEET PROVIDED

### Chapter 7. g-----grams, unit measure of weight m----meters, unit measure of length l---liters, unit measure of volume

Chapter 7 g-----grams, unit measure of weight m----meters, unit measure of length l---liters, unit measure of volume ) find cm, cm, 5mm, 60mm, 05mm, dm,.dm,.5cm, 0.5cm One liter of coke. The amount of

### Learning Centre CONVERTING UNITS

Learning Centre CONVERTING UNITS To use this worksheet you should be comfortable with scientific notation, basic multiplication and division, moving decimal places and basic fractions. If you aren t, you

### Metric Units of Weight and Volume

7.3 Metric Units of Weight and Volume 7.3 OBJECTIVES 1. Use appropriate metric units of weight 2. Convert metric units of weight 3. Estimate metric units of volume 4. Convert metric units of volume The

### Measurements 1. BIRKBECK MATHS SUPPORT www.mathsupport.wordpress.com. In this section we will look at. Helping you practice. Online Quizzes and Videos

BIRKBECK MATHS SUPPORT www.mathsupport.wordpress.com Measurements 1 In this section we will look at - Examples of everyday measurement - Some units we use to take measurements - Symbols for units and converting

### Math Questions & Answers

What five coins add up to a nickel? five pennies (1 + 1 + 1 + 1 + 1 = 5) Which is longest: a foot, a yard or an inch? a yard (3 feet = 1 yard; 12 inches = 1 foot) What do you call the answer to a multiplication

### HESI PREP TEST. SLC Lake Worth Math Lab

1 PREP TEST 2 Explanation of scores: 90% to 100%: Excellent Super job! You have excellent Math skills and should have no difficulty calculating medication administration problems in your program. 80% to

### CHM 130LL: Introduction to the Metric System

CHM 130LL: Introduction to the Metric System In this experiment you will: Determine the volume of a drop of water using a graduated cylinder Determine the volume of an object by measuring its dimensions

### Task: Representing the National Debt 7 th grade

Tennessee Department of Education Task: Representing the National Debt 7 th grade Rachel s economics class has been studying the national debt. The day her class discussed it, the national debt was \$16,743,576,637,802.93.

### Chapter 2 Measurement and Problem Solving

Introductory Chemistry, 3 rd Edition Nivaldo Tro Measurement and Problem Solving Graph of global Temperature rise in 20 th Century. Cover page Opposite page 11. Roy Kennedy Massachusetts Bay Community

### 2 Fractions, decimals and percentages

2 Fractions, decimals and percentages You can use fractions, decimals and percentages to help you solve everyday practical problems. Fractions Write fractions in their simplest form. Do this by dividing

### MathWorks 10 Workbook. Errata. Printings of MathWorks Workbook contain the following errors. We apologize for any inconvenience these may have caused.

Errata Printings of MathWorks Workbook contain the following errors. We apologize for any inconvenience these may have caused. 111 Example 1 The final steps of the solution should be replaced with the

### TEKS TAKS 2010 STAAR RELEASED ITEM STAAR MODIFIED RELEASED ITEM

7 th Grade Math TAKS-STAAR-STAAR-M Comparison Spacing has been deleted and graphics minimized to fit table. (1) Number, operation, and quantitative reasoning. The student represents and uses numbers in

### Interpreting Graphs. Interpreting a Bar Graph

1.1 Interpreting Graphs Before You compared quantities. Now You ll use graphs to analyze data. Why? So you can make conclusions about data, as in Example 1. KEY VOCABULARY bar graph, p. 3 data, p. 3 frequency

### Chapter 2 Formulas and Decimals

Chapter Formulas and Decimals Section A Rounding, Comparing, Adding and Subtracting Decimals Look at the following formulas. The first formula (P = A + B + C) is one we use to calculate perimeter of a

### Healthcare Math: Using the Metric System

Healthcare Math: Using the Metric System Industry: Healthcare Content Area: Mathematics Core Topics: Using the metric system, converting measurements within and between the metric and US customary systems,

### GRADE 6 MATHEMATICS CORE 1 VIRGINIA STANDARDS OF LEARNING. Spring 2006 Released Test. Property of the Virginia Department of Education

VIRGINIA STANDARDS OF LEARNING Spring 2006 Released Test GRADE 6 MATHEMATICS CORE 1 Property of the Virginia Department of Education 2006 by the Commonwealth of Virginia, Department of Education, P.O.