Chapter 6. Ratio, Proportion and Measurement

Transcription

1 Chapter 6. Ratio, Proportion and Measurement 6.1 Ratios 6.2 Proportion 6.3 American Units of Measurement 6.4 Metric Units of Measurement 6.5 Converting between American and Metric Units 1

2 6.1 Ratios 1. Write ratio as fractions 2. Simplify ratios involving decimals and mixed numbers 3. Convert units to write ratios 4. Write rates as fractions 5. Find unit rates 6. Find the best buy based on unit price 2

3 6.1 Ratios 1. Write ratio as fractions (partly review) Ratio A ratio is the quotient of two numbers or the quotient of two quantities that have the same units. Three ways to write a ratio, for example 50 1, 14 to 10, 2:3 3

4 6.1 Ratios 1. Write ratio as fractions (review) Be careful: 1 st number as numerator, 2 nd number e.g.1 Write each ratio as a fraction: 4 a. 4 to 9 Ans. b. 8:15 9 Ans. e.g.3 BASKETBALL NBA basketball counts are 50 wide and 94 feet long. Write the ratio of the width to the length as fraction in simplest form Ans Write the ratio of the length to the width as fraction in simplest form 47 Ans

5 6.1 Ratios 2. Simplify ratios involving decimals and mixed numbers (review) e.g.4 Write the ratio 0.6 to 4.8 as a fraction in simplest 1 form. Ans. 8 3 e.g.5 Write the ratio 6 to 1 as a fraction in simplest 4 8 form. 1 Ans

6 6.1 Ratios 3. Convert units to write ratios (review) e.g.6 Write the ratio 18 seconds to 2 minutes as a fraction in simplest form. 3 Ans. 20 6

7 6.1 Ratios 4. Write rates as fractions (review) Rate A ratio is the quotient of two quantities that have different units. 16 computers for 75 students 1,550 feet in 4.5 seconds e.g.7 HOSPITAL In a 6-hour span, 21 patients were treated in a hospital emergency room. Write the rate of patients treated in the emergency room as a fraction in simplest form. 7 patients Ans. 2 hrs Keep the word! 7

8 5. Find unit rates (review) 6.1 Ratios Unit Rate A unit rate is a rate in which the denominator is 1. e.g.8 NUTRITION There are 180 calories in a 12-ounce serving of apple juice. Write this rate as unit rate. Ans. 15 calories/oz, or 15 calories per ounce e.g.9 PART-TIME JOBS A student earns $90 for working 8 hours in a school cafeteria. Write this rate as unit rate. Ans. $11.25/hr, or $11.25 per hour 8

9 6.1 Ratios 6. Find the best buy based on unit price (review) Unit Price A unit price is a rate that tells how much is paid for one unit (or one item). It is the quotient of price to the number of units. Unit price = price number of units e.g.10 GUITAR LESSON A music store charge $27 for a 30-minutes guitar lesson and $36 for a 45-minutes lesson. Which is the best buy? Ans. 45-minute lesson 9

10 6.2. Proportion 1. Write proportions 2. Determine whether proportions are true or false 3. Solve a proportion to find an unknown term 4. Write proportions to solve application problems 10

11 1. Write proportions (review) 6.2. Proportion Proportion A proportion is a statement that two ratios (or rates) are Equal. e.g.1 Write each statement as a proportion. a. 45 is to 50 as 9 is to Ans. = b. 900 applicants is to 600 jobs as 3 applicants is to 2 jobs 900 applicants 3 applicants Ans. = 600 jobs 2 jobs 11

12 6.2. Proportion 2. Determine whether proportions are true or false (review) e.g.2 Determine whether each proportion is true or false by simplifying = False = a. b. e.g.3 Determine whether each proportion is true or false by cross multiply = False = a. b. True True 12

13 6.2. Proportion 2. Determine whether proportions are true or false (review) e.g.4 Determine whether each proportion is true or false a. = False b = True e.g.5 Determine whether 6, 8 and 81, 99 are proportional? Not proportional 13

14 6.2. Proportion 3. Solve a proportion to find an unknown term (review) e.g.6 Solve the proportion: e.g.7 Solve the proportion: 8 = 30 4 x 3.6 x = Ans. x = 5.4 e.g.8 Solve the proportion: x 1 = Ans. x =

15 6.2. Proportion 4. Write proportions to solve application problems e.g.9 GROCERY SHOPPING If 3 avocados cost $2.67, find the cost of 10 avocados. Ans. $8.90 e.g.10 SCALE DRAWINGS The distance between the wheels in the scale drawings of the airplane is 1.25 inches. If one inch on the drawing represents 6 feet of actual distance What is the actual distance between the wheels? Ans. the actual distance is 7.5 feet 15

16 6.2. Proportion 4. Write proportions to solve application problems e.g.11 BAKING A recipe for coffee cake calls for 1 cups 4 1 of sugar for every 5 cups of flour. If a baker has 7 4 only cup sugar, how much flour should she add to 8 make the coffee cake batter? 3 Ans cups of flour 16

17 6.3 American Units of Measurement 1. Use a ruler to measure the length in inches 2. Define American units of length 3. Convert from one American unit of length to another 4. Define American units of weight 5. Convert from one American unit of weight to another 6. Define American units of capacity 7. Convert from one American unit of capacity to another 8. Define units of time 9. Convert from one unit of time to another 17

18 6.3 American Units of Measurement 1. Use a ruler to measure the length in inches e.g.1 Find the length of the paper clip shown here. Need book and ruler. Ans in 18

19 6.3 American Units of Measurement 2. Define American units of length American Unit of Length 1 foot (ft) = 12 inches (in) one yard (yd) = 36 inches (in) 1 yard (yd) = 3 feet (ft) one mile (mi) = 5,280 feet (ft) 3. Convert from one American unit of length to another e.g.3 Convert 5 yards to feet. Ans. 15 ft 1 4 e.g.4 Convert feet to inches. 2 Ans. 27 in 19

20 6.3 American Units of Measurement 3. Convert from one American unit of length to another e.g.5 THE MASTERS GOLF TOURNAMENT Hole number 8 of the Augusta National courses is 570 yards long. Convert the length of the hole to miles. Give the exact answer and a decimal approximation, rounded to the nearest hundredth of a mile. Ans mi 0.32 mi 20

21 6.3 American Units of Measurement 4. Define American units of weight American Units of Weight 1 pound (lb) = 16 ounces (oz) 1 ton (T) = 2,000 pound (lb) 5. Convert from one American unit of weight to another e.g.6 Convert 20 ounces to pound. 1 Ans. 1 lb = lb e.g.7 Convert 90 pounds to ounces. Ans. 1,440 oz 21

22 6.3 American Units of Measurement 6. Define American units of capacity American Units of Capacity 1 cup (c) = 8 fluid ounces (fl oz) 1 pint (pt) = 2 cups (c) 1 quart (qt) = 2 pints (pt) 1 gallon (gal) = 4 quarts (qt) 7. Convert from one American unit of capacity to another e.g.8 DESSERTS If a recipe for homemade ice cream calls for 4 pints of cream, how many fluid ounces of cream should be used? Ans. 64 fl oz 22

23 6.3 American Units of Measurement 8. Define units of time Units of Time 1 minute (min) = 60 seconds (sec) 1 hour (hr) = 60 minutes (min) 1 day = 24 hours 9. Convert from one unit of time to another e.g.9 SPACE FLIGHT On Feb. 20, 1962, John Glenn was the first American astronaut to orbit the Earth. The Mercury-Atlas 6 mission in the spacecraft Friendship 7 lasted a total of 295 minutes. Express this time in hours. 11 Ans hr 23

24 6.4 Metric Units of Measurement 1. Define metric units of length 2. Use a ruler to measure the lengths 3. Use unit conversion factors to convert metric units of length 4. Use a conversion chart to convert metric unit of length 5. Define metric units of mass 6. Convert from one metric unit of mass to another 7. Define metric unit of capacity 8. Convert from one metric unit of capacity to another 9. Define a cubic centimeter 24

25 6.4 Metric Units of Measurement 1. Define metric units of length Metric Units of Length Prefix kilo- hecto- deka- deci- centi- millimeter meter meter meter meter meter meter Meaning of 0.01 of of meters meters meters meter a meter a meter a meter Abbreviation km hm dam m dm cm mm km, m, cm, mm are commonly used. 25

26 6.4 Metric Units of Measurement 2. Use a ruler to measure the lengths e.g.1 Find the length of the paper clip shown here. Need book and ruler with cm and mm. Ans. 36 mm 26

27 6.4 Metric Units of Measurement 3. Use unit conversion factors to convert metric units of length Metric Units of Length 1 kilometer (km) = 1,000 meters 1 meter = 10 decimeters (dm) 1 hectometer (hm) = 100 meters 1 meter = 100 centimeters (cm) 1 dekameter (dam) = 10 meters 1 meter = 1,000 millimeters (mm) The blue ones frequently used. e.g.3 Convert 410 centimeters to meters. Ans. 4.1 m 27

28 6.4 Metric Units of Measurement 4. Use a conversion chart to convert metric unit of length km hm dam m dm cm mm largest unit Smallest unit e.g. to convert from cm to m, we need to move two decimal places to the left. e.g.4 Convert 1.9 meters to millimeters. Ans. 1,900 mm e.g.5 Convert 9.1 centimeters to kilometers. Ans km 28

29 6.4 Metric Units of Measurement 5. Define metric units of mass Metric Units of Mass Prefix kilo- hecto- deka- deci- centi- milligram gram gram gram gram gram gram Meaning of 0.01 of of grams grams grams gram a gram a gram a gram Abbreviation kg hg dag g dg cg mg kg, g, mg are commonly used. 29

30 6.4 Metric Units of Measurement 5. Define metric units of mass Metric Units of mass 1 kilogram (kg) = 1,000 grams 1 gram = 10 decigrams (dg) 1 hectogram (hg) = 100 grams 1 gram = 100 centigrams (cg) 1 dekagram (dag) = 10 grams 1 gram = 1,000 milligrams (mg) The blue ones frequently used. 30

31 6.4 Metric Units of Measurement 6. Convert from one metric unit of mass to another kg hg dag g dg cg mg largest unit Smallest unit e.g. to convert from cg to g, we need to move two decimal places to the left. e.g.6 Convert 1.21 kilograms to grams. Ans. 1,210 g e.g.7. MEDICATIONS A drug taken for high cholesterol contains 65 tablets. If each tablet contains 120 mg of active ingredient. How many grams of active ingredient are there in the bottle? Ans. 7.8 g 31

32 6.4 Metric Units of Measurement 7. Define metric unit of capacity Metric Units of Capacity Prefix kilo- hecto- deka- deci- centi- milliliter liter liter liter liter liter liter Meaning of 0.01 of of liters liters liters liter a liter a liter a liter Abbreviation kl hl dal L dl cl ml kl, L, ml are commonly used. 32

33 6.4 Metric Units of Measurement 7. Define metric unit of capacity Metric Units of Capacity 1 kiloliter (kl) = 1,000 liters 1 liter = 10 deciliters (dl) 1 hectoliter (hl) = 100 liters 1 liter = 100 centiliters (cl) 1 dekaliter (dal) = 10 liters 1 liter = 1,000 milliliters (ml) The blue ones frequently used. 33

34 6.4 Metric Units of Measurement 8. Convert from one metric unit of capacity to another kl hl dal g dl cl ml largest unit Smallest unit e.g. to convert from cl to L, we need to move two decimal places to the left. e.g.8 ORANGE JUICE How many milliliters are in the six 2-liter cartons of orange juice? Ans. 12,000 ml 34

35 6.4 Metric Units of Measurement 9. Define a cubic centimeter 1 cc = 1 cm 3 = 1 ml cc: cubic centimeter 35

36 6.5 Converting between American and Metric Units 1. Use unit conversion factors to convert between American and metric units 2. Convert between Fahrenheit and Celsius temperatures 36

37 6.5 Converting between American and Metric Units 1. Use unit conversion factors to convert between American and metric units Equivalent Lengths American to metric Metric to American 1 in = 2.54 cm 1 cm 0.39 in 1 ft 0.30 m 1 m 3.28 ft 1 yd 0.91 m 1 m 1.09 yd 1 mi 1.61 km 1 km 0.62 mi 37

38 6.5 Converting between American and Metric Units 1. Use unit conversion factors to convert between American and metric units e.g.1 CLOTHING LABELS The length of a sleeve of a dress shirt made in Italy is 92 cm. Express the length of the sleeve to the nearest inch. Ans. 36 in e.g.2 VOLCANOS The elevation of the Lassen Peak volcano in California is 10,456 feet. The elevation of the Fuego volcano in Guatemala is 3,763 meters. Which volcano is higher? Ans. Fuego volcano 38

39 6.5 Converting between American and Metric Units 1. Use unit conversion factors to convert between American and metric units Equivalent Weights and Masses American to metric Metric to American 1 oz g 1 g oz 1 lb 0.45 kg 1 kg 2.20 lb e.g.3 Convert 40 pounds to gram. Ans. 18,144 g (using formula in the 2 nd row, get different answer) 39

40 6.5 Converting between American and Metric Units 1. Use unit conversion factors to convert between American and metric units e.g.4 WEIGHTLIFTING Which weighs more, a 45-lb iron plate or a 15-kg dumbell? Ans. 45-lb iron plate 40

41 6.5 Converting between American and Metric Units 1. Use unit conversion factors to convert between American and metric units Equivalent Capacities American to metric Metric to American 1 fl oz ml 1 L fl oz 1 pt 0.47 L 1 L 2.11 pt 1 qt 0.95 L 1 L 1.06 qt 1 gal 3.79 L 1 L gal 41

42 6.5 Converting between American and Metric Units 1. Use unit conversion factors to convert between American and metric units e.g.5 MOTOR OIL A can contains 850 milliliter of motor oil. Convert this measure to quarts. Round to the nearest tenth. Ans. 0.9 qt 42

43 6.5 Converting between American and Metric Units 2. Convert between Fahrenheit and Celsius temperatures Conversion Formula for Temperature If F is the temperature in degrees Fahrenheit and C is the corresponding temperature in degrees Celsius, then C 5 9 = ( F 32) and F = C 9 5 e.g.6 HAMBURGERS The recommended safe minimal internal temperature when cooking ground beef is 160 F. Express this temperature in degree Celsius. Round to the nearest tenth of a degree Ans C 43

44 6.5 Converting between American and Metric Units 2. Convert between Fahrenheit and Celsius temperatures C 5 9 = ( F 32) and F = C e.g.7 OLD FAITHFUL Just before it erupts, the temperature of the water in the Old Faithful geyser in Yellowstone National Park reaches 95.6 C. Express this temperature in degrees Fahrenheit. Round to the nearest degree. Ans. 204 F 44