Wmath 11 Unit 2 Math 20-2 Unit 1 LEARNING GUIDE - MEASUREMENTS PDF

## WMath 11 Unit 2 - Math 20-2 Unit 1 **LEARNING GUIDE - MEASUREMENTS** **INSTRUCTIONS:** Using a pencil, complete the following questions as you work through the related lessons. Show ALL of your work as is explained in the lessons. Do your best and always ask questions if there is anything tha...

## WMath 11 Unit 2 - Math 20-2 Unit 1 **LEARNING GUIDE - MEASUREMENTS** **INSTRUCTIONS:** Using a pencil, complete the following questions as you work through the related lessons. Show ALL of your work as is explained in the lessons. Do your best and always ask questions if there is anything that you don't understand. **2.1 UNITS** 1. Enter the correct length for each arrow on the measuring tape. Remember to include the correct unit (inches or centimetres). 2 examples are provided for you - a) 3 1/4" - b) 4 1/2" - c) 6 3/8" - d) 4.5 cm - e) 9.7 cm - f) 14.4 cm 2. Label the following measurements (a-f) on the measuring tape with an arrow and the letter of the question. 2 examples have been done for you. - x. 37 1/2" - y. 1.01m - a. 39 1/8 in. - b. 3 ft. 4 3/4 in. - c. 3.5 ft. - d. 93 cm - e. 0.992 m - f. 107.5 cm 3. Choose the metric unit that would be appropriate for each of the following. Circle your answer. - a) the capacity of a swimming pool? - 3 liters - 3 milliliters - 3 centiliters - **3 kiloliters** - b) the height of a glue stick - 3 meters - 3 millimeters - **3 centimeters** - 3 kilometers - c) the height of a mountain? - 2 millimeters - **2 meters** - 2 centimeters - 2 kilometers - d) the height of a flagpole? - 4 millimeters - **4 meters** - 4 centimeters - 4 kilometers - e) the weight of a toothbrush? - 18 centigrams - **18 grams** - 18 kilograms - 18 milligrams - f) the weight of a small airplane? - 9 milligrams - 9 grams - **9 tonnes** - 9 kilograms - g) the length of a paperclip? - 25 millimeters - **25 centimeters** - 25 meters - 25 kilometers - h) the height of a refrigerator? - 2 millimeters - 2 meters - 2 centimeters - 2 kilometers - i) the length of a car? - 3 millimeters - **3 meters** - 3 centimeters - 3 kilometers - j) the length of an American football field? - 110 millimeters - 110 centimeters - **110 meters** - 110 kilometers 4. Find the area and perimeter of each figure. | Figure | Perimeter | Area | |---|---|---| | a | P = 2 + 2 + 3 + 3 + 5 + 5 + 7 + 7 = 34 units | A = 7 x 2 + 5 x 2 + 3 x 2 = 14 + 10 + 6 = 30 units² | | b | P = 1 + 1 + 2 + 2 + 5 + 5 + 6 + 6 = 28 units | A = 5 x 2 + 8 x 1 = 10 + 8 = 18 units ² | | c | P = 2 + 2 + 3 + 5 + 6 + 6 + 10 + 10 = 44 units | A = 10 x 2 + 5 x 4 + 6 x 3 = 20 + 20 + 18 = 58 units ² | 5. A carpenter is building a temporary fence around a building site. How many metres of fencing are required for a site that is 47.8 m × 30.3 m? Round your answer up to the nearest metre. Draw a diagram and show all work. - P = 47.8m + 47.8m + 30.3m + 30.3m = 157m 6. How many studs will a carpenter need to frame the exterior walls of the building below? Use the formula given below to estimate the number of studs. Show all work. - Number of studs = perimeter - 14' + 14' + 14' + 28' + 30'8" + 52' = 160' - 160 - 80' - 2 7. Olympic swimmers compete in a pool with required dimensions 25 meters by 50 meters by 2 meters. What is the volume of the Olympic-sized pool? - V = 25m x 50m x 2m = 2500 m³ 8. Raphael drives a standard-sized dump truck. The dimensions of the bed of the truck are length 15 feet, width 8 feet, and height 6 feet. What is the volume of the bed of the dump truck? - V = 15ft x 8ft x 6ft = 720 ft³ 9. Janine keeps her jewelry in a jewelry box like the figure below. Find the volume of Janine's jewelry box. - V = 29/8 x 37/4 x 5 = 5365/32 = 167.03 inches³ 10. Kyle will fill the candle mold with liquid candle wax. Find the amount of liquid wax that will be contained in the mold. (Ignore the thickness of the walls of the container) - V = 11" x 3" x 3" = 99 inches³ 11. A landscape horticulturalist needs to order enough sand to create a border 152 mm deep around a square surface, as shown below. How many cubic meters of sand are needed? - 152mm = 0.152m - 14m² = 196m² - 9.25 m² = 85.5625m² - 196 - 85.5625 = 110.4375 m² - 110.4375 x 0.152 = 16.785 m³ - 16.79 m³ ## WMath 11 Unit 2 - Math 20-2 Unit 1 **2.2 METRIC CONVERSIONS** 1. Fill in the blacks with 10, 100 or 1000 for the conversions for metric units. - km x 1000 = m - m x 100 = cm - cm x 10 = mm - km ÷ 1000 = m - m ÷ 100 = cm - cm ÷ 10 = mm - kg x 1000 = g - g x 100 = cg - cg x 10 = mg - kg ÷ 1000 = g - g ÷ 100 = cg - cg ÷ 10 = mg 2. 256 m = 25,600 cm 3. 97.25 cm = 972.5 mm 4. 952 g = 952,000 mg 5. 0.574 m = 57.4 cm 6. 1.5 l = 1500 ml 7. 785.3 km = 785,300 m 8. 84.363 km = 8,436,300 cm 9. 872 km = 872,000 m 10. 95 824 cm = 958,240 mm 11. 8.26 l = 8,260 ml 12. 36 mm = 3.6 cm 13. 857 cm = 8,570 mm 14. 8.52 mg = 0.00852 g 15. 975 mm = 97.5 cm 16. 9 824 cm = 98.24 m 17. 74.21 cm = 0.0007421 km 18. 0.254 g = 0.000254 kg 19. 96 mm = 0.096 m 20. 12.5 cm = 0.125 m 21. 0.85 ml = 0.00085 l 22. 286 g = 286,000 mg 23. 87.2 mm = 8.72 cm 24. 1 mm = 0.1 cm 25. 973.5 cm = 0.009735 km 26. 534 cm = 5.34 m 27. 984 g = 0.984 kg 28. 8.64 m = 8,640 mm 29. 64.3 ml = 0.0643 l 30. 8.47 km = 8,470 m 31. 74 201 mm = 0.074201 km 32. 24 mg = 0.000024 kg 33. 7.4 kl = 7400 l 34. 874 m = 87,400 cm 35. 1 cm = 0.00001 km 36. 8.412 mm = 0.008412 m 37. 68.2 mg = 0.0682 g 38. 8.5743 cm = 0.000085743 km 39. 95 870 m = 95,870,000 mm 40. 5471 ml = 547,000 ml 41. 1 km = 1,000,000 mm ## WMath 11 Unit 2 - Math 20-2 Unit 1 **2.3 OTHER CONVERSIONS** Use dimension analysis to complete the following conversions. Give answer to 2 decimal places 1. 18 meters = 59.06 feet - 18 m x 1 ft/0.3048 m = 59.06 ft 2. 20.5 mph = 32.99 kmph - 20.5 mph x 1.609 kmph/1 mph = 32.99 kmph 3. 4 centimeters = 1.57 inches - 4 cm x 1 in/2.54 cm = 1.57 in 4. 16.5 centimeters = 6.5 inches - 16.5 cm x 1 in/2.54 cm = 6.5 in 5. 5.5 centimeters = 2.17 inches - 5.5 cm x 1 in/2.54 cm = 2.17 in 6. 8.5 miles = 13.68 kilometers - 8.5 miles x 1.609 km/ 1 mile = 13.68 km 7. 8 yards = 7.32 meters - 8 yds x 0.9144 m/ 1 yd = 7.32 m 8. 2.5 yards = 2.29 meters - 2.5 yds x 0.9144 m / 1 yd = 2.29 m 9. 7.5 mph = 12.07 kmph - 7.5 mph x 1.609 kmph/1 mph = 12.07 kmph 10. 20 feet = 6.1 meters - 20 ft x 0.3048 m/ 1ft = 6.1 m ## WMath 11 Unit 2 - Math 20-2 Unit 1 **2.4 RATES** 1. Reduce each ratio to its lowest terms. Show all work - Example: - 12:8 = 12 ÷ 4 = 8 ÷ 4 - 3:2 - a) 4:20 = 4 ÷ 4 = 1 - 20 ÷ 4 = 5 - 1:5 - b) 30:36 = 30 ÷ 6 = 5 - 36 ÷ 6 = 6 - 5:6 - c) 96:144 = 96 ÷ 48 = 2 - 144 ÷ 48 = 3 - 2:3 - d) 16:100 = 16 ÷ 4 = 4 - 100 ÷ 4 = 25 - 4:25 - e) 225:550 = 225 ÷ 25 = 9 - 550 ÷ 25 = 22 - 9:22 - f) 10:49 = 10 ÷ 7 = 30 - 49 ÷ 7 = 7 - 30:7 - g) 275:125 = 275 ÷ 25 = 11 - 125 ÷ 25 = 5 - 11:5 - h) 125:50 = 125 ÷ 25 = 5 - 50 ÷ 25 = 2 - 5:2 2. Write each ratio as a fraction in lowest terms. Show all work - Example: - 2:4 = 2 ÷ 2 = 1 - 4 ÷ 2 = 2 - 1/2 - a) 6:20 = 6 ÷ 2 = 3 - 20 ÷ 2 = 10 - 3/10 - b) 5:45 = 5 ÷ 5 = 1 - 45 ÷ 5 = 9 - 1/9 - c) 10:550 = 10 ÷ 5 = 2 - 550 ÷ 5 = 110 - 2/110 - d) 8:124 = 8 ÷ 4 = 2 - 124 ÷ 4 = 31 - 2/31 - e) 9:42 = 9 ÷ 3 = 3 - 42 ÷ 3 = 14 - 3/14 - f) 12:480 = 12 ÷ 12 = 1 - 480 ÷ 12 = 40 - 1/40 - g) 12:40 = 12 ÷ 4 = 3 - 40 ÷ 4 = 10 - 3/10 - h) 24:36 = 24 ÷ 12 = 2 - 36 ÷ 12 = 3 - 2/3 3. Express each phrase as a rate and unit rate. Round your answer to the nearest hundredth. - Example: $170 for 4 calculators - Rate: $170/4 calculators - Unit rate: $42.50 per calculator - a) 20 cm of snow in 6 hours - Rate: 20 cm/6 hours - Unit rate: 3.33 cm/hr - b) $17 will buy 8 chocolate bars - Rate: $17 / 8 chocolate bars - Unit rate: $2.13 per chocolate bar - c) For $40.00 you can buy 6 movie tickets - Rate: $40.00 / 6 movie tickets - Unit rate: $6.67 per ticket - d) $16 for 6 books - Rate: $16 / 6 books - Unit rate: $2.67 per book - e) 320 km on 26 l of gas - Rate: 320 km/26 l of gas - Unit rate: 12.31 km/l 4. Compare each of the items on sale below. Calculate the unit rate for each set of items. Then use the unit rate to determine which item gives you the best value. Circle the item/unit rate with the best value. - a) T-shirts - Store A: $48 / 3 shirts - Unit rate: $16/shirt - Store B: $96 / 16 shirts - Unit rate: $6/shirt - Store C: $56 / 14 shirts - Unit rate: $4/shirt - b) Detergent - Tide: $12.16 / 64 loads - Unit rate: $0.19/load - Gain: $19 / 100 loads - Unit rate: $0.19/load - Purex: $12.24 / 72 loads - Unit rate: $0.17/load ## WMath 11 Unit 2 - Math 20-2 Unit 1 **2.5 APPLICATIONS** 1. Raina is redecorating her bedroom. She wants to order furniture and decorations from a French company. The company measures items in metric units, but Raina wants to know the measurements in imperial units. She plans on placing her new bed and dresser as shown in this blueprint. - a) How long is Raina's room in centimeters? - 9 ft x 12 inches/1 ft = 108 inches - 108 inches x 2.54 cm/1 inch = 274.32 cm - Raina's room is 274.32 cm - b) When the door is closed, how many centimeters will be left between the foot of Raina's bed and her bedroom door? - 274.32 cm - 190 cm = 84.32 cm - There will be 84.32 cm of space between the foot of Raina's bed and the bedroom door when it's closed. - c) If Raina's bedroom door is 24 inches wide, will she have space to open her door completely? Explain. - 24 inches x 2.54 cm/1 inch = 60.96 cm - 84.32 cm > 60.96 cm. - Yes, Raina will have enough space to open her door completely because the remaining space (84.32cm) is greater than the door Width (60.96cm). - d) Raina has a square mirror that she wants to place on her new dresser. The mirror is 40 inches wide. Will the mirror fit on top of this dresser? Explain. - 40 inches x 2.54 cm/1 inch = 101.6cm - 101.6cm > 92.5cm, so the mirror will not fit on the dresser. - e) Raina orders curtains from the same company. The shortest curtains that the company sells are 62 centimeters long. Will those curtains be long enough to cover the entire length of her bedroom window? Explain. - 36 inches x 2.54 cm/1 inch = 91.44 cm - 91.44 cm > 62 cm, so the curtains will not be long enough. - f) Each item Raina orders will ship separately. Find the approximate weight of each item in pounds. Round each answer to the nearest tenth. - Item | Weight (kg) | Approximate Weight (lb.) - -------- | ---------- | -------- - Curtains | 0.82 | 0.82 kg x 2.205 lb/1 kg = 1.8 lb - Bed | 24.2 | 24.2 kg x 2.205 lb/1 kg = 53.4 lb - Dresser | 26.3 | 26.3 kg x 2.205 lb/1 kg = 58.0 lb ## WMath 11 Unit 2 - Math 20-2 Unit 1 2. The length of a swimming pool is 30m. Miss Mitchell swims 0.21 km every morning. How many lengths is this? - 0.21 km x 1000m/1 km = 210m - 210m ÷ 30m = 7m 3. At the weekend I walked 2.75 km. My Dad walked 200m further than me. How far did he walk? - 2.75 km x 1000 m/ 1 km = 2750 m - 2750 m + 200 m = 2950 m 4. The Harrison family sets off on a 52.4 km journey to visit their relatives. They have driven 23 000m so far. How much further do they have to drive? - 52.4 km x 1000 m/ 1 km = 52,400 m - 52,400 m - 23,000 m = 29,400 m - The Harrison Family has 29,400 m further to drive.