The US Customary System of Measurement AND CONVERSIONS
description
Transcript of The US Customary System of Measurement AND CONVERSIONS
![Page 1: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/1.jpg)
The US Customary System of Measurement AND
CONVERSIONS
MSJC ~ San Jacinto CampusMath Center Workshop Series
Janice Levasseur
![Page 2: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/2.jpg)
Measurements
• A measurement includes a number and a unit.
![Page 3: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/3.jpg)
Length• The U.S. Customary System units of length are
– Inch (in)– Foot (ft)– Yard (yd)– Mile (mi)
• The following measurements are equivalent12 in = 1 ft3 ft = 1 yd5280 ft = 1 mile
![Page 4: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/4.jpg)
Weight
• Weight is a measure of how strongly gravity is pulling on an object (decreases as elevation increases)
• The U.S. Customary System units of weight are– Ounce (oz)– Pound (lb)– ton
• The following measurements are equivalent:16 oz = 1 lb2000 lb = 1 ton
![Page 5: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/5.jpg)
Capacity
• Liquid substances are measured in units of capacity.• The U.S. Customary System units of capacity are
– Fluid ounces (fl oz)– Cups (C) – Pints (pt)– Quarts (qt)– Gallons (gal)
• The following measurements are equivalent: 8 fl oz = 1 C 2 C = 1 pt 2 pt = 1 qt 4 qt = 1 gal
![Page 6: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/6.jpg)
Area• Area is a measure of the amount of surface in a region.• The U.S. Customary System units of area are
– Square inches (sq in)– Square feet (sq ft)– Square yard (sq yd)– Square mile (sq mi)– Acre
• The following measurements are equivalent: 144 sq in = 1 sq ft 9 sq ft = 1 sq yd 43,560 sq ft = 1 acre 640 acres = 1 sq mi
![Page 7: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/7.jpg)
Dimensional Analysis
• Dimensional Analysis (also called Factor-Label Method or the Unit Factor Method) is a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value (Multiplication Property of 1 – the Magic One.)
• Use the units to dictate the form of the Magic One
![Page 8: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/8.jpg)
Equivalences• Units of Weight
– 16 oz = 1 lb– 2000 lb = 1 ton
• Units of Capacity– 8 fl oz = 1 C– 2 C = 1 pt– 2 pt = 1 qt– 4 qt = 1 gal
• Units of Length– 12 in = 1 ft– 3 ft = 1 yd– 5280 ft = 1 mi
• Units of Area– 144 sq in = 1 sq ft– 9 sq ft = 1 sq yd– 640 acres = 1 sq mi
![Page 9: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/9.jpg)
Ex: Convert 14 ft to yds (leave your answer in fraction form)• Write the original measurement as a unit
fraction• Multiply the unit fraction by a magic one –
the form of which is dictated by the units– the numerator unit is the unit you want– the denominator unit is the unit you want to
eliminate
• Write your answer in the specified form (fraction form)
![Page 10: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/10.jpg)
114 ft
ftyd31 yds
314
yds324
Ex: Convert 14 ft to yds
![Page 11: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/11.jpg)
Ex: Convert 7920 ft to mi (leave your answer in fraction form)• Write the original measurement as a unit
fraction• Multiply the unit fraction by a magic one –
the form of which is dictated by the units– the numerator unit is the unit you want– the denominator unit is the unit you want to
eliminate
• Write your answer in the specified form (fraction form)
![Page 12: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/12.jpg)
17920 ft
ftmi
52801 mi
52807920
mi528026401
mi211
Ex: Convert 7920 ft to mi
![Page 13: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/13.jpg)
Ex: Convert 3 lbs to oz
• Write the original measurement as a unit fraction
• Multiply the unit fraction by a magic one – the form of which is dictated by the units– the numerator unit is the unit you want– the denominator unit is the unit you want to
eliminate
• Write your answer in the specified form
![Page 14: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/14.jpg)
lb1
oz16
1
lb3 = 48 oz
Ex: Convert 3 lbs to oz
![Page 15: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/15.jpg)
Ex: Convert 2 ¼ gal to qt
• Write the original measurement as a unit fraction
• Multiply the unit fraction by a magic one – the form of which is dictated by the units– the numerator unit is the unit you want– the denominator unit is the unit you want to
eliminate
• Write your answer in the specified form
![Page 16: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/16.jpg)
1412 gal
galqt
14 qt44
12
qt
14
49
qt9
Ex: Convert 2 ¼ gal to qt
![Page 17: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/17.jpg)
Ex: Convert 17 C to qt (write your answer in fraction form)
• Write the original measurement as a unit fraction
• Multiply the unit fraction by a magic one – the form of which is dictated by the units– the numerator unit is the unit you want– the denominator unit is the unit you want to
eliminate
• Write your answer in the specified form (fraction form)
![Page 18: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/18.jpg)
117 C
Cpt21
ptqt21
qt417
qt414
Ex: Convert 17 C to qt
![Page 19: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/19.jpg)
Ex: At a nursing staff meeting, 60 nurses are expected to attend.
Each nurse is expected to drink 2 C of coffee. The industrial size coffee
maker brews coffee in gallons. How many gallons of coffee should be prepared for the staff meeting?
• What should we do?
• How many cups of coffee is needed?
![Page 20: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/20.jpg)
We can use several equivalences stepping up to gallons
Cups Pints Quarts Gallons
Is there a direct equivalence between C and gallons?
1120 C
Cpt21
ptqt21
qt4
gal1 gal
16120
gal162
7
gal817
![Page 21: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/21.jpg)
More Practice
Convert 25 yds to feet• Write the original measurement as a unit
fraction• Multiply the unit fraction by a magic one –
the form of which is dictated by the units– the numerator unit is the unit you want– the denominator unit is the unit you want to
eliminate
• Write your answer in the specified form
![Page 22: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/22.jpg)
175
13
125 ft
ydftyds
= 75 ft
Ex: Convert 25 yds to feet
![Page 23: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/23.jpg)
Even More Practice
Ex: Convert 60 in into ft• Write the original measurement as a unit
fraction• Multiply the unit fraction by a magic one –
the form of which is dictated by the units– the numerator unit is the unit you want– the denominator unit is the unit you want to
eliminate
• Write your answer in the specified form
![Page 24: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/24.jpg)
1260
121
160 ft
inftin
= 5 ft
Ex: Convert 60 in into ft
![Page 25: The US Customary System of Measurement AND CONVERSIONS](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a9b550346895dc81b54/html5/thumbnails/25.jpg)