Chapter 2 Measuring Length 2 1 Imperial units

Chapter 2 Measuring Length

2. 1 Imperial units of measure � Inch – A unit of length used in the imperial system. The symbol used to show inches is ie. 1” would be one inch (12” = 1 ft) Foot – The basic unit of length in the imperial system. The symbol used is ‘ ie. 4’ would be four feet (1’ = 12”) Yard – A unit of measure consisting of 3 ft (1 yd = 3 ft) , ,

Adding imperial units � When them. the units are the same we will just add ie. 4” + 11” = 15” Since imperial units can come in fractions we need to be able to deal with fractions. ie. 4 1/8” + 5 1/16” = ? ? ? (lets review)

Steps to adding fractions 1. Change both numbers into improper fractions. 4 1/8” + 5 1/16” = becomes… 33/8” + 81/16” = Now we need to get a common denominator

Common Denominator Multiply to get the bottom of the fractions to be the same. 33/8” + 81/16” = Both fractions can have 16 as their denominator. So, multiply the top and bottom of the first fraction by 2. 66/16” + 81/16” =

Add the numerators � Add the top of the fractions and write them over the common denominator. 66/16” + 81/16” = 147/16 Now convert the improper fraction back to a mixed number. 147/16 = 9 3/16”

Example 1 � Two kitchen cupboards are being build. The first is 13 ¾”. The second cupboard measures 17 ½”. What is the width of both cupboards when they are installed?

Example 2 An exhaust system needs to be repaired in two separate places. The first piece of pipe needs to be 17 5/16”. The second piece of pipe will need to be 9 ¼”. What is the total length of pipe?

You Try A phone charger is 34 ½” long. If the outlet adaptor is 2 1/8” long, what is the farthest it can reach?

Practice � Worksheet on adding fractions with unlike denominators.

Converting between imperial measurements � Remember : 1’ = 12” 3’ = 1 yd Express using feet and inches 3’ 4” + 9” = 4’ 10” + 2’ 6 = 23 yds + 23” =

Applied problem � Henry requires 15 feet of cable in order to install digital television in a house. If he has a spool with 300 yards of cable in his van, how many installations can he do with this spool of cable?

Perimeter measurements � Perimeter (P) : Is the measure of distance around the outside of a closed figure/shape.

Perimeter shapes can vary

Calculating perimeter � Add all the side lengths together to find the perimeter. � If there any fractions in the measurements then follow the rules for adding fractions. � Often if the sides have the same length they will only show it once. You still have to add it twice!

Perimeter of a badminton court P = 20’ + 44’ P = 128’ *Always make sure you add all of the outside lengths.

Perimeter with repeat indicators � What is the perimeter of this shape? The matching marks indicate the lengths are the same.

Textbook practice Page 62 #4, 5, 6, 7, 10 Page 66 #6 Page 68 # 3, 5

2. 2 SI Length Measurement � Also known as the metric system. � The most common system of measurement in the world today. � Was developed to simplify measurements

Who likes metric?

Units of the metric system

Common units of the metric system (see your formula sheet)

How to use metric scales If you want to change to a different unit it is always based on a change of a factor of 10. Lets say you want to change 2. 5 m to any other unit of metric measure. 0. 0025 km→ 0. 025 hm→ 0. 25 dam→ 2. 5 m→ 25 dm→ 250 cm→ 2500 mm Each time you move left, divide by 10. Each time you move right, multiply by 10.

How to remember metric ketchup has destroyed my delicious chocolate milk km hm dam m dm cm mm **This works for the common units You can also look on your formula sheet

Lets try it! � Convert each measure to the requested unit. 1 m = _____cm 4. 2 km = _____m 44 mm = _____ m 10 cm = _____ km (silly but true)

A universal system � This same system applies to length, mass, and volume. � For length the meter (m) is the base unit. � For mass the gram (g) is the base unit. � For volume the liter (L) is the base unit.

Practice 1. 2. Converting feet and inches worksheet. Converting between metric units.

2. 3 Metric & Imperial Conversions 1. 2. 3. 4. 5. You need the conversion factor for the two units you are working with. Set up a proportion using the fact. Make sure you keep the units matched on top and bottom. Solve for the unknown side of the fraction. Make sure to write the new units of length with the answer.

Example 1 Convert 5 in to centimeters (1 in = 2. 54 cm)

Example 2 A marathon race is run over a distance of 26 miles. How many kilometers is this? (1 mi = 1. 609 km)

Example 3 If a bridge is 8’ 6” high, can a 2. 5 m tall truck fit under the bridge? (1 m = 3. 281 ft) (12 in = 1 ft)

Example 4 � Chris is 162 cm tall. Convert her height to feet and inches. Round the answer to the nearest inch. (1 cm = 0. 3937 in)

Conversions 1 mm = 0. 03937 in 1 in = 2. 54 cm 1 cm = 0. 3937 in 1 ft = 30. 48 cm 1 m = 39. 37 in 1 yd = 91. 44 cm 1 m = 3. 281 ft 1 yd = 0. 9144 m 1 km = 0. 6214 mi 1 mi = 1. 609 km

2. 4 Working with length We have worked with length when… - calculating perimeter - converting imperial measure - metric measurements The length measurements we have worked with will work for any multiple sided shape or perimeter. What if we are dealing with a circle? ? ?

How do we deal with a circle? � The diameter and radius are easy to measure. It can be very difficult to measure the circumference!

Terms to know � Radius: The distance from the center of the circle to the outside of the circle. � Diameter: The distance from one side of the circle to the opposite. (passing through the center) � Circumference: The distance around the outside of the circle.

There is a formula for that… � This problem was solved thousands of years ago with a simple formula. 1. C = 2 π r or 2. C = π d Both solve for circumference. If you know the radius you can use formula 1. If you know the diameter you can use formula 2.

Finding Circumference � When diameter is given you can use C = πd. Your calculator should have the π button on it.

Finding Circumference � When the radius is given you can use C = 2πr

Radius & diameter are related � If you do not have the right parameter for the formula you can change it by multiplying by 2 or dividing by 2. � d/2 � 2 r =r =d

Circumference practice � 1. Finding circumference from radius. � 2. Finding circumference from diameter. � 3. Extra perimeter worksheet. � End of Chapter 2.