Working with the customary system

Customary Units of Measure

What do we hope to accomplish?

• We will convert between customary measures

• We will try to use a new tool, a conversion factor, in dimensional analysis

We will choose appropriate measures, solve applications, and convert withinthe customary system.*

Choosing Appropriate Measuresa. Weight of a truck

b. Length of a hallway rug

c. Length of a swimming pool

d. Weight of a baby

e. Length of a pencil

f. Capacity of an eyedropper

g. Weight of a paperclip

h. Volume of a baby bottle

i. Distance to Australia

j. Length of a sports field

tons

feet or yards

feet or yards

pounds

inches

fluid ounces

ounces

fluid ounces

miles

yards

Measurement ConversionEveryone has their own way of converting within a

measurement system.

I have processes that are comfortable to me, personally….You do, too.

Using something called a “conversion factor” is a technique that is useful when a comfortable methoddoesn’t occur to you……..

Using a conversion factor to convert measures within the same system, or between measurement systems, iscalled dimensional analysis.

We will practice this new method. You WILL hear it againin future math classes…..don’t be afraid to try something new.

What is a conversion factor????

A conversion factor is a ratio of two different units that are equal to each other.If I were converting gallons to quarts, I would use the conversion factor of

gal

qtor

qt

gal

1

4

4

1

Look back at the customary measures chart. Conversion factors comefrom “things” that are equal to each other!

ft

inor

in

ft

1

12

.12

1yd

ftor

ft

yd

1

3

3

1pt

cupsor

cups

pt

1

2

2

1

With conversions factors, the order in which you write the two, equal measuresdepends on how you want to set up your conversion problem!

What is a conversion factor????

10 qt. = ? gallons

Let’s use the text example and convert 10 qt to gallons…..yes, I know it’s 2 ½ gallons .

1

10qt

The conversion factor you write is equal to 1.You choose the order in which you writethe units based on what will cancel withthe unit you are converting. This is sometimescalled a “unit multiplier.”

gal2

12

2

5

Let’s look at this process in detail…..First you write the measures you have…….

Next you create a ratio (unit multiplier) thatcontains the measure you have and thenew unit you are wanting…..Solve…..

qt

gal

4

15

2

oz

lb

16

1

Practice the Process

We are to convert 14 oz. into lbs.

We want to write a conversion factor = 1 that shows the relationship between ounces and pounds.

1

14:oz

GivenThe ounces cancelout. We are left onlywith pounds and a fraction to simplify.

lblbGiven8

7

16

14:

?

.14:in

Given.12

1

in

ft ftft

6

11

12

14

We are to convert 14 inches to feet.

Our conversion factor for ft/inches is…….

Cancelling our like units leaves us with a fraction to simplify.

We are converting pints to quarts. We have 14 pt.

Our conversion factor for pt/quarts???

1

.14:pt

Givenpt

qt

2

1

Cancelling our like units and simplifying what is left gives us our result.

qtqt 72

14

1 gallon

4 quarts =8 pints =

16 cups =

Customary measures of capacity often give people problems. If you do not use these regularly, they are often difficult to remember.The basic ones to know are:

ApplicationAt Store A, cashews cost $15.99 for a 4 ¼ lb. bag.

Store B charges the same price for a 76-oz. bag. What is the better buy? At which store do you get more for your money?

The price is the same, so let’s see how many ounces are in the 4 ¼ lb bag. We already have the ounces for store B.

lbGiven4

14:

Conversion factor for pounds/ounces?lb

oz

1

16

1

16

4

17 oz

4 Store A give you 68 ounces.

Store B is the better buy.

4

17lb

Complete each equation:

3 ½ lb = _____ oz

3 ½ yd = _______ft.

3 ½ pt. = _______c

lb2

7

2

13

lb

ozlb

1

16

2

7

8

56

yd2

7

2

13

yd

ftyd1

3

2

7 ft

2

21

10 ½

pt2

7

2

13 pt

cpt1

2

2

77

Conversion factors are most helpful when converting between systems. 1in = 2.54 cm.

If I wanted to know how many cm were in 2 feet, I could use conversion factors….

in

cm

ft

inft

1

54.2

1

12

1

.2 cm)54.2(24

This could then be converted into meters, mm, or any other measure……

While you might not see a need for this skill now, the abilityto set up a conversion factor will be important in future math classes. Try it whenever possible.

Small Group Practice p. 255 (24-36)

ozlb ___4

3 ptqt ___

2

13 inyd ___

3

11

lbton ___5

1 cupspt ___7 ftmiles ___

2

15

lb

ozlb

1

16

4

34

12

qt

ptqt

1

2

2

7

7

yd

inyd

1

36

3

412

48

ton

lbton

1

2000

5

1

400

pt

cpt

1

2

1

7

14

mile

ftmiles

1

5280

2

112640

2640264029040

29,040

Julia clears 9 ½ ft in the pole vault.Maya clears 112 in. Which one clears the greatest height?

inft 112______2

19

ft

inft1

12

2

19 6114 inches

>

Julia jumped higher.

Estimation: Matching…….

31.height of a 7-year old

32.weight of a bag of apples

33.width of your palm

34.amount of water in a vase

35.weight of a peach

36.amount of juice in a child’s cup

4 ft. C

4 lb. B

4 in. F

4 c D

4 oz E

4 fl oz A

A.4 fl. Oz.B.4 lbC.4 ft.D.4 cupsE.4 oz.F.4 inches

What did we accomplish?

• We converted between customary measures

• We tried to use a new tool, a conversion factor, in dimensional analysis

Example of unit conversion…..To find how many centimeters in 2 miles……

. . .

If you changed your mind and wanted this distance in meters?????