MODULE A - 5

Conversion and Cancel

OBJECTIVES

• At the end of this module, the student will be able to… Given a mathematical problem requiring

conversion between measurements systems and the appropriate conversion factors, derive the correct answer.

Given a mathematical problem requiring conversion within the metric system, derive the correct answer.

Setting up a conversion problem

• What is a unit of measure? Attached to a number Indicates how something is being measured

EXAMPLES:• Pounds or Grams• Inches or Meters• Gallons or Liters

Setting up a conversion problem

• Convert: 100 lbs to ___ kgs

Units of measure

Setting up a conversion problem

• What is a “Given” and an “Unknown”? Given is the starting value or quantity. Unknown is answer.

EXAMPLES:

• Convert: 100 pounds to ___ kilograms

• Convert: 100 milliliters to ___ Liters

Setting up a conversion problem

• Convert: 100 lbs to ____ kgs

GIVEN VALUEUNKNOWN VALUE

Setting up a conversion problem

(Given) (Conversion factor) (Answer)

Problems requiring conversions will be solved easier when a standardized procedure of set-up and solution is used.

Units Unknown in AnswerUnit Given

Unit UnknownUnit Given

1

Setting up a conversion problem

• Set the problem up like you are multiplying two fractions.

• The unit of measure in the given value must cancel out.

• The remaining unit of measure will be in the answer.

The Conversion Problem

Given (given) x Unknown (unit) = Unknown (looking for)

1 Given (unit)

* Convert: 100 lbs to kgs

* Set up the problem:

1. lbs is the Given value or starting value

2. kg is the Unknown or what you are looking for (end)

(Given) (Answer)(Conversion factor)

Conversion Factor

Convert: 100 lbs to kgs:

GIVEN: 100 pounds

UNKNOWN: ? Kg

CONVERSION FACTOR: 2.2 lbs = 1 kg

* Place the conversion factor into the formula so the Given units will cancel out .

Conversion from one system to another

Conversion Factor Samples:

2.2 lbs per kg

0.45 kg per lb. 0.62 miles per kilometer

454 gm per lb. 1.0567 qts. per liter

28.3 gm per ounce 3.785 liters per gallon

473 ml per pint

39.37 inches per meter

2.54 cm per inch

0.3937 inches per cm

* Conversion factors also provided in Lesson #4 handout

Conversion Practice

Convert: 500 kgs into lbs

Conversion factor: 2.2 lbs = 1 kg

Conversion Practice

Given x Unknown = Unknown

1 Given

Convert : 50 cm to inches

Conversion factor: 2.54 cm per inch

50 cm x ____ in = ______ in = __________ in

1 cm

(Given) (Conversion factor) (Answer)

Conversion Practice

Given x Unknown = Unknown

1 Given

Convert : 12 inches to centimeters

Conversion factor: 2.54 cm = inch

_____ in x ____ cm = ______ cm = _________cm

1 in

Conversion Practice

Given x Unknown = Unknown

1 Given

Convert: 20 liters to gallons

Conversion factor: 3.785 liters per gallon

20 L x ______ gallon = ______ gallon = _____ gallon

1 L

Conversion Practice

Convert: 26 gallons to L

Conversion factor: 3.785 liters per gallon

Conversion within the metric system.

• You will need a copy of the metric table to perform these calculations

Conversion within the metric system.

• Use the same formula:

Given x Unknown = Unknown

1 Given

(Given) (Conversion factor) (Answer)

Metric Conversion

Count the number of places you are moving on the metric table to determine the conversion factor.

Each is a multiple of 10.

One place = 10 Two places = 100 Three places = 1000

Metric Conversion

Determine where that conversion factor should be placed in the formula.

Ask yourself “Which is larger, the Given unit of measure or the Unknown unit of measure?”

The larger number gets 1 and the smaller gets the conversion factor.

Metric Conversion – Set up

Given x Unknown = Unknown

1 Given

Convert: 50 mL to Liters

50 mL x ____ L = ______ L = _____

1 ____ mL

(Given) (Conversion factor) (Answer)

Metric Conversion – Determine the Factor

Convert: 50 mL to Liters

Determine conversion factor by counting places:

LL dL cL mLmL = 3 places

1000 100 10

* mL is 1000 times smaller than a Liter because it is to the right of the Liter 3 places

Metric Conversion –Insert the Factor

Convert: 50 mL to Liters

50 mL x __1__ L = _______ L = ______

1 1000 mL

• Place conversion factor into formula with larger unit receiving the “1”

• mL is 1000 times smaller than a 1 Liter

Metric Conversion - Solve

Given x Unknown = Unknown

1 Given

Convert: 30 L to mL

____ L x _____mL = ______ mL = ____

1 ____ L

Liter is larger so it gets the “___” and mL is ___ times smaller.

Practice - Metric Conversion

• Convert from or to the basic unit:

25 Liters to mL = ______________

50 mL to Liters = _______________

45 Liters to mL = _______________

6 ML to Liters = ________________(remember M = Mega)

Practice - Metric Conversion

• Convert across or to sides of basic unit:

25 L to mL = ______________

45 kg to Mg = _______________

ASSIGNMENTS

• Sibberson Math Book: Chapter 1

• Read Page 1 – 3

• Do First & Second Sample Set - pgs 2 & 3

• Practice problems – page 7, #1 – 15

• Continue work on objectives.