In this section you will … Describe the features of the Conversion Factor Method Use the Conversion Factor Method to make measurement conversions Describe the benefits of using the conversion factor method.

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Technical Science

Scientific Tools and Methods

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The Conversion Factor Method

● In this section you will …

– Describe the features of the Conversion Factor

Method

– Use the Conversion Factor Method to make

measurement conversions

– Describe the benefits of using the conversion

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Features of the Conversion

Factor Method

● Making conversions in the metric system is simply

a matter of moving the decimal.

● Unfortunately, converting within the English

system and between the English and Metric systems isn’t that easy.

● The Conversion Factor Method works for any type

of measurement conversion.

● In this section, you will learn to make

measurement conversions in the English System and between the English and Metric Systems.

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Features of the Conversion

Factor Method

● The following slides describe the properties

of conversion factors.

● The Conversion Factor Method works by

multiplying a measurement by a conversion

factor.

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2 feet x

Initial Measurement

12 inches 1 foot

Conversion Factor

= 24 inches

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Features of the Conversion

Factor Method

– 12 inches is the same distance as 1 foot

– 1 kilogram is the same mass as 1,000 g

– 2.54 cm is the same distance as 1 inch

● Conversion Factors are fractions with the same

measured quantity on the top and bottom of the fraction.

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12 inches 1 foot

1 kilogram 1,000 g

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Features of the Conversion

Factor Method

● All conversion factors have a value of 1.

● Multiplying a number by 1 does not change the

value of the number.

● Fractions that have the same amount on the top

and bottom are equal to 1.

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12 inches 1 foot

= 1 19 19 5

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Features of the Conversion

Factor Method

● Because the conversion factor equals one, the

initial measurement equals the converted measurement. 2 feet = 24 inches.

● Since conversion factors are equal to one, a

measurement can be multiplied by a conversion factor without changing the amount of the initial measurement.

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2 feet x 12 inches

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Features of the Conversion

Factor Method

● Remember: When you convert a measurement the

amount stays the same only the units change.

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● The length of the board didn’t change only the

units in which it was measured changed.

12 in 24 in 0 in

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Features of the Conversion

Factor Method

● The same holds true for conversion factors. Units

of the same measure cancel out if they are on the top and bottom.

● When fractions are multiplied, numbers that show

up on the top and bottom cancel out.

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2 feet x 12 inches _{1 foot} = 24 inches 3

5 x

2 3

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Features of the Conversion

Factor Method

● When we converted from feet to inches we used

the conversion factor 12 inches = 1 foot.

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● You were probably already familiar with this

conversion factor but there are many others that you won’t know from memory.

● No one can remember every conversion factor so

from time to time you will have to refer to a table of conversion factors.

● Click the button to see the table then print a copy

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Features of the Conversion

Factor Method

● Conversion factors are ___________ that

have the same measured quantity on top and

on the bottom. This is why conversion

factors have a value of _______.

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fractions

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Features of the Conversion

Factor Method

● Which of the fractions below is

not

a

conversion factor? Explain your choice.

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1 yard 3 feet

4 quarts 1 gallon

12 ounces 1 pound

A. B. C.

Α

Choice C is not a conversion factor

because 12 ounces does not equal 1 pound.

Conversion factors must have the same

amount on the top and on the bottom of the

fraction.

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Using the Conversion

Factor Method

● You will see the process step by step and

then practice some problems on your own.

● Remember: the Conversion Factor Method

will work to make any type of measurement

conversion.

● You know what conversion factors are so

you are ready to use the Conversion Factor

Method to make measurement conversions.

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Using the Conversion

Factor Method - Example 1

● 500 yards is equal to how many miles?

Step 1. Read the problem carefully. Write down the initial measurement and the units to which you

want to convert.

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500 yards

Initial Measurement

______ miles

Final Units

– Put the initial measure over 1 to make it look like a fraction.

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Using the Conversion

Factor Method

Step 2. Find a conversion factor on the table that relates the unit of the initial measure to the units needed for the final measure.

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500 yards 1

Initial Measurement

______ miles

Final Units

1760 yards 1 mile

Conversion Factor

English Conversions 12 inches = 1 foot 3 feet = 1 yard 1760 yards = 1 mile 5280 feet = 1 mile

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Using the Conversion

Factor Method

Step 3. Multiply the initial measure by the conversion factor.

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500 yards 1

______ miles 1760 yards 1 mile

Conversion Factor x _________ =

– Put the units you want to eliminate in the opposite position of the initial measure.

1760 yards

– Put the other half of the conversion factor in the other position.

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Using the Conversion

Factor Method

Step 4. Cancel the units.

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500 yards 1

– The same units must show up on the top and bottom to cancel.

1760 yards

– If the units you want to eliminate don’t cancel then your setup is not correct.

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Using the Conversion

Factor Method

Step 5. Perform the calculation. Start with the initial measure. Multiply by any number on top of a

fraction and divide by any number on the bottom

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500 yards 1

500 x 1 ÷ 1760 = 0.284 1760 yards

1 mile 0.284

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Using the Conversion

Factor Method

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● In the next example we will follow the same

five steps to convert from miles to yards.

● There are a few things to which you should

pay close attention

– What conversion factor will we use?

– Does the setup of the conversion factor change?

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Using the Conversion

Factor Method - Example 2

● 2.5 miles is equal to how many yards?

want to convert.

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2.5 miles

Initial Measurement

______ yards

Final Units

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Using the Conversion

Factor Method

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2.5 miles 1 Initial Measurement ______ yards Final Units 1760 yards 1 mile Conversion Factor

– Notice: the same conversion factor is used in this example.

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Using the Conversion

Factor Method

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2.5 miles 1

______ yards 1760 yards 1 mile

1 mile

– Put the rest of the conversion factor in the other position. 1760 yards

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Using the Conversion

Factor Method

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2.5 miles 1

1 miles

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Using the Conversion

Factor Method

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2.5 miles 1

2.5 x 1760 = 4400 1 mile

1760 yards 4400

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Using the Conversion

Factor Method

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● In the first two examples, we found a

conversion factor that went directly from

our initial measure to the desired units.

● Sometimes you will need to use two or more

conversion factors to get the final units.

● The next example will show you how to

make this type of conversion.

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Using the Conversion

Factor Method - Example 3

● 48 inches is equal to how many yards?

want to convert.

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48 inches

Initial Measurement

______ yards

Final Units

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Using the Conversion

Factor Method

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48 inches 1

______ yards

– There is no conversion factor that relates inches to yards directly.

Conversion Factors

– An intermediate unit is needed to bridge the gap between inches and yards.

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Using the Conversion

Factor Method

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48 inches 1

______ yards 12 inches 1 foot Conversion

Factors – We can’t go directly from

inches to yards.

1 yard 3 feet

– This means using 2 conversion factors. – So, convert from inches to feet and then

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Using the Conversion

Factor Method

Step 3. Multiply the initial measure by the conversion factors.

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48 inches 1

______ yards 12 inches 1 foot x _________

– Eliminate the initial units, inches, first. The rest of that conversion factor goes in the other position

12 inches

– Stopping here would leave us with the units feet. But we want to convert to yards.

1 foot

– Eliminate the units, feet, next. The rest of the second conversion factor goes in the other position.

1 yard 3 feet

x _________ = 3 feet

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Using the Conversion

Factor Method

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48 inches 1

______ yards 12 inches 1 foot x _________

12 inches 1 foot

1 yard 3 feet

x _________ = 3 feet

1 yard

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Using the Conversion

Factor Method

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48 ÷ 12 ÷ 3 = 1.33

– Although there are 2 conversion factors you don’t need 2 calculations. It doesn’t matter how many conversions are made. All the calculations can be done at once.

48 inches 1

______ yards

12 inches 1 foot x _________

12 inches 1 foot

1 yard 3 feet

x _________ = 3 feet

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Using the Conversion

Factor Method

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● In the next example, we convert a metric

measure using the conversion factor method.

● You probably wouldn’t use this method for a

simple metric conversion.

● We are doing it because you need to know

how to use metric conversion factors when

convert between systems.

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Using the Conversion

Factor Method - Example 4

● 5 kilograms is equal to how many grams?

want to convert.

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5 kg

Initial Measurement

______ grams

Final Units

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Using the Conversion

Factor Method

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5 kg 1

______ grams

– Metric conversion factors aren’t written like the English factors (1ft = 12 in)

Metric Conversions Kilo

Hecto Decka

Base Unit - gram

– We will have to use the table of metric prefixes to generate the conversion

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Using the Conversion

Factor Method

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5 kg 1

______ grams

– Write the initial and final units.

Metric Conversions Kilo

Hecto Decka

Base Unit - gram

– Put the number 1 with the bigger unit. kg

g 1

– The number on the smaller unit will be a multiple of 10. (10, 100, 1,000, etc) Count the places separating the units. This will be the number of zeros you need.

3 places

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Using the Conversion

Factor Method

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5 kg 1

______ grams

1 kg

– Put the rest of the conversion factor in the other position. 1000 grams 1 kg

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Using the Conversion

Factor Method

● 5 Kilograms is equal to how many grams?

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5 kg 1

______ grams

1 kg

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Using the Conversion

Factor Method

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5 kg 1

______ grams

5 x 1000 = 5000 1 kg

1000 grams 5000

– This time we multiplied by 1000 because 1000 ended up on the top of the conversion factor.

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Using the Conversion

Factor Method

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● The final example is a conversion between

the English and Metric systems.

● This will be a two step problem. In other

words it will require two conversion factors.

● One of the conversion factors will be strictly

metric.

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Using the Conversion

Factor Method - Example 5

● 18 inches is equal to how many meters?

want to convert.

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18 inches

Initial Measurement

______ meters

Final Units

– This problem will require two conversion factors. The intermediate unit we will use will be centimeters.

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Using the Conversion

Factor Method

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18 inches 1

______ meters 1 inch 2.54 cm Conversion

Factor #1 – We can’t go directly from

inches to meters.

English / Metric Conversions 1 inch = 2.54 cm 1 foot = 30.5 cm 1 yard = 0.914 meters

Conversion Factors _– _{This means using 2 conversion factors.}

– So, convert from inches to centimeters then convert to meters.

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Using the Conversion

Factor Method

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18 inches 1

______ meters

1 inch 2.54 cm – The second conversion factor

must relate cm to meters.

English / Metric Conversions 1 inch = 2.54 cm 1 foot = 30.5 cm 1 yard = 0.914 meters

– So, we need to generate a strictly metric conversion factor from the table of metric prefixes.

cm

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Using the Conversion

Factor Method

Step 3. Multiply the initial measure by the conversion factors.

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18 inches 1

______ meters 1 inch 2.54 cm x _________

– Eliminate the initial units, inches, first. The rest of that conversion factor goes in the other position

1 inch

– Stopping here would leave us with centimeters. But we want to convert to meters.

2.54 cm

– Eliminate the units, cm, next. The rest of the second conversion factor goes in the other position.

100 cm 1 meter

x _________ = 100 cm

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Using the Conversion

Factor Method

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18 inches 1

______ meters

1 inch 2.54 cm x _________

1 inch 2.54 cm

100 cm 1 meter

x _________ = 100 cm

1 meter

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Using the Conversion

Factor Method

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18 x 2.54 ÷ 100 = 0.4572

– Although there are 2 conversion factors you don’t need 2 calculations. It doesn’t matter how many conversions are made. All the calculations can be done at once.

18 inches 1

______ meters

1 inch 2.54 cm x _________

1 inch 2.54 cm

100 cm 1 meter

x _________ = 100 cm

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Using the Conversion

Factor Method

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● Complete the practice problems using the

conversion factor method.

● Then click to see a solution.

● There can be more than one way to get the

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Using the Conversion

Factor Method - Practice

● 24 ounces is equal to how many pounds?

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24 ounces 1

______ pounds 16 ounces 1 pound

24 ÷ 16 = 1.5 16 ounces

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Using the Conversion

Factor Method - Practice

● 65 fluid ounces is equal to how many quarts?

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65 ÷ 16 ÷ 2 = 2.03 65 ounces

1

______ quarts

16 ounces 1 pint x _________

16 ounces 1 pint

2 pints 1 quart

x _________ = 2 pints

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Using the Conversion

Factor Method - Practice

● 2.5 liters is equal to how many fluid ounces?

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2.5 x 1000 ÷ 29.6 = 84.46 2.5 liters

1

______ ounces

1 ounce 29.6 ml x _________

1 liter 1000 ml

1000 ml 1 liter

x _________ = 29.6 ml

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Using the Conversion

Factor Method

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● Use the conversion factor method to complete the

following conversions. Then click for the answers.

● 3.6 miles = meters

● 88 km = miles

● 150 pounds = kilograms

● 10 grams = ounces

● 680 pounds = tons

● 15.3 quarts = gallons

● 12 oz = milliliters

● 120 gallons = liters

● 5796

● 55

● 68

● 0.35

● 0.34

● 3.825

● 355

● 455

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Benefits of the Conversion

Factor Method

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● By now, you should be able to convert

measurements using the conversion factor method.

● You have made many of these conversions before

learning this method. For instance, to convert from feet to inches you probably just multiplied by 12.

● Solving problems in your head may work in

familiar situations but it won’t work for unfamiliar problems.

● Having a method means having a consistent way of

solving a problem.

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Benefits of the Conversion

Factor Method

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● The first benefit is that the conversion factor

method can be used to make any conversion.

● You can covert from...

English to English Metric to Metric

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Benefits of the Conversion

Factor Method

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● Second, the conversion factor method

provides a way to check your work.

● The units you want to eliminate should

cancel. If they don’t, rethink your set-up.

2 feet 1

1 foot 12 inches

● The units in this problem won’t cancel. This

means the conversion factor should be

flipped over.

1 Foot

12 inches

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Benefits of the Conversion

Factor Method

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● A third benefit is that multi-step problems

can be done with one set-up.

● There is no need to calculate an intermediate

answer then use that answer in another

calculation. That often leads to errors.

● You can put as many conversion factors in a

row as you need to solve the problem.

65 ounces 1

______ quarts x _________

16 ounces

1 pint _{x _________}₌ 2 pints

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Benefits of the Conversion

Factor Method

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● Finally conversion factors tell you when to

multiply and when to divide.

● In converting inches to meters, you may know

(2.54 cm = 1 in. & 100 cm = 1 m) but do you multiply or divide by those numbers?

● Starting with the initial measure, multiply by any

number on top and divide by any number on the bottom of the conversion factors.

18 x 2.54 ÷ 100 = 0.4572 18 inches

1

______ meters x _________

1 inch

2.54 cm _{x _________}₌ 100 cm

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Benefits of the Conversion

Factor Method

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● What are three benefits of using the conversion

factor method?

Α It provides a consistent way of solving these

problems.

Α It works for all types of conversions.

Α It allows you to check your work by canceling

units.

Α You can do multi-step problems with one set-up. Α It tells you when to multiply and divide.

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