1. Factor-Label Technique (aka Dimensional Analysis)
This technique involves the use of conversion factors and writing all measurements with both numerical values and the unit of measurement
A conversion factor is where you have the same amount (entity) represented by two different units of measurement with their corresponding numerical values

2. Conversion Factors Here are some examples 1 foot = __ inches
1 meter = ____ millimeters
1 inch = 2.54 centimeters
1 gallon = __ quarts
1 acre = 4840 square yards
1 day = ___ hours

3. Missing answers to previous slide
1 foot = 12 inches
1 meter = 1000 millimeters
1 gallon = 4 quarts
1 day = 24 hours

4. Conversion Factors….Part 2
One member of a dinner party orders a 16 ounce steak and another orders a one pound steak- Compare the two steaks
They are the same since 16 oz dry wt. = 1 pound

5. Conversion Factors….Part 3
In grade school we learned that 1 gallon contained 4 quarts or stating that relationship as an equality:
1 gallon = 4 quarts
Since 1 gallon and 4 quarts represent the same amount, we have a Conversion Factor

6. Conversion Factors….Part 4 More About Gallons and Quarts
Start with 1 gallon = 4 quarts
Now divide each side by 1 gallon
we get this equation
1 gallon = 4 quarts
1 gallon gallon
Since 1 gallon divided by 1 gallon equals 1
Our equality becomes: 1 = 4 quarts
1 gallon

7. Conversion Factors….Part 5 Still more about Gallons & Qts.
Again start with 1 gallon = 4 quarts
But this time we’ll divide each side of the equality by 4quarts
The resulting equation is
1 gallon = 4 quarts
4 quarts quarts
Which becomes

8. Conversion Factors….Part 5 Continued……………
The right side of our equation becomes one because 4 quarts divided by 4 quarts is 1
1 gallon = quarts
Rearranging this becomes 1 = 1 gallon
4 quarts

9. Conversion Factors….Part 5 Continued……………
A mid-presentation summary
We know that 1 gallon = 4 quarts
Using a little mathematical magic
1 gallon = 1 and 4 quarts = 1
4 quarts gallon
Why is this an important concept?

10. Conversion Factors….Part 6 How Do They Work
Now a little math review…………….
What is 5 x 1?
What is 5 x ? 2
Both expressions give you the same answer- why?
Because 2/2 equals 1 and therefore the second equation is just like the first and
We did not change the initial value of 5

11. Putting It Together Here’s An Example
How many quarts are in 15 gallons ?
Remember we do NOT want to change the amount represented by 15 gallons, only the units in quarts
So we’ll use the conversion factor between gallons and quarts; that is
1 gallon = 4 quarts

12. Our Example continued…….
We set it up like this:
15 gallons x 4 quarts
1 gallon
This works because we have already shown that 4 quarts divided by 1 gallon is like multiplying 15 gallons by 1

13. The Answer…………… Solving this equation we get 60 quarts
The 60 comes from 15 x 4 in our equation
we get quarts because the gallons cancelled each other out
So, 15 gallons and 60 quarts represent the same quantity-

14. Confused over the units ? Or what happened to the gallons
We had: gallons x 4 quarts
1 gallon
Perhaps it will be more visible, err clear, if we change 15 gallons to a fraction by placing it over 1. Like below:
15 gallons x 4 quarts =
gallon

15. Continuing our Discussion
The gallons cancel one another out just like the “a” in this algebraic equation
5a x = 5 a
There is one “a” in the numerator and an “a” in the denominator
So the gallons cancelled leaving quarts

16. The Steps
Preliminary chores: From the problem determine the following:
What the Known quantity is (number and units) which is called the Given
Identify what the Desired units are
What do we know about the relationship between the two units of measurement- “the conversion factor”

17. Step 1: Write the initial (Given) quantity, both the number and its units
Step 2: Write the times sign “x” after the Given
Step 3: Draw the fraction line after the times sign
Step 4: Write the unit of the Given under the fraction line forming the denominator of the conversion factor
Step 5: Write the unit of the Desired above the fraction line creating the numerator of the conversion factor

18. Step 6: Write in the appropriate numerical values thereby making a correct conversion factor
Step 7: Cancel units (not the number in front of the units) and perform the necessary mathematical operations
Step 8: If the resulting unit is not the one you need for the final answer, repeat steps 2 through 7 until you’re there
Now it’s your turn solving the problems in the Factor-Label Problem Set