Factor Labeling

Who turned off the lights?

who

Thanks, that sure is bright!

Let’s review the

method

Using the

we’ll determine the number of kilometers in 1 mile

To do this we need toknow some basic

conversions.

1 mile = 5280 feet1 foot = 12 inches

1 inch = 2.54 centimeters

1 meter = 100 centimeters

1 kilometer = 1000 meters

You should learn these common conversions.





To start the conversion from miles to kilometers we draw a set of brackets.





Then draw a horizontal linethat divides the brackets,

top to bottom.





Again, we are converting 1 mile into kilometers so we’ll place 1 mile

above the line.

1 mi.





There’s no denominator so we’ll leave the bottom

blank.

1 mi.Leave this

blank

Leave this

blank





1 mi.

We need to convert miles into feet,feet into inches, inches into centimeters, centimeters into meters and finally meters into kilometers.





Let’s get started and convert the miles into feet!

1 mi.





Draw another set of brackets with a horizontal line next

to the first set.

1 mi.





We’re going to match units in the numerator with units in the denominator.

Place miles in the bottom of the second set of brackets. This matches the miles

already on the top in the first set of brackets.

1 mi.mi.





We will change miles into feet so place feet directly above miles

1 mi.mi.ft.





There’s 5280 feet in 1 mile.

To fill in the conversion, place5280 next to feet and

1 next to miles.

1 mi. 52801 mi.

ft.





1 mile = 5280 feet

As you can see, the miles on the top of the first set of brackets matches

with the miles in the bottom of the second set of brackets.

1 mi.mi.ft.5280

1

mi.

mi.





1 mi.mi.ft.5280

1

mi.

mi.

reduces to one

so we have changed to feet.

mi.mi.mi.





1 mi.mi.ft.5280

1

mi.

mi.

The same process will be used to change feet into inches!

Watch closely as it’s done.





1 mi.mi.ft.5280

1

mi.

mi.

Draw a set of brackets and then

the horizontal line.





1 mi.mi.ft.5280

1

mi.

mi.

Match units top to bottom.

ft.





1 mi.mi.ft.5280

1

mi.

mi.

Place in the conversion units.

(What are we converting to? In this case feet into inches.)

ft.

in.





1 mi.mi.ft.5280

1

mi.

mi.

Fill in the conversion numbers.

ft.

in.12

1





1 foot = 12 inches

1 mi.mi.ft.5280

1

mi.

mi.

Cross out the units that reduce.

ft.

in.12

1





1 mi.mi.ft.5280

1

mi.

mi. ft.

in.12

1

Again reduces to

leaving inches.

ft.ft.

ft.

ft.





1 mi.mi.ft.5280

1

mi.

mi. ft.

in.12

1

ft.

ft.

The next step is to convert inches into centimeters.





1 mi.mi.ft.5280

1

mi.

mi. ft.

in.12

1

ft.

ft.

Follow the steps as I demonstrate!.

in.

cm.

in.

in. 2.541






1 mi.mi.ft.5280

1

mi.

mi. ft.

in.12

1

ft.

ft.

Now convert centimeters into meters.

in.

cm.

in.

in. 2.541





cm.m.1

100 cm.

cm.


1 mi.mi.ft.5280

1

mi.

mi. ft.

in.12

1

ft.

ft.

The final step, converting meters into kilometers.

in.

cm.

in.

in. 2.541





cm.m.1

100 cm.

cm.

m.

km.11000 m.

m.


1 mi.mi.ft.5280

1

mi.

mi. ft.

in.12

1

ft.

ft.

Our units are now in kilometers!

in.

cm.

in.

in. 2.541





cm.m.1

100 cm.

cm.

m.

km.11000 m.

m.

1 mi.mi.ft.5280

1

mi.

mi. ft.

in.12

1

ft.

ft.

To finish up we multiply all of the numbers

on the top.

(1 x 5280 x 12 x 2.54 x 1 x 1)

in.

cm.

in.

in. 2.541





cm.m.1

100 cm.

cm.

m.

km.11000 m.

m.

=160934

1 mi.mi.ft.5280

1

mi.

mi. ft.

in.12

1

ft.

ft.

Multiply all of the numbers on the bottom

and then divide.

(1 x 1 x 1 x 100 x 1000 )

in.

cm.

in.

in. 2.541





cm.m.1

100 cm.

cm.

m.

km.11000 m.

m.

=160934

100000

= 1.61 km.

1 mi.mi.ft.5280

1

mi.

mi. ft.

in.12

1

ft.

ft. in.

cm.

in.

in. 2.541





cm.m.1

100 cm.

cm.

m.

km.11000 m.

m.

=160934

100000

= 1.61 km.

Ready to do a more complicated conversion?





OK,Lets convert

70 kilometers/hour to

meters/second?





We start the conversion the same way as before. Draw a set of

brackets and a horizontal line.





70

Next, fill in the 70 kilometers per hour.





km.hr.

Kilometers on the top,hours on the bottom.

For right now ignore the hours and convert kilometers to meters.





70 km.hr.

To change km to m, draw another set of brackets

with the horizontal line.





70 km.hr.

Fill in your units… km on the bottom to

match the km on the top .





70 km.hr. km.

And then meters on the top.





70 km.hr. km.

m.

There are 1000 meters in1 kilometer.





70 km.hr. km.

m.


1000

1





70 km.hr. km.

m.1000

1

The reduce and drop out. km.

km.

We now have meters per hour

and have to change hours into seconds.





70 km.hr. km.

m.1000

1

Another bracket set and

horizontal line.





70 km.hr. km.

m.1000

1

Place hours on top andminutes on the bottom.





70 km.hr. km.

m.1000

1

hr.

min.

There are 60 minutes in 1 hour!





70 km.hr. km.

m.1000

1

hr.

min.60

1

The hours reduce to oneand drop out.





70 km.hr. km.

m.1000

1

hr.

min.60

1

Now, convert

minutes into seconds!





70 km.hr. km.

m.1000

1

hr.

min.60

1

By now you should have the hang of it so,

watch me do it!





70 km.hr. km.

m.1000

1

hr.

min.60

1 min.1

60 sec.

We now have meters on the top and

seconds on the bottom!





70 km.hr. km.

m.1000

1

hr.

min.60

1 min.1

60 sec.

All that is left is to...





70 km.hr. km.

m.1000

1

hr.

min.60

1 min.1

60 sec.

Multiply the top,





70 km.hr. km.

m.1000

1

hr.

min.60

1 min.1

60 sec.

Multiply the bottom,

And then divide the bottom into the top

70000 m.

sec.360019.4

m.

sec.





70 km.hr. km.

m.1000

1

hr.

min.60

1 min.1

60 sec.

70000 m.

sec.360019.4

m.

sec.

Now let’s do a real

tough one!,





How about changing





2m

cm

sec

2

3

2

3min

We’re going to solve thisexactly the same way as the

other examples and for now we’llIGNORE the exponents.





2 m

min

2

3

First change meters into centimeters.





2 m

min

2

3 m

cm

1

100

Notice the SPACE

I left after the units and between the numbers

and the units!





2 m

min

2

3 m

cm

1

100

SPACE

SPACE

SPACE

SPACE

This SPACE is going to be used for the exponents.





2 m

min

2

3 m

cm

1

100

Since the meters is squared in the first set of brackets, we will square the meters

in the second set.





2 m

min

2

3 m

cm

1

100

2

Now, If we square the meters,

we MUST square everything else!





2 m

min

2

3 m

cm

1

100

2

2

2

2





2 m

min

2

3 m

cm

1

100

2

2

2

2

We’ll do the same thing again

changing

into3

min3

sec

sec

min

60

1





2 m

min

2

3 m

cm

1

100

2

2

2

2

Remember to leave SPACE

for theexponents!

sec

min

60

1





2 m

min

2

3 m

cm

1

100

2

2

2

2

We’re changing from minutes cubed

so everything in the third bracket

is cubed

sec

min

60

13

3

3

3





2 m

min

2

3 m

cm

1

100

2

2

2

2

Lets REDUCE

sec

min

60

13

3

3

3





2 m

min

2

3 m

cm

1

100

2

2

2

2

And we’re left with….

sec

min

60

13

3

3

3m

cm

1

100

2

2

2

2

cm

sec

2

3





2 m

min

2

3 m

cm

1

100

2

2

2

2

To finish up, multiply the top and divide by the bottom!

sec

min

60

13

3

3

3m

cm

1

100

2

2

2

2





2 m

min

2

3 m

cm

1

100

2

2

2

2

2 x 1002

603

sec

min

60

13

3

3

3m

cm

1

100

2

2

2

2.09 cm

sec

2

3





2 m

min

2

3 m

cm

1

100

2

2

2

2

Now, wasn’t that easy!

sec

min

60

13

3

3

3m

cm

1

100

2

2

2

2.09 cm

sec

2

3

Hey, Who turned out the lights?

Factor Labeling

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