Free Pre-Algebra
Lesson 29 ! page 1
Lesson 29
Converting4 Between
Units
feet 9 inches -> inches - Google
Search
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How many minutes in a year? How
many feet in sixteen and one-quarter miles? The need to convert
between units arises
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so frequently that you can type your current and desired units into the Google search box and get an instant answer:
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4 feet 9 inches -> inches
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4 feet 9 inches = 57 inches
More
More about calculator.
In this lesson, we take over from Google to do theseI conversions
ourselves. The idea is simple and powerful, and brings
am only 4 feet 9 inches tall and I'm 17. I look like a 7 year ...
Mar 11, 2007 ... I would recomend visiting an Endocrinologist. They can test your blood and
together a lot of topics we’ve already covered.
see if you are making the normal amount of hormones. ... i am 34 yrs ...
www.answerbag.com/q_view/161789 - Cached - Similar
WikiAnswers - How much should you weigh at 4 feet 9 inches
Measurement Systems
How much should you weigh if you are twelve and four feet two inches? Well I'm like, 4 foot 9
I'm 9 years old (no offense, but you're kinda short). ...
There are two main systems of measurement in use and
today.
People living in the United States use the American
wiki.answers.com/.../How_much_should_you_weigh_at_4_feet_9_inches
- Cached -system
Similar of
measurement in everyday life, and the metric system for science. The American system measures length in inches, feet,
WikiAnswers - What is 4 feet 9 inches in centimeters
yards, and miles, temperature in degrees Fahrenheit, weight
in ounces
pounds,
in cups,
Hobbies and
Collectiblesand
question:
What is and
4 feet liquid
9 inchesvolume
in centimeters?
144.78quarts,
cm or - and
another way, 1.4478 metres To convert, simply multiply the ...
gallons. The metric system measures length in meters,inwiki.answers.com/Q/What_is_4_feet_9_inches_in_centimeters
temperature
in degrees Celsius, and weight- in
grams.
The
metric
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system is used in everyday life everywhere else besidesShow
the more
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It’s helpful
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from wiki.answers.com
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so converting between feet and inches is
www.blurtit.com/q989833.html
a matter of multiplying or dividing by twelve. But since
meters
and
inches
come
from
different systems, there is no simple
Feet Inches to Centimeters Conversion Calculator and Table ...
4 feet 4 inches.
132.08. 4 feet
5 inches.
4 feetHere
6 inches.
4 feet 7 inches.
whole number conversion factor – there are approximately
39.3700787
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conversions within the American system, since it is more
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is 4 ft 9 inches in centimeters? - True Knowledge
Oct 5, 2009 ... What is the equivalent of the length 4 feet and 9 inches in centimetre, the SI
unit of lengths (one hundredth of a metre)?
This method, called dimensional analysis, or the unit-factor
method, is frequently used in science classes. The method uses
www.trueknowledge.com/.../what_is_4_ft_9_inches_in_centimeters - Cached - Similar
an equation relating two units to create a fraction equal to 1, called a unit fraction. The units in the numerator and
4 feet 9 inches in meters - True Knowledge
denominator of the fraction are set up to cancel with units
the... problem
to find the
answer
in the
more
desirable
Oct 5,in
2009
What is the equivalent
of the
length 4 feet
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in metres
(the SI units.
and metric unit of length, defined as the distance light travels ...
www.trueknowledge.com/q/4_feet_9_inches_in_meters - Cached - Similar
For example, to change 4 feet to inches, we would do theShow
multiplication
below.
more results from
www.trueknowledge.com
Here’s the step-by-step explanation.
I12
am 4inches
feet 9 inches and I'm19 years old? - Yahoo! Answers
4 feet • Oct 17, 2009 ... I honestly
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answers.yahoo.com/question/index?qid... - Cached - Similar
How many inches is 4"9? - Apr 19, 2009
If im 4 foot 9 inches can i get a handicap sign? - Jan 2, 2009
How many inches are in 5 feet 9 inches? - Jul 25, 2008
Can you convert 4 foot 9 inches into Meters and Centimeters for me ... - Jun 23, 2008
More results from answers.yahoo.com »
Step 1: Making Unit Fractions
Charts
Measurements
If a unit of measurement is a multiple of another unit,Conversion
we can write
anfor
equation
relating the units. If we want to convert feet to
3 feet 7 inches. 109.22. 3 feet 8 inches. 111.76. 3 feet 9 inches. 114.30. 3 feet 10 inches.
inches, we write an equation relating feet and inches.116.84.
There
are11 one
12119.38.
inches
in0 one
foot,
3 feet
inches.
4 feet
inches
... I write 1 foot = 12 inches .
iceryder.net/measureconvert.html - Cached - Similar
From this equation, I can make a fraction, by dividing both sides of the equation by 1 foot:
1 of 3
1 foot
1 foot
=
12 inches
1 foot
The numerator and denominator on the left hand side of this equation cancel completely, so are equal to 1 =
© 2010 Cheryl Wilcox
.
6/8/10 3:53 PM
12 inches
1 foot
.
Free Pre-Algebra
Lesson 29 ! page 2
If I had divided both sides by 12 inches,
one), but it would still be equal to 1:
1 foot
1 foot
=
1 foot
12 inches
12 inches
1 foot
, I would have a different fraction (the reciprocal of the first
=1
The great thing about the number 1 is that it has the easiest times table: when you multiply anything by 1, it doesn’t change.
So if I multiply anything by either of the fractions above (which are equal to 1), the form may change, but the amount stays
the same. These unit fractions are the key to converting between units.
Example: Write two unit fractions from the equation
1 yard = 3 feet.
1 yard
3 feet
= 1=
3 feet
1 yard
Example: Write two unit fractions from the equation
1 day = 24 hours.
1 day
24 hours
= 1=
24 hours
1 day
Step 2: Setting Up the Cancellation
There are two unit fractions from each equation relating units. The next step is to decide which to use. The goal is to cancel
the original units of the problem, so the original units must go in the denominator of the fraction. The new units, the ones we
are trying to find, go in the numerator.
To Change Feet to Inches:
Cancel feet in the original by putting feet in the denominator:
4 feet 12 inches
•
1
1 foot
Example: Set up the unit fraction to change 18 feet to
yards.
18 feet 1 yard
•
1
3 feet
© 2010 Cheryl Wilcox
To Change Inches to Feet:
Cancel inches in the original by putting inches in the
denominator:
48 inches
1 foot
•
1
12 inches
Example: Set up the unit fraction to change 3 days to
hours.
3 days
1
•
24 hours
1 day
Free Pre-Algebra
Lesson 29 ! page 3
Step 3: Multiply
Once you’ve chosen the unit fraction you can just go ahead and multiply. The answer is there waiting for you.
To Change Feet to Inches:
Cancel feet in the original by putting feet in the denominator:
4 feet 12 inches
•
= 48 inches
1
1 foot
To Change Inches to Feet:
Cancel inches in the original by putting inches in the
denominator:
4
48 inches
1 foot
•
= 4 feet
1
12 inches
Complete Walkthrough
Example: How many yards in 18 feet? (3 feet = 1 yard)
1 Use the equation to make unit
fractions:
2 Set up the unit fraction to cancel the
original units:
1 yard
3 feet
= 1=
3 feet
1 yard
18 feet 1 yard
•
1
3 feet
3 Multiply to find the new units:
6
18 feet 1 yard
•
= 6 yards
1
3 feet
Example: How many hours in 3 days? (24 hours = 1 day)
1 Use the equation to make unit
fractions:
2 Set up the unit fraction to cancel the
original units:
1 day
24 hours
= 1=
24 hours
1 day
3 days
1
•
3 Multiply to find the new units:
3 days
24 hours
1
1 day
•
24 hours
1 day
= 72 hours
Example: How many ounces in 3/4 of a pound? (16 ounces = 1 pound)
1 Use the equation to make unit
fractions:
1 pound
16 ounces
= 1=
16 ounces
1 pound
© 2010 Cheryl Wilcox
2 Set up the unit fraction to cancel
the original units:
3
pounds
16 ounces
4
•
1
1 pound
3 Multiply to find the new units:
3
4
4
• 16 ounces = 12 ounces
It was convenient to just get rid of the
cancelled units here because of the
fraction.
Free Pre-Algebra
Lesson 29 ! page 4
More than One Step
Unit fractions can be chained so that we convert several levels of units at once.
Example: How many minutes in 3 days? (60 minutes = 1 hour; 24 hours = 1 day)
We’re trying to get from days to minutes, but there is an intermediate unit, hours. We have two conversion equations, so
there will be two unit fractions. We go in order of size of unit.
days ! hours ! minutes
We could do this in two separate one-step equations like the ones we just did:
3 Days to Hours
3 days
1
72 Hours to Minutes
•
24 hours
1 day
72 hours 60 minutes
•
= 4320 minutes
1
1 hour
= 72 hours
Or, the two unit fractions can be chained, one after the other:
3 days
1
•
24 hours
1 day
•
60 minutes
1 hour
= 4320 minutes
Example: How many miles is 10,000 inches? (12 inches = 1 foot; 5280 feet = 1 mile).
My plan is to change inches to feet, then feet to miles.
Begin by cancelling inches:
10,000 inches
1 foot
•
1
12 inches
I can see that I’ll need to multiply again to cancel feet and end up with miles. So I just continue the chain:
10,000 inches
1 foot
1 mile
•
•
1
12 inches 5280 feet
Now multiply and cancel:
10,000 inches
1 foot
1 mile
10,000
•
•
=
miles
1
12 inches 5280 feet 63,360
10,000
2•2•2•2 •5•5•5• 5
125
=
=
miles
63,360 2 • 2 • 2 • 2 • 2 • 2 • 2 • 3 • 3 • 5 • 11 792
While this answer is very proper, we’d probably write it as a decimal (coming soon) in real life. At any rate, we’ve found out
that 10,000 inches is less than one mile. If you round the numerator and denominator to the nearest hundred, you get
100/800 or about 1/8 of a mile.
© 2010 Cheryl Wilcox
Free Pre-Algebra
Lesson 29 ! page 5
Using Conversion Factors From a Table
In some situations you have a table of conversion information and you need to find what’s relevant to your problem.
Example: Find the number of fluid ounces in 3 and 1/2 gallons.
U.S. Units of Liquid Volume
My plan is to go down in size,
gallons ! quarts ! cups ! ounces
1 gallon = 4 quarts
1 quart = 2 pints
I don’t need the information about pints, since I can go directly from
quarts to cups.
3
3
1 quart = 4 cups
1
gallons
4 quarts 4 cups 8 ounces
2
•
•
•
1
1 gallons 1 quarts
1 cup
1 pint = 2 cups
1 cup = 8 fluid ounces
1
gallons 4 quarts 4 cups
8 ounces ! 1 $
2
•
•
•
= # 3 & 4 4 8 ounces
1
" 2%
1 gallons 1 quarts
1 cup
( )( )( )
=
7
64
• 128 ounces
2
= 448 ounces
!
© 2010 Cheryl Wilcox
Free Pre-Algebra
Lesson 29 ! page 6a
Lesson 29: Converting Between Units
Worksheet
1. Write two unit fractions from the
equation
Name ________________________________________
a. How many minutes is 300 seconds?
b. How many seconds is 18 minutes?
a. How many meters is 2300 cm?
b. How many cm is 51/2 meters?
a. How many quarts are in 91/8 gallons?
b. How many gallons is 38 quarts?
a. Write two unit fractions from the
equation
b. How many square feet is 1080
square inches?
60 seconds = 1 minute
2. Write two unit fractions from the
equation
100 centimeters = 1 meter
3. Write two unit fractions from the
equation
1 gallon = 4 quarts
4. A square foot has length 12 inches
and width 12 inches, so the area is:
1 sq foot = 144 sq in
© 2010 Cheryl Wilcox
Free Pre-Algebra
Lesson 29 ! page 7a
5. Use the equations
6. How many hours is one million seconds?
60 seconds = 1 minute
60 minutes = 1 hour
to find the number of seconds in 24 hours.
7. How many days is one million seconds?
8. The amazing vehicle traveled 500 feet per second for
2 minutes. How far did it travel?
a. Change 2 minutes to seconds.
b. Calculate the distance traveled, in feet.
c. There are 5280 feet in 1 mile. How many miles did the
vehicle travel?
Estimate the number of seconds in one month, to the
nearest million.
Estimate the number of seconds in one year, to the nearest
million.
© 2010 Cheryl Wilcox
Free Pre-Algebra
Lesson 29 ! page 8
Lesson 29: Converting Between Units
Homework 29A
Name ________________________________________
1. Measure the line. Add another line 3/4 inch long to the end
of the line. Find the total length. 2 and 9/16 inches
2. Find the blue shaded area. Measurements are in inches.
1 and 13/16 inches
1
2
3
Write and solve the associated addition problem.
3. Solve with a multiplication.
4. Solve with a division.
a. What is 1/3 of 366 days?
a. How many 3/4 oz. pieces can be cut from a bar weighing
27 oz?
b. What is 1/2 of $1,000,000?
b. How many 23/8 inch lengths can be cut from a ribbon
38 inches long?
5. Divide the rectangles so they have the same number and
size parts. Write equivalent fractions for the shaded areas
with a common denominator.
xxxxxxxxxxxx
1
4 xxxxx
1
3 xxxxx
© 2010 Cheryl Wilcox
6. After the potluck, Mahmood had 1/4 tray of brownies left
and Darshani had 1/3 tray of brownies left. Darshani gave
hers to Mahmood, and he ate them all. How much did he
eat?
Did he eat more or less than 1/2 a tray?
Free Pre-Algebra
7. Find equivalent fractions with a
common denominator.
Lesson 29 ! page 9
7a. Add the fractions.
7b. Add the mixed numbers.
23 5
+
45 9
5
8a. Subtract the fractions.
8b. Subtract the mixed numbers.
1 2
!
5 3
1 2
5 !
5 3
23
45
23
5
+2
45
9
5
9
8. Find equivalent fractions with a
common denominator.
1
5
2
3
9. Simplify.
10. Simplify.
4a 7a
+
5 10
! 7b 1 $
40 #
+
" 20 8 &%
11. Evaluate !3x 2 + x when x =
1
.
4
13. How many days is 300 hours? (1 day = 24 hours)
© 2010 Cheryl Wilcox
12. How many inches is 300 feet? (1 foot = 12 inches)
14. How many hours is 200,000 seconds?
(1 hour = 60 minutes, 1 minute = 60 seconds)
Free Pre-Algebra
Lesson 29 ! page 10
Lesson 29: Converting Between Units
Homework 29A Answers
1. Measure the line. Add another line 3/4 inch long to the end
of the line. Find the total length. 2 and 9/16 inches
1 and 13/16 inches
2. Find the blue shaded area. Measurements are in inches.
3/4 inches
1
2
Square – Rectangle =
3
! 3 $ ! 3 $ ! 1$ ! 1$
#" 4 &% #" 4 &% ' #" 2 &% #" 8 &%
Write and solve the associated addition problem.
13 3
13 12
+ =1 +
16 4
16 16
25
9
9
= 1 = 1+ 1 = 2
16
16
16
1
=
9
1
8
1
'
=
=
16 16 16 2
Area is 1/2 square inch.
3. Solve with a multiplication.
4. Solve with a division.
a. What is 1/3 of 366 days?
a. How many 3/4 oz. pieces can be cut from a bar weighing
27 oz?
1
3
122
b. What is 1/2 of $1,000,000?
1
2
9
• 366 days = 122 days
500,000
• $1,000,000 = $500,000
5. Divide the rectangles so they have the same number and
size parts. Write equivalent fractions for the shaded areas
with a common denominator.
1 3
=
4 12
1 4
=
3 12
© 2010 Cheryl Wilcox
27 ÷
3 27 4
=
• = 36 pieces
4
1 3
b. How many 23/8 inch lengths can be cut from a ribbon
38 inches long?
2
38 ÷ 2
3 38 19 38 8
=
÷
=
•
= 16 lengths
8
1
8
1 19
6. After the potluck, Mahmood had 1/4 tray of brownies left
and Darshani had 1/3 tray of brownies left. Darshani gave
hers to Mahmood, and he ate them all. How much did he
eat?
1 1 3
4
7
+ =
+
=
4 3 12 12 12
He ate 7/12 of a tray.
Did he eat more or less than 1/2 a tray?
More, 7/12 > 6/12 = 1/2
Free Pre-Algebra
Lesson 29 ! page 11
7. Find equivalent fractions with a
common denominator.
7a. Add the fractions.
7b. Add the mixed numbers.
23 5
+
45 9
5
23
23
23
=
=
45 3 • 3 • 5 45
=
5
5
5 25
=
• =
9 3 • 3 5 45
8. Find equivalent fractions with a
common denominator.
! 23 25 $
23
5
+
+2 = 5+2 +#
45
9
" 45 45 &%
23 25 48
3
1
+
=
=1
=1
45 45 45
45
15
(
=7+1
)
1
1
=8
15
15
8a. Subtract the fractions.
8b. Subtract the mixed numbers.
1 2
!
5 3
1 2
3 10
5 ! =5
!
5 3
15 15
1 1 3 3
= • =
5 5 3 15
=
2 2 5 10
= • =
3 3 5 15
3 10
7
!
=!
15 15
15
9. Simplify.
=4
18 10
8
!
=4
15 15
15
10. Simplify.
3
4a 7a 8a 7a 15 a 3a
+
=
+
=
=
5 10 10 10
2
10
2
5
! 7b $
! 1$
! 7b 1 $
+
40
40 #
+ & = 40 #
&
# & = 14b + 5
" 20 8 %
" 20 %
" 8%
2
11. Evaluate !3x 2 + x when x =
1
.
4
2
" 1%
" 1%
" 1% 1
= !3 $ ' + $ ' = !3 $ ' +
# 4&
# 4&
# 16 & 4
=
12. How many inches is 300 feet? (1 foot = 12 inches)
300 feet 12 inches
•
= 3,600 inches
1
1 foot
!3 4
1
+
=
16 16 16
13. How many days is 300 hours? (1 day = 24 hours)
25
300 hours
1 day
•
1
24 hours
14. How many hours is 200,000 seconds?
(1 hour = 60 minutes, 1 minute = 60 seconds)
500
200,000 sec
1
2
25
1
=
days = 12 days
2
2
© 2010 Cheryl Wilcox
•
1 min
60 sec
3
=
•
1 hour
60 min
3
500
5
hours = 55 hours
9
9
Free Pre-Algebra
Lesson 29 ! page 12
Lesson 29: Converting Between Units
Homework 29B
Name _________________________________________
1. Measure the line. Add another line 1/2 inch long to the end
of the line. Find the total length. 2 and 9/16 inches
2. Find the blue shaded area. Measurements are in inches.
1 and 13/16 inches
1
2
3
Write and solve the associated addition problem.
3. Solve with a multiplication.
4. Solve with a division.
a. What is 3/4 of $1,000,000?
a. How many 5/8 oz. pieces can be cut from a bar weighing
25 oz?
b. What is 2/3 of 48 months?
b. How many 61/4 inch lengths can be cut from a string
500 inches long?
5. Divide the rectangles so they have the same number and
size parts. Write equivalent fractions for the shaded areas
with a common denominator.
6. Mercedes had 1/4 of a cup full of coffee, and Romelia
poured in another 1/2 cup. How much coffee was there
then?
1
4 xxxxx
How much more coffee would be needed to make 1 cup?
1
2
© 2010 Cheryl Wilcox
xxxxxxxxxxx
Free Pre-Algebra
7. Find equivalent fractions with a
common denominator.
3
5
Lesson 29 ! page 13
7a. Add the fractions.
7b. Add the mixed numbers.
3 5
+
5 9
3
5
5 +2
5
9
8a. Subtract the fractions.
8b. Subtract the mixed numbers.
3 11
!
14 21
5
5
9
8. Find equivalent fractions with a
common denominator.
3
14
3 11
!
14 21
11
21
9. Simplify.
10. Simplify.
7 y 5y
+
5
7
! 7b 3 $
20 #
+
" 20 4 &%
11. Evaluate x ! x 2 when x =
3
.
2
13. How many cups is 20 quarts? (1 quart = 4 cups)
© 2010 Cheryl Wilcox
12. How many miles is 1,000,000 yards?
(1 mile = 1760 yards)
14. How many days is 3,000 minutes?
(1 hour = 60 minutes, 1 day = 24 hours)