[Numeracy 129] Re: introductions
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Tue Feb 9 11:19:22 EST 2010
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This is exactly why our students have difficulty!
Laura E. Sherwood
Literacy Coordinator
Adult Education
College of Lake County
Grayslake, IL 60030
847-543-2616
lsherwood at clcillinois.edu
"Their story, yours, mine - it's what we all carry with us on this trip
we take, and we owe it to each other to respect our stories and learn
from them." William Carlos Williams
From: numeracy-bounces at nifl.gov [mailto:numeracy-bounces at nifl.gov] On
Behalf Of Maureen Carro
Sent: Monday, February 08, 2010 11:04 PM
To: The Math and Numeracy Discussion List
Subject: [Numeracy 124] Re: introductions
Carolyn writes:
Suppose the numbers are 15 and 21. The LCD would be 3: 15 = 3 *
5; 21 = 3 * 7. The number they have *in common* is 3.
3 is the Greatest Common Factor: GCF, not the Lowest Common
Denominator: LCD
Suppose the numbers are 49 and 98. The LCD would be 49: 49 = 7 * 7; 98 =
7 * 7 * 2. The numbers they have *in common* are 7 and 7, and 7 * 7 =
49.
The Lowest Common Denominator would be 98
The Lowest Common Denominator is used to create equivalent fractions for
the purpose of adding and subtracting fractions with like
denominators... ( same size pieces)
Equivalent fractions are fractions in "higher terms" than the original
fractions.
I think there is confusion among: Least Common Denominator, Least
Common Multiple, and Greatest Common Factor.
The Least Common Denominator is the same as the Least Common Multiple.
It is called the Least Common Denominator when it is serving as the
denominator of equivalent fractions that have been created in order to
create the "same size pieces" so they can be added or subtracted .
The "new" denominator is always either the larger of the original
denominators ( if the smaller one is a factor if it) or larger than the
original ones.... thus is is a common multiple of the two original
denominators. Barbara's example, a few posts ago.... illustrated this.
Otherwise, when NOT serving as a DENOMINATOR of a fraction, the lowest
multiple that two ( or more) numbers have in common is called the
Least Common Multiple. It is CONTEXT that changes the scenery here and
it is called by a different name depending on the context. .
Try 45 and 21 for the LCM. What is the smallest number that is a
multiple of both numbers? 45 = 3 * 3 * 5, 21 = 3 * 7. The LCM = 3 * 3 *
5 * 7 or 105. (Each number has a 3, so the first three only counts
once. There is an extra 3 in 45, plus the 5. 21 still has a 7. Multiply
all those together.
Or let's try 15 and 49. 15 = 3 * 5, 49 = 7 * 7. No numbers in
common, so multiply them all together. LCM = 3 * 5 * 7 * 7 or 735.
Carolyn's example above is an example of finding the Least Common
Multiple ( sometimes known as Lowest Common Denominator) by using Prime
Factorization.
Maureen Carro, MS, ET
Academic Learning Solutions
Alamo, CA
mcarro at lmi.net
On Feb 8, 2010, at 3:18 PM, Carolyn Dickinson wrote:
What is the difference between the Lowest (or least) Common Denominator
and the Least Common Multiple and what different functions do they
accomplish?
The LCD is the smallest number that will go INTO each of the numbers,
while the LCM is the smallest number that each of the numbers will
divide into (the smallest number that is a multiple of both numbers).
Suppose the numbers are 15 and 21. The LCD would be 3: 15 = 3 * 5; 21 =
3 * 7. The number they have *in common* is 3.
Suppose the numbers are 49 and 98. The LCD would be 49: 49 = 7 * 7; 98 =
7 * 7 * 2. The numbers they have *in common* are 7 and 7, and 7 * 7 =
49.
Try 45 and 21 for the LCM. What is the smallest number that is a
multiple of both numbers? 45 = 3 * 3 * 5, 21 = 3 * 7. The LCM = 3 * 3 *
5 * 7 or 105. (Each number has a 3, so the first three only counts
once. There is an extra 3 in 45, plus the 5. 21 still has a 7. Multiply
all those together.
Or let's try 15 and 49. 15 = 3 * 5, 49 = 7 * 7. No numbers in common, so
multiply them all together. LCM = 3 * 5 * 7 * 7 or 735.
Does that help?
Carolyn Dickinson
Western Nebraska Community College
Scottsbluff, Nebraska
On Sat, Feb 6, 2010 at 12:56 PM, George Demetrion <gdemetrion at msn.com>
wrote:
Good afternoon all.
While I am an experienced adult educator I am a newbie math teacher, but
I'm plugging away in my first transitions to college basic math course.
We've had two three hour sessions thus far in a 15 week course and
things are moving along okay.
To be sure I've put a lot of time practicing my math through basic
algebra and concentrating on the assignments in our weekly sessions.
I'm learning and I'm also getting a good experiential dose of math
phobia, which in turn, in the process of transforming in the process of
learning and then drawing on my overall teaching skills, especially
incorporating basic explanation, a lot of practice and collaborative
scaffolding instructional processes.
One technical question:
What is the difference between the Lowest (or least) Common Denominator
and the Least Common Multiple and what different functions do they
accomplish?
Keep it simple and straightforward, please.
George Demetrion
East Hartford, CT
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