Monday, January 12, 2009
Extra Credit Opportunity #5
Fifth grade students often have a hard time distinguishing between when to find the L.C.M. (least common multiple) and the G.C.F. (greatest common factor). We've been learning how to add and subtract fractions with unlike denominators and we have just started reducing fractions to lowest terms. With both of these objectives G.C.F. and L.C.Ms were discussed. How would you explain to a frustrated classmate the difference between the two and when to use them to help him/her understand? Any tips? Rules? Pointers?
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The GCF (greatest common fraction) is when you are trying to figure out which fraction is larger and the LCM (least common fraction) is when you are adding or subtracting fractions. Say I had to add 4/5 and 2/3 you would first have to do the LCM. You would do this by multiplying the first four multiples (1 times ___ 2 times _____ 3 times____ 4 times____) of that number. You do this to the other fraction and the least common number that is the same as the top one is your LCM (note, you may have to go higher than four multiples). Say if you had 3/6 and 4/8. You would have to use the GCF to figure out the higher fraction. First you must see what will go into 3 and 6 evenly. It would be three. You do the same to 4/8 (what will go into 4 and 8 evenly). It is 4 . So with the numbers that will go into each other you divide that number into each number and then you compare the fractions to see which one is larger.
You use the LCM for adding and subtracting fractions with unlike denominators. You use the GCF to reduce fractions to lowest terms. The difference is when you have to use the LCM you start with the denominator itself and start listing multiples after that. Usually only 4 times will do it. You have to think about 8 for example, if that was the first denominator. 8x1=8, that explains why you start with the number itself unlike the GCF where you start with 1. After you think of 8x2=16, and so on. Then you move on to the next denominator. With the GCF, you have a fraction that can be reduced this stategy helps you reduce to lowest terms. You list all of the factors, or NUMBERS that will go into this numerator on the top bar that looks like this______________
Next, you list the denominators keep going until you come to the same number you are working with. Find what Factor, or NUMBER that goes into both of them. See there is a big difference, and just remember, LCM= M stands for Mom In a family, a multiply family, GCF= in the G and the C a G take away the - and you have C! You reduced G to make C something SMALLER!!!!!!
I often get confused with what the LCM is too. This is something I will have to review in my math book to make sure I understand.
G.C.F stands for greatest common factor and L.C.M stands for lowest common multiple. You use G.C.F when reducing fractions and L.C.M when finding equivelent fractions. I think I might have left out some stuff.
I would look at each number and see if it could be divided by the same number and start reducing it to get the lcm.
5. Definitions:
The L. C. M., Least Common Multiple of two numbers is the smallest number that is a multiple of both.
The GCF, Greatest Common Factor, is the greatest factor that divides two numbers.
When to use: The L. C. M. is used every time to find the common denominator for a set of fractions containing different denominators. A common denominator is required in order to compare parts of a whole.
The GCF can be used to simplify, or reduce fractions.
G.C.F.-The Greatest Common Factor is the largest number that is a common factor of two or more numbers. Example: Determine if there is a common factor of the numbers. A common factor is a number that will divide into both numbers evenly. Two is a common factor of 4 and 14. Divide both of the numbers by this common factor.
Repeat this process with the resulting numbers until there are no more common factors.
Multiply all of the common factors together to get the Greatest Common Factor. The Least Common Multiple is the smallest number that two or more numbers will divide into evenly. Find the Greatest Common Factor of the numbers, multiply the numbers together, divide the product of the numbers by the Greatest Common Factor. Example:Determine the Greatest Common Factor of 15 and 12 which is 3, Either multiply the numbers and divide by the GCF (15x12=180, 180/3=60) OR - Divide one of the numbers by the GCF and multiply the answer times the other number (15/3=5, 5x12=60)!
I would not be able to explain to another classmate because I do not understand it.
GCF is the largest factor between two numbers. LCM is the least common factor between two numbers
GCF is the largest factor between two numbers. LCM is the least common factor between two numbers
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