The Ladder MethodFor Finding LCD, GCF and Simplifying FractionsBecky Afghani, LBUSD Math Curriculum Office, 2003

Becky Afghani, LBUSD Math Curriculum Office, 2003The Ladder Method...is a method of factoring which allows you to factor two numbers at once in order tofind the LCM of the two numbersfind the GCF of the two numberssimplify a fraction with these numbers as numerator and denominator

Becky Afghani, LBUSD Math Curriculum Office, 2003

Becky Afghani, LBUSD Math Curriculum Office, 2003Use the ladder to factor6 and 8You will divide out any common factors of the two numbersWhat number goesinto both 6 and 8?Now divide both6 and 8 by the 2Does any # besides 1go into both 3 and 4?No? Then you are done.

Becky Afghani, LBUSD Math Curriculum Office, 2003

Becky Afghani, LBUSD Math Curriculum Office, 2003Lets find the Least Common Multiple (LCM) of 6 and 8The LCM is the product of all the numbers on the left and the bottom.The LCMof 6 and 8is 24.

Becky Afghani, LBUSD Math Curriculum Office, 2003

Becky Afghani, LBUSD Math Curriculum Office, 2003Which numbers in the ladder give you the LCM?

Becky Afghani, LBUSD Math Curriculum Office, 2003

Becky Afghani, LBUSD Math Curriculum Office, 2003What about the Greatest Common Factor (GCF) of 6 and 8?The GCF is the product of all the numbers on the left.The GCFof 6 and 8is 2.

Becky Afghani, LBUSD Math Curriculum Office, 2003

Becky Afghani, LBUSD Math Curriculum Office, 2003Which numbers in the ladder give you the GCF?

Becky Afghani, LBUSD Math Curriculum Office, 2003

Becky Afghani, LBUSD Math Curriculum Office, 2003How can we use the Ladder Method to simplify ?The simplified numerator and denominator are on the bottom.

Becky Afghani, LBUSD Math Curriculum Office, 2003

Becky Afghani, LBUSD Math Curriculum Office, 2003Which numbers in the ladder give you the simplified fraction?

Becky Afghani, LBUSD Math Curriculum Office, 2003

Becky Afghani, LBUSD Math Curriculum Office, 2003Lets try some bigger numbers.Divide out all the common factors down the left side.What numbergoes into both24 and 60?Does any # besides 1go into both 12 and 30?How about6 and 15?Anything else?No?Youre done.

Becky Afghani, LBUSD Math Curriculum Office, 2003

Becky Afghani, LBUSD Math Curriculum Office, 2003Find the LCM.=120The LCMof 24 and 60is 120.

Becky Afghani, LBUSD Math Curriculum Office, 2003

Becky Afghani, LBUSD Math Curriculum Office, 2003Find the GCF.=12The GCFof 24 and 60is 12.

Becky Afghani, LBUSD Math Curriculum Office, 2003

Becky Afghani, LBUSD Math Curriculum Office, 2003Simplify .

Becky Afghani, LBUSD Math Curriculum Office, 2003

Becky Afghani, LBUSD Math Curriculum Office, 2003Practice. Find the LCM and GCF for 28 and 42. Simplify .LCM = 2 7 2 3 = 84 GCF = 2 7 = 14

Becky Afghani, LBUSD Math Curriculum Office, 2003

Becky Afghani, LBUSD Math Curriculum Office, 2003Extension Questions1. Do you have to factor out prime numbers?2. Can you factor three numbers at once and still get the right GCF and LCM? Try factoring small numbers to find out - like 4, 6, and 8.

Becky Afghani, LBUSD Math Curriculum Office, 2003