Transcript Slide 1

10/13/08
GCF, LCM Word Problems
#20
Warm-up
Nicholas bikes every third day and skates
every other day. Today is April 5, and Nicholas
biked and skated. On what date will he both
bike and skate?
April 11
Today’s Plan:
Warm-up and tests back
GCF & LCM word problems
Assignment:Problem Solving 2-5 & 2-6
Both sides, odds or evens all on graph paper showing all work
including factor tree and prime factorization line up.
2-5 Greatest Common Factor
Additional Example 3: Problem Solving Application
You have 120 red beads, 100 white
beads, and 45 blue beads. You want to
use all the beads to make bracelets that
have red, white, and blue beads on each.
What is the greatest number of
matching bracelets you can make?
Course 2
2-5 Greatest Common Factor
Additional Example 3 Continued
1
Understand the Problem
Rewrite the question as a statement.
• Find the greatest number of matching bracelets
you can make.
List the important information:
• There are 120 red beads, 100 white beads,
and 45 blue beads.
• Each bracelet must have the same
number of red, white, and blue beads.
The answer will be the GCF of 120, 100, and 45.
Course 2
2-5 Greatest Common Factor
2
Additional Example 3 Continued
Make a Plan
You can list the prime factors of 120, 100,
and 45 to find the GFC.
3
Solve
120 = 2 · 2 · 2 · 3 · 5
100 = 2 · 2 · 5 · 5
45 = 3 · 3 · 5
The GFC of 120, 100, and 45 is 5.
You can make 5 bracelets.
Course 2
2-5 Greatest Common Factor
Additional Example 3 Continued
4
Look Back
If you make 5 bracelets, each one will have
24 red beads, 20 white beads, and 9 blue
beads, with nothing left over.
Course 2
2-5 Insert
Lesson
TitleFactor
Here
Greatest
Common
Try This: Example 3
Nathan has made fishing flies that he
plans to give away as gift sets. He has
24 wet flies and 18 dry flies. Using all of
the flies, how many sets can he make?
Course 2
2-5 Insert
Lesson
TitleFactor
Here
Greatest
Common
Try This: Example 3 Continued
1
Understand the Problem
Rewrite the question as a statement.
• Find the greatest number of sets of flies
he can make.
List the important information:
• There are 24 wet flies and 18 dry flies.
• He must use all of the flies.
The answer will be the GCF of 24 and 18.
Course 2
2-5 Greatest Common Factor
Try This: Example 3 Continued
2
Make a Plan
You can list the prime factors of 24 and 18
to find the GCF.
3
Solve
24 = 2 · 2 · 2 · 3
18 = 2 · 3 · 3
2·3=6
Multiply the prime factors
that are common to both
24 and 18.
You can make 6 sets of flies.
Course 2
2-5 Insert
Lesson
TitleFactor
Here
Greatest
Common
Try This: Example 3 Continued
4
Look Back
If you make 6 sets, each set will have
3 dry flies and 4 wet flies.
Course 2
2-5 Greatest
Insert Lesson
Common
TitleFactor
Here
Lesson Quiz: Part 2
The math clubs from 3 schools agreed to a
competition. Members from each club must be
divided into teams, and teams from all clubs
must be equally sized. What is the greatest
number of members that can be on a team if
Georgia has 16 members, William has 24
members, and Fulton has 72 members?
8
Course 2
2-6 Insert
Lesson Title
Here
Least Common
Multiple
Try This: Example 3
Two satellites are put into orbit over the same
location at the same time. One orbits the earth
every 24 hours, while the second completes an
orbit every 18 hours. How much time will
elapse before they are once again over the
same location at the same time?
Find the LCM of 24 and 18.
24 = 2 · 2 · 2 · 3
18 = 2 · 3 · 3
The LCM is 2 · 2 · 2 · 3 · 3 = 72.
Course 2