Definitions
Define "factor"
A number that is multiplied with another number to create a value.
Find the GCF of this pair:
45 and 81
9
Find the LCM.
14 and 21
42
James says that 12 is a common factor of 3 and 4. June says that 12 is a common multiple of 3 and 4. Who is correct?
June, because 3 and 4 can be multiplied together to make 12.
How would you use a number line to explain ordering integers from greatest to least?
Right to left
Define "multiple"
Multiple sets of a value.
A number that can be divided by another number with no remainder.
ex. 5, 10, 15, 20
Find the GCF of 28 and 70.
14
Find the LCM
16 and 24
48
Mel has to put the greatest number of bolts and nuts in each box so each box has the same number of bolts and the same number of nuts. Should Mel use greatest common factor or the least common multiple to solve the problem?
Greatest Common Factor
Katia and Thomasina play a computer game and record these scores.
Katia: 8, 6, -?4, -?7, 2, 0, 3
Thomasina: ?-11, 0, 8, 7, 5, ?-7, 11
Compare Katia’s and Thomasina’s least scores.
-7>-11 or -11<-7
What types of problems can be solved using the greatest common factor?
Problems in which two different amounts must be split into the same number of groups.
For football tryouts, 12 coaches and 42 players will split into groups. Each group will have the same number of coaches and players. What is the greatest number of teams in which the two groups can be arranged if each has the same number of coaches and players? How many will be in each?
6 teams
2 coaches
7 players
You buy a lily and an African violet on the same day. You are instructed to water the lily every 4th day and water the violet every 7th day.
What is the first day you will water them on the same day?
How can you tell which days in the future will the plants be watered on the same day?
Both will be watered on day 28; the next days will be multiples of 28.
The plants will be watered together on day 28, day 56, day 84, and so on.
Melanie took 48 pictures of flowers and 36 pictures of pretty scenery. She wants to display the pictures so there is the same number of each kind of picture in each display. What is the greatest number of displays she can make?
12 displays
Ali graphed the absolute values of -?3 and -4 on the number line. Which number is further from 0? Explain.
-4, because even with its absolute value of positive 4, it is still 4 further away on the number line.
What types of problems can be solved using the least common multiple?
Problems with events that occur on different schedules, require every x number of people, etc.
Rose picked 18 tulips and 20 daffodils. She divided the flowers into groups so that the same number of tulips and daffodils were in each bouquet. What is the greatest number of bouquets she could have made?
2
Julie has two email accounts. She checks one of them every 2 hours. The other one she uses less often -- only checking it every 24 hours. She checked each account on Monday at 2 p.m. When will she again check each account at the same time?
a. next Monday at 2 a.m.
b.. next Monday at 2 p.m.
c. Tuesday at 2 a.m.
d. Tuesday at 2 p.m.
Tuesday at 2 PM
A student expressed a sum of two whole numbers as 5x(8+3). What were the two whole numbers?
40+15 = 55
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Describe how you would teach someone to find the least common multiple of 3 numbers. Give an example with numbers!
To find the LCM of 3 numbers, you should list the multiples of each and take the least multiple that is common to all 3. For example, find the LCM of 6, 8, and 12. The multiples of 6 are 6, 12, 18, 24...the multiples of 8 are 8, 16, 24... and the multiples of 12 are 12, 24. This makes the LCM 24.
A student expressed a sum of two whole numbers as 2x(8+49). What was the sum?
16 + 86
Kevin solved a problem by making these lists.
12: 12, 24, 36, 48, 60
15: 15, 30, 45, 60
Write a problem that Kevin might be solving.
Any LCM problem that contains:
-Which will match up after x amount of units between 12 and 15
A park district has 25 elm trees and 20 oak trees to be planted. They want each area to have the same number of elm trees and the same number of oak trees. What is the greatest number of areas that can be created?
5 areas
5 elm trees
4 oak
Which of the following statements is not true?
A. ?-5 ?< -?4
B. 4 ?< 5
C. ?-2 <-?3
D. ?-2 <? 5
C