• Elena, Joe, Owen, Samantha, and Tuck have weighed their backpacks.
• Elena's backpack weighs the most. • Owen’s backpack weighs 0.45 lb less than Joe's
backpack. • Samantha's lunch weighs 1.5 lb. With that lunch
out of the backpack, the backpack weighs 16.55 lb.
• Tuck's backpack weighs more than Owen's. • How much does each person's backpack
weigh?
Answer
• Elena: 19.8 lbJoe: 19.35 lbOwen: 18.9 lbSamantha: 18.05 lbTuck: 19.5 lb
Lesson 5-8LCM and Comparing and
Ordering Rational Numbers
LCM
• A multiple is a product of natural numbers. Ex: 3 x 4 = 12, 12 is a multiple of 3 and 4.
• The least common multiple is the common multiple that is less than any other common multiple of two or more numbers.
• Three ways to find LCM: Listing multiples, prime factorization, cake method.
Listing Multiples
• List multiples of each number from least to greatest.
• Ex. 12 and 8
12: 12 24 4836
8: 8 16 24 32 40 48
Listing Multiples
• List multiples of each number from least to greatest.
• Ex. 12 and 8
12: 12 24 4836
8: 8 16 24 32 40 48
The LCM is 24.
Prime Factorization
16 24
4 4
2 2 2 2
4 6
2 2 2 3
• 2 x 2 x 2 x 2
• 2 x 2 x 2 x 3
Prime Factorization
16 24
4 4
2 2 2 2
4 6
2 2 2 3
• 2 x 2 x 2 x 2
• 2 x 2 x 2 x 3
•Common: 2 x 2 x 2 x 2 x 3 = 48 LCM = 48
Cake Method
18 32 2
9 16
LCM = 288
12 18 2
6 9 3
2 3
2 x 2 x 3 x 3 = 36
LCM = 36
Your Turn
• Find the LCM of 10 and 15 by listing multiples.
• Find the LCM of 45 and 75 by using prime factorization.
• Find the LCM of 32 and 48 by using the cake method.
LCM = 30
LCM = 96
LCM = 225
LCD
• A common denominator is a common multiple of 2 denominators. The least common denominator (LCD) is the LCM of the denominators.
• Find the LCD of:
712
818
The LCD is 36
Compare the Fractions Using < or >
56
79
15
750
916
710
>
>
<
Order From Least to Greatest
12
0.6 48% 12
0.648%=
210
0.322% = 210
0.322%
15 0.182% =
150.182%
Homework
• Complete Lesson 5-8 # 2-20 evens
• Don’t forget that you have a Chapter 5
Test on Friday!! Start Studying
