• 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