Comparing and Ordering Fractions and Mixed Numbers Topic 9-5 Pgs

How can you compare fractions? Problem: Shawna and Tom walked two different paths in Trout park. Shawna walked 5/6 mile. Tom walked ¾ mile. Which is greater, 5/6 or ¾? Problem: Shawna and Tom walked two different paths in Trout park. Shawna walked 5/6 mile. Tom walked ¾ mile. Which is greater, 5/6 or ¾?

Which is greater 5/6 or ¾? One Way One Way To compare fractions, find a common denominator by writing the multiples of each denominator 4: 4, 8, 12, 16, 20… 6: 6, 12, 16, 18, 24… Use 12 as the common denominator Multiply your fractions by the number it takes to get 12 as a denominator 5 x 2 = x 3 = /12 > 9/12 so, 5/6 > 3/4

Which is greater 5/6 or ¾? Another Way: Another Way: You can multiply the denominators to find a common denominator. Compare ¾ and 5/6 Multiply denominators: 4 x 6= 24 4 x 6= 24 Use 24 as the common denominator Multiply your fractions by the number it takes to get 24 as the denominator 5 x 4 = x 6 = 18 4 x /24 > 18/24 so 5/6 > 3/4

How can you order fractions and mixed numbers? Write 2 5/12, 11/12, 3 1/6, 2 1/3 in order from least to greatest Write 2 5/12, 11/12, 3 1/6, 2 1/3 in order from least to greatest You know that 11/12 < 1 and all the mixed numbers are greater than 1. So 11/12 is the least number You know that 11/12 < 1 and all the mixed numbers are greater than 1. So 11/12 is the least number When comparing mixed numbers, look at the whole number parts. Since 3>2, you know that 3 1/6 is greater than both 2 1/3 and 2 5/12 When comparing mixed numbers, look at the whole number parts. Since 3>2, you know that 3 1/6 is greater than both 2 1/3 and 2 5/12 Next, compare 2 1/3 and 2 5/12. Since the whole numbers are the same, compare the fractions. Next, compare 2 1/3 and 2 5/12. Since the whole numbers are the same, compare the fractions. Compare 1/3 and 5/12. Change 1/3 to 4/12 Compare 1/3 and 5/12. Change 1/3 to 4/12 4/12 < 5/12 so 2 1/3 < 2 5/12 4/12 < 5/12 so 2 1/3 < 2 5/12 From greatest to least, the numbers are 3 1/6, 2 5/12, 2 1/3, 11/12 From greatest to least, the numbers are 3 1/6, 2 5/12, 2 1/3, 11/12

Let’s Try it Together Compare the following fractions Compare the following fractions , or =?, or =? Order from least to greatest 1) , 4, 10 Answer: ¼, 2/3, 9/10 2) Answers: 1 2/3, 1 9/10, 2 1/4

Independent Practice #7-12 Use your notes to determine the correct answer for #7-12. Use your notes to determine the correct answer for #7-12. We will review the answers in 10 minutes We will review the answers in 10 minutes Good Luck! Good Luck!

Common Factors and Greatest Common Factors 9-6 Pgs

Vocabulary If a number is a factor of two numbers, it is called a common factor If a number is a factor of two numbers, it is called a common factor The greatest common factor (GCF) of two numbers is the greatest number that is a factor of both numbers The greatest common factor (GCF) of two numbers is the greatest number that is a factor of both numbers

How can you find the greatest common factor of 20 and 30? Problem: A pet store has goldfish and angelfish that have to be put into the fewest number of glass containers. Each container must contain the same number of fish, and each must contain all goldfish or all angelfish. Problem: A pet store has goldfish and angelfish that have to be put into the fewest number of glass containers. Each container must contain the same number of fish, and each must contain all goldfish or all angelfish. Find the GCF of 20 and 30 Find the GCF of 20 and 30 One Way: To find the greatest common factor of 20 and 30, you can list all the factors of each and circle the numbers they have in common 20: 1, 2, 4, 5, 10, 20 30: 1, 2, 3, 5, 6, 10, 15, 30 Of all the numbers they have in the common what is the largest number? 10 so the GCF of 20 and 30=10

How can you find the greatest common factor of 20 and 30? Another way is to use prime factorization to find the GCF Another way is to use prime factorization to find the GCF Find GCF of 24 and 18 (pg. 232) Find GCF of 24 and 18 (pg. 232) 1. Find the prime factors of each number 2. List the prime factors of each number 24= 2 x 2 x 2 x 3 24= 2 x 2 x 2 x 3 18= 2 x 3 x 3 18= 2 x 3 x 3 3. Circle the prime factors that both numbers share which are 2 and 3 4. Multiply the common factors: 2 x 3=6 So, the GCF of 18 and 24 is 6

Let’s Try it Together! Find the GCF of each pair of numbers Find the GCF of each pair of numbers 1) 9 and 12 2) 20 and 45 3) 7 and 28 4) 18 and 32 5) If two numbers are prime, what is their GCF? Answers:

Independent Practice Complete #7-14 and we will review them as a class Complete #7-14 and we will review them as a class Good Luck Good Luck