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Topic 10

What you know and what you are going to knowYou know how to add and subtract whole numbers, like 6 + 9 Today you are going to learn how to add and subtract fractions with like denominators.

*

How do you add fractions?

How do you subtract fractions?

*ObjectiveAdd and subtract fractions and mixed numbers expressing answers in simplest form.

When do you think you might need to add or subtract fractions?Following a recipe

Measuring or cutting lengths

Think back to some of the things you already knowSimplest formEquivalent fractionsCommon denominatorsFactors (GCF) and (LCF)Multiples (GCM) and (LCM)How to compare

*Writing Fractions in Simplest FormA fraction is in simplest form when the only common factor of the numerator and denominator is 1.

2 1 = 2 3 1 = 3

2. 27 36

1. List the common factors.2. Find the GCF.3. Divide by the GCF.

*Mixed Number / Improper FractionWhen changing a mixed number to an improper fraction, you need to multiply the denominator by the integer, then add the numerator to the product.

Rewrite 4 1/2 as an improper fraction.9/2

*Adding FractionsCheck for common denominators.Once the denominators are the same, add the numerators.Always simplify your answer.If your answer doesnt match an answer choice, try to simplify the answer choices.

practice

Video with like denominatorshttp://www.youtube.com/watch?v=52ZlXsFJULI

*Find the Sum8/9 + 2/9 =

9/16 + 4/32 =

8 2/3 + 6 1/2 =

10/9 = 1 1/9

22/32 = 11/16

14 7/6 = 15 1/6

*Subtracting FractionsCheck for common denominators.Once the denominators are the same, subtract the numerator.Always simplify your answer.If your answer doesnt match an answer choice, try to simplify the answer choices.

*Find the Difference4/5 - 2/5 =

8/12 - 4/9 =

9 - 6 5/8 =

2/5

8/36 = 2/9

2 3/8

video with unlike denominatorshttp://www.graspr.com/videos/Adding-and-Subtracting-Fractions-With-UNLIKE-Denominators-1

*Review!How do you add fractions?

How do you subtract fractions?

*Find the Difference, Find the Sum5 - 2 3/4

4/5 + 3/10

2

1 1/10

BAIP Instructional Support Version 2**Writing Fractions in Simplest Form (PowerPoint #2)Teacher prompt: Introduce the term simplest form to students by telling them that a fraction is in simplest form when the only common factor of the numerator and denominator is 1. Teacher prompt: Ask students to list all of the factors of 2.Student response: The factors of 2 are 1, 2.Teacher prompt: Now list all of the factors of 3.Student response: The factors 3 are 1, 3.Teacher prompt: If I asked you to write the fraction 2/3 in simplest form, you would write 2/3 because the only factor the 2 and the 3 have in common is 1. One is the common factor. When you divide both the 2 and 3 by 1 you will still have the fraction 2/3. This means 2/3 is already written in simplest form.Teacher prompt: Now lets write the fraction 27/36 in simplest form. Working with a partner, list all of the factors of 27. List the factors in order from least to greatest. Student response: 27: 1, 3, 9, 27.Teacher prompt: Good. Now, with your partner, list the factors of 36 in order from least to greatest.Student response: 36: 1, 2, 3, 4, 6, 9, 12, 18, 36Teacher prompt: Using these two lists we are going to find the greatest common factor of 27 and 36.Teacher prompt: Show the two lists on the board, one underneath the other.27: 1, 3, 9, 27 List the factors for the numerator and denominator.36: 1, 2, 3, 4, 6, 9, 12, 18, 36 Find the greatest common factor (GCF)Teacher prompt: 9 is the greatest common factor. Use this number to divide both the numerator and denominator by. Rewrite the fraction in simplest form. Show your work.Student response: 27 9 = 3 36 9 = 4

BAIP Instructional Support Version 2**Writing a Mixed Number as an Improper Fraction (PowerPoint #3)Teacher prompt: Ask the students to define a mixed number. Student response: A mixed number is a number with an integer part and a fraction part.Teacher prompt: Ask the students to give an example of a mixed number.Student response: 4 Teacher prompt: Sometimes when multiplying fractions we run into mixed numbers. It is important to understand how to rewrite the mixed number as an improper fraction.Teacher prompt: When changing a mixed number to an improper fraction you need to multiply the denominator by the integer, then add the numerator to the product. The answer you get is your new numerator and the denominator stays the same. Teacher prompt: Demonstrate how to rewrite the mixed number 4 1/2 as an improper fraction.(See Teachers Guide)BAIP Instructional Support Version 2**Adding Fractions (including mixed numbers) With Like and Unlike Denominators and Writing the Answer in Simplest Form, (PowerPoint #4)Teacher prompt: Write the following problems on the board. 8/9 + 2/9 =9/16 + 4/32 =8 2/3 + 6 =Teacher Prompt: Ask the students to read the first problem.Teacher prompt: Ask the students what the two fractions have in common.Student response: They both have the same denominator.Teacher prompt: That is correct. When the denominators are the same, add the two numerators and keep the same denominator. Work number 1 now.Student response: 8 9 2 9 10 9 Teacher prompt: What kind of sum did you get?Student response: An improper fraction.Teacher prompt: Write the answer in simplest form.Student response: 1 1/9Teacher Prompt: Ask the students to read the second problem: 9/16 + 4/32 =Teacher prompt: Ask the students if the two fractions have anything in common.Student response: The denominators have common factors of 2, 4, 8, and 16.Teacher prompt: What do the two fractions need to have in common before we can add them?Student response: They need to have a common denominator.Teacher prompt: Which denominator should we change?Student response: We can either divide 32 by 2 to get 16 or we can multiply the 16 by 2 to get 32. It doesnt matter which fraction we change.Teacher prompt: Choose the method of your choice. Just remember whatever you do to the denominator you must do to the numerator and write your answer in simplest form.Student response: 9 2 = 18 16 2 = 32 4 4 +32 3222 = 11 32 16OR 9 9 16 16 4 2 = 2 + 32 2 = 16 11 16Teacher Prompt: Ask the students to read the third problem: 8 2/3 + 6 Teacher prompt: Ask the students; How is this addition problem different from the first two?Student response: We need to find the sum of two mixed numbers.Teacher prompt: When adding mixed numbers, you may add the fraction and whole number parts separately. Then combine the two parts to get the total sum.Teacher prompt: Add the mixed numbers now.Student response: 8 2 2 = 4 3 2 = 6+6 1 3 = 3 2 3 = 6 14 + 7/6 or 1 1/6 14 + 1 1 = 15 1 6 6Teacher prompt: What denominator did you choose when finding a common denominator?Student response: I chose 6 because both 2 and 3 are common factors of 6. Teacher prompt: Did you have to simplify when finding the sum?Student response: Yes, when adding the fraction, I came up with an improper fraction. I had to rewrite the improper fraction as a mixed number and then add the whole numbers together.Teacher prompt: You added correctly. BAIP Instructional Support Version 2**Subtracting Fractions (Including Mixed Numbers) With Like and Unlike Denominators and Writing the Answer in Simplest Form (PowerPoint #5)Teacher prompt: Write the following problems on the board. 4/5 - 2/5 =8/12 - 4/9 =9 - 6 5/8 =Teacher Prompt: Ask the students to read the first problem: 4/5 - 2/5 Teacher prompt: Ask the students what the two fractions have in common.Student response: They both have the same denominator.Teacher prompt: That is correct. When the denominators are the same, subtract the numerators and keep the same denominator. Work number 1 now.Student response: 3 5 2 -5 1 5 Teacher Prompt: Ask the students to read the second problem: 8/12 - 4/9 Teacher prompt: Ask the students if the two fractions have anything in common.Student response: The denominators are both multiples of 36.Teacher prompt: What do the two fractions need to have in common before we can add them?Student response: They need to have a common denominator.Teacher prompt: How will we change the denominators so that they have a common denominator?Student response: Since both 12 and 9 are multiples of 36, we need to multiply to use the factor of 3 and 4 to write equivalent fractions for 8/12 and 4/9. Teacher prompt: Do this now.Student response: 8 3 = 24 12 3 = 36 4 4 = 16 - 9 4 = 36 8 = 2 36 9Student response: Another way to work this problem is to reduce 8/12 to 2/3; then work the problem 2/3 4/9. I will use the common denominator 9. 2 3 = 6 3 3 = 9 4 = 4 - 9 = 9 2 9Teacher prompt: As you see there is more than one way to reduce fractions or make equivalent fractions. Butwe must always remember that we have to use common factors when multiplying and dividing. Teacher Prompt: Ask the students to read the third problem: 9 - 6 5/8 Teacher prompt: Ask the students; How is this subtraction problem different from the first two?Student response: This problem has an integer and a mixed numbers in it.Teacher prompt: How will you subtract from the whole number?Student response: I will have to borrow one whole from the 9.Teacher prompt: How will you do that?Student response: I will take one away from 9 and rewrite the 1 as a fraction. Teacher prompt: How do you determine which fraction to write?Student response: I use the denominator of the mixed numbers fraction. It is 8. The fraction I will borrow is 8/8. Teacher prompt: Work this problem using the borrowing method.Student response: 8 9 8/8 - 6 5/8 2 3/8Teacher prompt: Nicely done.

BAIP Instructional Support Version 2**: (PowerPoint #9)Teacher Prompt: Write the following examples on the board 1. 2/4 2/52. 4/5 + 3/103. 5 1/5 5 5/6Teacher prompt: Ask students to copy the first problem on the board.Student response: 2/4 2/5Teacher prompt: What do we need to do first before subtracting the two fractions?Student response: Find like denominators.Teacher prompt: What is the least common denominator of 4 and 5?Student response: 20Teacher prompt: 20 is the least common denominator of 4 and 5.Teacher prompt: Help students write equivalent fractions using 20 as the common denominator.Teacher prompt: 2 5 = 10 4 5 = 20 2 4 8 - 5 4 20 2 = 1 20 10Teacher prompt: Ask students to copy the second problem on the board: 4/5 + 3/10Student response: 4/5 + 3/10Teacher prompt: What do we need to do first before finding the sum?Student response: Find like denominators.Teacher prompt: What is the least common denominator for 5 and 10?Student response: 10 Teacher prompt: Help students write equivalent fractions using 10 as the common denominator.Teacher prompt: 4 2 = 8 5 2 =10 3 1 3 + 10 1 10 11 = 1 1 10 10Teacher prompt: Ask students to copy the third problem on the board: 5 1/5 5 5/6Student response: 5 1/5 5 5/6Teacher prompt: When finding the product of two mixed numbers what must we do first before we multiply?Student response: Rewrite the mixed numbers as improper fractions.Teacher prompt: Rewrite the mixed numbers as improper fractions with the students, guiding them through the operations.Student response: 5 1/5 5 5/65 x 5 + 1 6 x 5 + 5 26 35 5 6Teacher prompt: Help students simplify both improper fractions by taking out common factors.Teacher prompt: 13 726 35 5 6 1 3Teacher prompt: Multiply the numerators and denominators.Student response: 13 7 = 91 or 30 1 1 3 3 3