Adding & Subtracting Fractions with regrouping Woo hoo!

Do Now: 8-9-17 What is my overarching expectation? How do you spell my last name? What must you bring to class to be considered prepared? When is a good time to throw away paper? When is your Birthday?

Do Now 8-22-16 List the steps in adding and subtracting fractions and mixed numbers. For example, When adding fractions you must…. When subtracting fractions you must…..

Do Now: 8-10-17 Finish Unit one Pretest. Testing Procedures: Stay quiet. Raise hand. DO NOT COME TO ME. When finish, draw, color, read (YES, too technology). I will let you know when test is over.

Do Now: 8-14-17 Give yourself one goal for math. Take some time to think about it. Go beyond just thinking you want to do better in math this year. What about math makes you nervous, what do you hope to achieve? What can Ms. Tatem do to help you achieve this goal?

Do Now: 8-21-17 What is the definition for GCF and LCM?

Do Now 8-22-17 Use the Distributive Property to find the product. State the GCF and LCM of each. 24 + 45 = 36 – 34 =

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Standards MGSE6.NS.4. Find the common multiples of two whole numbers less than or equal to 12 and the common factors of two whole numbers less than or equal to 100.

Vocabulary Measurement Model of Division Algorithm Difference Minuend Distributive Property Multiple Dividend Quotient Divisor Partitive Model of Division Factor Reciprocal Greatest Common Factor Sum Least Common Multiple

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Greatest Common Factor Definition: The greatest common factor (GCF) of two numbers is the greatest factor shared by those numbers. EX: A florist makes bouquets from 18 roses and 30 tulips. All bouquets will include both roses and tulips. If all the bouquets are identical, what are the possible bouquets that can be made?

What factors are we comparing? 18: 30: GCF is 6! Good Work!

Can the florist make 5 bouquets?

Distributive Property Definition: The sum of two or more numbers as a product of their GCF and sum of numbers with no common factors. What is the GCF of 45 and 60?

Distributive Property What is the sum of 25 and 65 as a product of their GCF and a sum of a number with no common factor?

Distributive Property Tasha believes that she can rewrite the difference 120 – 36 as a product of the GCF of the two numbers and another difference . Is she correct? Explain your answer.

Is she correct? The GCF of 120 and 36 is 12, so 120 – 36 can be written as 12 × 10 – 12 × 3, which is 12 × (10 – 3) or 12 × 7. Think- Pair- Share

Least Common Multiple Definition: Least Common Multiple (LCM): Two or numbers is the least number, other than zero, that is a multiple of all the numbers. Ex: Ned is training for a biathlon. He will swim every sixth day and bicycle every eighth day. On what days will he both swim and bicycle?

The number 1 is neither prime nor composite. Numbers Prime number: Has only two factors: 1 and itself. Composite number: Has more than two factors.  The number 1 is neither prime nor composite.

Lets make Math simple! Ladder Method: What is the GCF and LCM of 12 and 24.

Tree Method What is the GCF and LCM of 12 and 24.

Lets make Math simple! Ladder Method: What is the GCF and LCM of 36 and 90 .

**Assignment 8-22-17** Page 35 #19-30 (even/odd) *( 32-34)

First………let’s remember this from last year………

How to change a mixed number to an improper fraction 1 9 Multiply the whole number times the denominator. Add your answer to the numerator. Put your new number over the denominator. + REMEMBER POPCORN.........?? 4 = x 2 2

Change this mixed number to an improper fraction 2 20 Multiply the whole number times the denominator. Add your answer to the numerator. Put your new number over the denominator. + 6 = x 3 3

Change this mixed number to an improper fraction 2 17 Multiply the whole number times the denominator. Add your answer to the numerator. Put your new number over the denominator. + 3 = x 5 5

Change this mixed number to an improper fraction 3 19 Multiply the whole number times the denominator. Add your answer to the numerator. Put your new number over the denominator. + 4 = x 4 4

Change this mixed number to an improper fraction 3 43 Multiply the whole number times the denominator. Add your answer to the numerator. Put your new number over the denominator. + 8 = x 5 5

Excellent!!!! Let’s keep moving…….

10 3 1 3 6 1 + 6 6 Mixed Numbers Shortcut to find the LCD. Will 3 divide into 6? Use 6 as your LCD. 1 10 3 6 1 3 + 6 6

10 3 1 3 6 1 + 6 6 x 2 = x 1 = Now find the equivalent fractions for Mixed Numbers Now find the equivalent fractions for 1/3 & 1/6. 1 10 3 6 x 2 = 1 3 + 6 x 1 = 6 Ask what do you multiply 3 by to get 6 and what do you multiply 6 by to get 6.

1 10 3 6 1 3 + 6 6 x 2 = x 2 = x 1 = x 1 = You are writing equivalent Mixed Numbers You are writing equivalent fractions, so fill in your Giant One. 1 x 2 = 10 3 6 x 2 = 1 x 1 = 3 + 6 x 1 = 6

1 2 10 3 6 1 1 3 + 6 6 x 2 = x 2 = x 1 = x 1 = Now multiply across. Mixed Numbers 1 2 Now multiply across. x 2 = 10 3 6 x 2 = 1 1 x 1 = 3 + 6 x 1 = 6

1 2 10 3 6 1 1 3 + 6 6 3 6 x 2 = x 2 = x 1 = x 1 = Add numerators. Mixed Numbers 1 2 Add numerators. x 2 = 10 3 6 x 2 = 1 1 x 1 = 3 + 6 x 1 = 6 3 6

Mixed Numbers 1 2 Add whole numbers. x 2 = 10 3 6 x 2 = 1 1 x 1 = 3 + 6 x 1 = 6 3 13 6

Mixed Numbers Simplify Your Answer ÷ 3 1 13 3 13 = 6 ÷ 3 2

just like you would with whole numbers. What if I’m supposed to subtract a larger fraction from a smaller fraction?_________ _______________________ Regroup just like you would with whole numbers. 6 + + 9 8 9 7 1 8 13 9 1 4 9 1 10 x x 3 8 - 3 7 9 4 - 6 8 5 6 9 2 3 3 3 3 4 5 = =

Can you regroup with unlike denominators? Sure, but first find the LCD and equivalent fractions. 8 x 7 2 3 21 14 35 21 1 9 x 7 Watch this! 21 5 7 x 3 15 5 - x 3 20 21 3

Let’s see that again! Remember, first find the LCD and equivalent fractions. 5 x 4 2 5 20 8 28 20 1 6 x 4 20 3 4 x 5 15 3 Watch this! - x 5 13 20 2

Then regroup as we have before! Remember to simplify if you need to. How about these! If you have a whole number, make a fraction with 0 in the numerator and the same denominator the mixed number has. 5 8 8 8 7 7 6 1 1 9 3 2 8 4 7 - 5 - 2 6 8 2 3 4 3 3 7 = Then regroup as we have before! Remember to simplify if you need to.

Now, you try!!!! 6 2 8 10 8 9 7 1 4 1 4 6 12 18 30 18 = = 1 10 = = 3 8 3 8 - 3 7 9 14 18 4 = - = 8 9 7 8 5 16 18 5 3 =

Your turn!!!! 8 14 6 6 9 9 9 1 15 1 1 2 6 4 9 - 6 - 7 4 6 7 2 3 = 8 5 9

**Assignment 8-22-17** Page 35 #19-30 (even/odd) Page 39 #