1. Multiplying Fractions and Mixed Numbers Grade 6

2. Copyright © Ed2Net Learning, Inc. 2 1) 3 1 3 + 6 1515 = 2) 2 3535 + 5 4545 = 3) 1 4747 + 2 4 21 = 4)1 2 10 - 3 2727 = 5)4 1212 - = 1 ---- Warm Up

3. Copyright © Ed2Net Learning, Inc. 3 Lets review what we have learned in the last lesson A mixed number has a whole number part and a fraction part To add or subtract any mixed number we first need to convert the mixed number to an improper fraction then proceed further…..

4. Copyright © Ed2Net Learning, Inc. 4 4 3737 + 2 5757 = 4 3737 + 2 5757 = 4 + 2 3 + 5 7 = 6 + = 7 1717 Add the fractions together and the whole numbers together Equal denominators 1 1717 = 6 8787 Adding Mixed Fractions with equal denominators

5. Copyright © Ed2Net Learning, Inc. 5 Addition of Mixed fractions with different denominators When the denominators are co-prime, we need to multiply the two denominators to get the common denominator When the two denominators have a common factor we find the least common denominator by factoring When one denominator is a multiple of the other denominator the multiple is the denominator

6. Copyright © Ed2Net Learning, Inc. 6 Example: Since 1/4 is not enough to be subtracted by 1/2, we have to convert all mixed numbers into improper fractions first then compute 5 1414 3 1212 - 5 1414 3 1212 = 5 x 4 + 1 3 x 2 + 1 4 2 - = 21 7 4 2 - = 21 14 4 4 - = 7474 = 1 3434 - Example: 5 1414 1212 - Denominators that are multiple of each other 4 is a multiple of 2 Subtraction of Mixed Numbers

7. Copyright © Ed2Net Learning, Inc. 7 5 7 69 -39 30 16 16 - = = 6 4 55 x 9 22 x 7 495-154 7 9 7 x 9 9 x 7 63 63 - = - == Equal Denominators Different denominators Do same as in Addition Multiple Take the multiple Common Factors Take LCM Prime Multiply the two 4 2 72 341 Lets see some more examples

8. Copyright © Ed2Net Learning, Inc. 8 Addition/Subtraction of mixed numbers Convert the mixed fraction in to an improper fraction or add/subtract the whole numbers and the fractions separately Find a common denominator Add/Subtract as required Simplify, then if it is an improper fraction then again convert in to a mixed fraction

9. Copyright © Ed2Net Learning, Inc. 9 Multiplying Fractions and mixed numbers Mixed numbers must be changed to improper fractions before any multiplication or division can be done When you multiply mixed numbers, it is not correct to multiply the whole number parts and multiply the fractions separately

10. Copyright © Ed2Net Learning, Inc. 10 Mixed fractions and Proper Fractions Mixed Fractions  The numerator is bigger than the denominator Proper fraction  The numerator is smaller than the denominator

11. Copyright © Ed2Net Learning, Inc. 11 Rules of multiplication between mixed numbers and fractions When multiplying mixed fractions, they do NOT need to have a common denominator To multiply a mixed fraction with a proper fraction, multiply across, numerator by numerator and denominator by denominator When multiplying mixed fractions and fractions, we can simplify the fractions and also simplify diagonally. This isn’t necessary, but it can make the numbers smaller and keep you from simplifying at the end If the answer can be simplified, then simplify it

12. Copyright © Ed2Net Learning, Inc. 12 First convert the mixed fraction in to an improper fraction Then multiply, numerator x numerator and denominator x denominator 5 1616 x 2424 = 31 2 6 4 x 31 x 2 6 x 4 == 3 1 31 12 Improper fraction 2 7 12 = Then again convert answer in to mixed number Multiplication of mixed fractions

13. Copyright © Ed2Net Learning, Inc. 13 Associative- The sum or product of three or more fractions is the same regardless of the way in which they are grouped 1 3 6 1 3 6 8 4 7 8 4 7 Property Examples Commutative-The product of two fractions is the same regardless of the way in which they are ordered 2 1 1 2 3 5 5 3 x= x xxxx= Properties of Multiplication

14. Copyright © Ed2Net Learning, Inc. 14 1 4 Inverse Reciprocal- The product of a fraction and its inverse is 1 6 8 8 6 Distributive -The sum of two fractions multiplied by a number is equal to the sum of products of each fraction and the number. 2 1 3 2 1 2 3 3 2 7 3 2 3 7 Identity- The product of any fraction and 1 is the fraction itself x 1 = PropertyExamples = 1x + x = + x Properties of Multiplication

15. Copyright © Ed2Net Learning, Inc. 15 1)2/7 x 9 1/3 2) 3 3535 x 7 4949 = = 18 67 5 9 x = 18 x 67 134 5 x 9 5 = = 26 2 13 7 3 = 2 13 7 3 X = 26 21 2 4545 x 1 5 21 = Lets see some examples of multiplication

16. Copyright © Ed2Net Learning, Inc. 16 Remember! If the product of two numbers is 1, they are the reciprocals of each other The number 0 has no reciprocals

17. Break Time!

18. Copyright © Ed2Net Learning, Inc. 18

19. Copyright © Ed2Net Learning, Inc. 19 1) 2 5353 x 4545 = 2) 7 1515 x 1212 = 3) 9 5757 x 3 8 = 4)5 2 9 x 2 2727 = 5)2 1212 x = 5 3 ___ Assessment

20. Copyright © Ed2Net Learning, Inc. 20 6) 1 1313 x 5 2525 = 7) 8 3434 x 2 1515 = 8) 5 3737 x 1 5 = 9)1 3434 x 1919 = 10)3 1717 x 2929 = Assessment

21. Copyright © Ed2Net Learning, Inc. 21 Assessment 11. James is hiking in the national park. He makes four evenly spaced stops after every 2/3 mile along the way. At what mile of the hike does he make his last stop ? What is the distance of his complete hike?

22. Copyright © Ed2Net Learning, Inc. 22 Assessment 12. When the notary public asked Kayla her age, Kayla answered, "I am twice as old as my sister Amy. Amy is one-fifth as old as my father. My father is eighty years old." How old is Kayla?

23. Copyright © Ed2Net Learning, Inc. 23 Assessment 13. Kaitlin is making white oatmeal cookies with raisins and pecans for her club. The recipe makes eighteen of the big, chewy kind of oatmeal cookies with lots of raisins and nuts. It takes four-fifths of a cup of nuts and four-fifths of a cup of raisins just for the eighteen cookies! There are forty-two members in Kaitlin's club. If she makes exactly forty-two cookies, how many cups of nuts will she need?

24. Copyright © Ed2Net Learning, Inc. 24 Lets review what we have learned in this lesson Multiplying Fractions and mixed numbers  Mixed numbers must be changed to improper fractions before any multiplication or division can be done  When you multiply mixed numbers, it is not correct to multiply the whole number parts and multiply the fractions separately

25. Copyright © Ed2Net Learning, Inc. 25 Rules of multiplication between mixed numbers and fractions When multiplying mixed fractions, they do NOT need to have a common denominator To multiply a mixed fraction with a proper fraction, multiply across, numerator by numerator and denominator by denominator When multiplying mixed fractions and fractions, we can simplify the fractions and also simplify diagonally. This isn’t necessary, but it can make the numbers smaller and keep you from simplifying at the end If the answer can be simplified, then simplify it

26. Copyright © Ed2Net Learning, Inc. 26 First convert the mixed fraction in to an improper fraction Then multiply, numerator x numerator and denominator x denominator 1 2727 x 1515 = 9 1 7 5 x = If the answer is an improper fraction then again convert answer in to mixed number 9 35 = 9 35 Multiplication of mixed fractions and fractions

27. You had a great lesson today! Be sure to practice what you have learned today!!