1. 5-4 6 th grade math Adding and Subtracting with Unlike Denominators

2. Objectives To add and subtract fractions and mixed numbers with unlike denominators

3. California State Standards NS 2.4 : Determine the LCM of whole numbers; use them to solve problems with fractions (e.g., to find a common denominator to add two fractions and to find the reduced form for a fraction) NS 2.0 : Calculate and solve problems involving addition, subtraction, … NS 2.1: Solve problems involving addition, subtraction, … of positive fractions and explain why a particular operation was used for a given situation

4. Vocabulary Unlike denominators – Fractions with denominators that are not the same ,  Like denominators – Fractions with denominators that are the same ,  Least Common Denominator (LCD) – the LCM of the denominators of two or more fractions 12 = LCD of ¼ and  Equivalent Fractions – Fractions that name the same number  = 2/4 = 4/8 = 5/10, …

5. How to solve subtracting with unlike denominators  -  1. Find the LCD of the fractions 2. Write the equivalent fractions 3. Subtract. 4. Simplify, if possible 1)LCD = 12 2)3 = x 3 = 9 4 = x 3 = 12 1 = x 4 = 4 3 = x 4 = 12 3)9 - 4 = 12 12 5 12

6. How to add with unlike denominators 5 + 2 12 15 1. Find the LCD of the fractions 2. Write the equivalent fractions 3. Subtract. 4. Simplify, if possible 1)LCD = 60 2) 5 x 5 = 25 12 x 5 = 60 2 x 4 = 8 15 x 4 = 60 3) 25 + 8 60 60 =33 60 4) Divide by 3 = 11 Divide by 3 = 20

7. How to add w/unlike denominators and “mixed/impropers” 8  + 10  1.Write equivalent fractions. 2.Add. 3.Simplify, if possible. 8  + 10  = 1.LCD = 12 2 x 4 = 8 3 x 3 = 9 3 x 4 = 12 4 x 3 = 12 2) 8 8 + 10 9 = 12 12 3) = 18 17 = 18 + 1 5 = 19 5 12 12 12

8. How to subtract w/unlike denominators and “to borrow” 6  - 4  1) Write the equivalent fractions using the LCD. 2) Rename. 3) Subtract. 4) Simplify, if possible. 6  - 4  1)LCD = 8 1 x 4 = 4 2 x 4 = 8 = 6 3 - 4 4 8 8 2) = 5 8+3 - 4 4 8 8 3) = 5 11 - 4 4 8 8 4) = 1 7 8

9. Try It! 1)8/9 + 4/ 15 2)1/9 + 1/6 + 1 /30 3)½ - 1/10 4)7/8 – 9/32 1)1 7/45 2)14/45 3)2/5 4)19/32

10. How it works … 1)8/9 + 4/ 15 LCD = 45 8 x 5= 40 + 4 x 3 = 12 9 x 5 45 15 x 3 = 45 40 + 12 = 45 52 = 1 7 45 2)1/9 + 1/6 + 1 /30 LCD = 90 1 x 20 = 20 1 x 30 = 30 1x 6 = 6 9 x 20 = 180 6 x 30 = 180 30 x 6 = 180 20 + 30 + 6 = 56 180 180 Divide by 4 = 14/45 3)½ - 1/10 LCD = 10 ½ = 5/10 = 5 -1 10 = 4/10 = 2/5 4)7/8 – 9/32 LCD = 32 7 x 4 = 28 8 x 4 = 32 = 28 – 9 32 = 19 32

11. Try Some More! 5)9 ¼ + 2  117 12 6) 6 13/15 + 4 2/33 1051 55 7) 12  - 3 7/10 8 27 40 8)6  - 4  1 10 21

12. How it works… 5)9 ¼ = 9 3/12 + 2  = + 2 4/12 11 7 12 6) 6 13/15 = 6 143/165 + 4 2/33 = + 4 10/165 10 153 = 165 10 51 55 7) 12  = 12 15/40 - 3 7/10 = 3 28/40 8 27 40 8)6  = 6 3/21 - 4  = - 4 14/21 521 + 3/21 = 5 24/21 - 4 14/21 1 10 21

13. Objectives Reviewed To add and subtract fractions and mixed numbers with unlike denominators Why? You are learning all number sense skills: add and subtract whole numbers, decimals, and fractions/mixed fractions.

14. Independent Practice Complete problems 12-23. For an extra challenge, try 24-27. Remember to show all work. Copy the original problem before solving. If time, complete the Mixed Review problems: 28-37. If still more time, complete Accelerated Math.