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

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

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

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, …

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 =

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

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) = ) = = =

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 = ) = ) = ) = 1 7 8

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

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

Try Some More! 5)9 ¼ + 2  ) 6 13/ / ) 12  - 3 7/ )6  - 4 

How it works… 5)9 ¼ = 9 3/  = + 2 4/ ) 6 13/15 = 6 143/ /33 = / = ) 12  = 12 15/ /10 = 3 28/ )6  = 6 3/  = / /21 = 5 24/ /

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.

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