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Addition & Subtraction Copyright © 1999 Lynda Greene

Addition & Subtraction Fractions with the same denominator II. The Butterfly Shortcut for adding and subtracting fractions Copyright © 1999 Lynda Greene

3+1 = 5 = 1 Fractions with Common Denominators 1) ADD THE TOPS 3) ALWAYS REDUCE IF POSSIBLE 3+1 = 5 2) KEEP THE BOTTOM 1) SUBTRACT THE TOPS 2) KEEP THE BOTTOM  4 = 1 3) ALWAYS REDUCE IF POSSIBLE Copyright © 1999 Lynda Greene

Fractions with Common Denominators 1) ADD THE TOPS 2) KEEP THE BOTTOM 3) ALWAYS REDUCE IF POSSIBLE 1) SUBTRACT THE TOPS 2) KEEP THE BOTTOM 3) ALWAYS REDUCE IF POSSIBLE Copyright © 1999 Lynda Greene

Adding & Subtracting Fractions The ‘Butterfly’ Method Copyright © 1999 Lynda Greene

The “Butterfly” is a short-cut method used for adding & subtracting any two fractions. The usual method is called finding a “Common Denominator” which is outlined in a different lesson on this CD. The Butterfly Method is in many textbooks and yet many teachers and students have never seen it. It is faster than using common denominators but the answer must be reduced and it only works on two fractions at a time. NOTE: Always ask your teacher if it’s OK to use a math short-cut before you try to use it on an assignment. Copyright © 1999 Lynda Greene

Fractions: The Butterfly Method + x = Bottoms: Step 1: bottom x bottom = new bottom Copyright © 1999 Lynda Greene

+ 22 10 12 + = 22 = Step 2: Find the Top Number I. Cross-Multiply: (start with top left) Write this number on the left II. Cross-Multiply: (start with top right) Write this number on the right second: 4 x 3 = 12 first: 2 x 5 = 10 + = 22 This is the new top number III. Add bring down the sign in the middle 10 12 + = 22 You must check to see if the fraction is reduced Copyright © 1999 Lynda Greene

- 23 35 12 23 = - Subtraction Example: This is the new top number Cross-Multiply: 2 x 6 = 12 Cross-Multiply: 5 x 7 = 35 - 23 This is the new top number STEP I. Bottom x Bottom = New Bottom X = 35 - 12 23 = III. Subtract bring down the sign in the middle You must check to see if the fraction is reduced Copyright © 1999 Lynda Greene

(based on whether the problem is addition or subtraction) Summary When adding or subtracting fractions, you can find an answer using the following steps: bottom times bottom = new bottom top left times bottom right = left number top right times bottom left = right number New Top: Add or subtract left and right. Bring down the signs (based on whether the problem is addition or subtraction) Copyright © 1999 Lynda Greene

When finding the top number, the order you follow matters. Signed Fractions When finding the top number, the order you follow matters. Always start with the top left number and write that answer on the left, then do the top right. Last, bring the positive or negative signs straight down. Step 3 4 x 3 = 12 Step 2 2 x 5 = 10 Step 5 reduce the fraction if possible -2 Step 4 bring down the sign Step 1:Bottom 3 x 5=15 - 10 12 = -2 LEFT - RIGHT = ANSWER Copyright © 1999 Lynda Greene

-19 - + Signed Fractions 21 2 = -19 Step 2 7 x 3 = 21 Step 3 1 x 2 = 2 reduce the fraction if possible -19 Step 1:Bottom 2 x 3 = 6 Step 4 bring down the signs + - 21 2 = -19 Copyright © 1999 Lynda Greene

-51 - Signed Fractions 36 15 = - 51 Step 2 6 x 6 = 36 Step 3 reduce the fraction if possible Step 2 6 x 6 = 36 Step 3 5 x 3 = 15 -51  3 Step 4 bring down the signs - Step 1:Bottom 3 x 6 = 18 36 15 = - 51

Practice Problems 1. 2. 3. Solutions: 1. 2. 3. Copyright © 1999 Lynda Greene