SLIDE SHOW INSTRUCTIONS This presentation is completely under

SLIDE SHOW INSTRUCTIONS This presentation is completely under your control. This lesson will show only one step at a time, to see the next step you must press a key. (Actual names written on a key are in green) • TO STOP THE SLIDE SHOW: press ‘escape’ (Esc, top left of keyboard) • TO MOVE FORWARD: press the “spacebar” or Enter (Page. Dn, , , also work) • TO MOVE BACKWARD: press the key (Page. Up, or also work)

Addition & Subtraction Copyright © 1999 Lynda Greene

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

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

Fractions with Common Denominators 1) ADD THE TOPS 3) ALWAYS REDUCE IF POSSIBLE 2) KEEP THE BOTTOM 1) SUBTRACT THE TOPS 3) ALWAYS REDUCE IF POSSIBLE 2) KEEP THE BOTTOM 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 Bottoms: + x = Step 1: bottom x bottom = new bottom Copyright © 1999 Lynda Greene

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

Subtraction Example: Cross-Multiply: 2 x 6 = 12 Cross-Multiply: 5 x 7 = 35 X 23 = STEP I. Bottom x Bottom = New Bottom This is the new top number 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

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

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 10 - 12 Step 1: Bottom 3 x 5=15 = -2 LEFT - RIGHT = ANSWER Copyright © 1999 Lynda Greene

Signed Fractions Step 2 7 x 3 = 21 Step 3 1 x 2=2 -19 Step 4 bring down the signs Step 5 reduce the fraction if possible Step 1: Bottom 2 x 3=6 - 21 + 2 = -19 Copyright © 1999 Lynda Greene

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

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