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2. Addition & Subtraction
Copyright © 1999 Lynda Greene

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

4. 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

5. 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

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

7. 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

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

9. + 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

10. - 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

11. (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

12. 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

13. -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

14. -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

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