Download Rename Fractions with LCD

10.5 Addition and Subtraction with
unlike denominators
Steps:
1. Find a least common denominator (LCD)
2. Rename fractions
3. Add or subtract numerators
REVIEW:
3 2 1 7
6 7 13
  
 

3 7 3 7
21 21 21
How to get a LCD with RE
1. Factor the denominators
2. Take one of each factor
–
Even if both addends don’t have the same
factor
– If the addends have the same factor just take
one and take the one with the highest
exponent
Example:
3
5

( x  1) ( x  1)
LCD  ( x  1)( x  1)
Rename Fractions with LCD
• Compare the LCD to the denominator of
each addend
• Multiply the numerator and denominator of
the fraction by a number or polynomial to
make your denominator match your LCD
Example:
3
5


x 1 x 1
3(x - 1)

5(x + 1)
 x  1 x  1  x  1 x  1
Add numerators:
3(x - 1)

5(x + 1)
 x  1 x  1  x  1 x  1
3x  3 5x  5
 x  1 x  1
8x  2
 x  1 x  1
2  4 x  1
 x  1 x  1
Example 1
7
2


x 1 x 1
7  x  1
2  x  1
9x  5


x  1x  1 x  1x  1 x  1x  1
Example 2:
2
3


x  2 2x
4x

3  x  2

7x  6
x  22 x  x  22 x  x  22 x 
Example 3:
a a  4 2a  4
a 1 a4
  2  2 2  2
a
a
a
a
a a

2  a  2
a
2
3x
12 x
 2
x2 x 4
12 x
 x  2   3x 
 x  2   x  2   x  2  x  2 
Example 4:
3x  6 x +12 x
2
 x  2 x  2
3x  6 x
 x  2  x  2 
2
3x  x  2 
 x  2  x  2 
3x
x2
Example 5:
5x
3  x  1

 x  1 x 1  x 1  x  1
5 x  3x  3
 x  1 x  1
8x  3
 x  1 x  1
5x
4


2
x 9 x3
5x
4
x  3


 x  3 x  3  x  3  x  3
Example 6:
 4x 12
5x

 x  3 x  3  x  3 x  3
x  12
 x  3 x  3
Example 7
You try! Raise your hand when you are done!
First person done with the correct answer
will earn a math buck!$$$
 x  1
 x  1
 x  1 x  1
x  2x  3  
2
x 1 
 x  1 x  1
x  3x  4
 x  1 x  1
2
 x  4  x  1 x  4
 x  1 x  1 x  1
Example 8
You try! Raise your hand when you are
done! First person done with the correct
answer will earn a math buck!$$$
4x
x 1

2
x 1 x 1
x  1

4x

 x  1 x  1  x  1
 x  1
 x  1
4x  x  2x  1
 x  1 x  1
2
x  2x 1
 x  1 x  1
2
 x  1 x  1
 x  1 x  1
Example 9
You try! Raise your hand when you are done!
First person done with the correct answer
will earn a math buck!$$$
2  y  5

 y  5 y  4  y  4  y  5
y
y 2 y  10
 y  5 y  4
3 y  10
 y  5 y  4
Example 10
You try! Raise your hand when you are done!
First person done with the correct answer
will earn a math buck!$$$
1
6

t2
t2

t2
6t  13

t2

t2
Example 11
You try! Raise your hand when you are done!
First person done with the correct answer
will earn a math buck!$$$
3
x y


2
2
xy
x y
2
x y
2

2
x y
2

3x  xy  y

2 2
x y
2
x y
2
2
Assignment:
Page 448 (2-34) even