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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:
2 1
7 3
21 21 21
3
3 7
7
6 7 13
How to get a LCD with RE1. Factor the denominators
2. Take one of each factor– If there are duplicates take the one with the
highest exponent
Rename Fractions with LCD• Compare the LCD to the denominator of
each fraction• Multiply the numerator and denominator of
the fraction by a number or polynomial to make your denominator match your LCD
7 2
1 1x x
111111
xxxxxx
7 1x 2 1x 9 5x
Example 1
xx 2
3
2
2
xxxxxx 222222
4x 3 2x 7 6x
Example 2:
2
1 4a
a a
2 2 2
4a
a a a
2
2 2a
a
a
a
a2
2 4a
a
Example 3:
2
3 12
2 4
x x
x x
2
2
x
x
3 12
2 2 2
x x
x x x
+12
2 2
x
x x
23 6x x
23 6
2 2
x x
x x
3 2
2 2
x x
x x
3
2
x
x
Example 4:
5 3
1 1 1
x
x x x
1
1
x
x
5 3 3
1 1
x x
x x
8 3
1 1
x
x x
Example 5:
3 3x x
2
5 4
9 3
x
x x
5 4
3 3 3
x
x x x
5
3 3
x
x x
3
3
x
x
4 12x
12
3 3
x
x x
Example 6:
Example 7
You try! Raise your hand when you are done! First person done with the correct answer
will earn a math buck!$$$
4
1
x
x
1 1x x
1
1
x
x
2 2 3
1 1
x x
x x
1x
2 3 4
1 1
x x
x x
4 1
1 1
x x
x x
Example 8
You try! Raise your hand when you are done! First person done with the correct
answer will earn a math buck!$$$
14
1 1 1
xx
x x x
4
1 1
x
x x
1
1
x
x
2 2 1x x
2 2 1
1 1
x x
x x
1
1
1
1
x
x
x
x
2
4 1
1 1
x x
x x
Example 9
You try! Raise your hand when you are done! First person done with the correct answer
will earn a math buck!$$$
2
5 4 4
y
y y y
5 4
y
y y
5
5
y
y
2 10y
3 10
5 4
y
y y
Example 10
You try! Raise your hand when you are done! First person done with the correct answer
will earn a math buck!$$$
2
16t
222
ttt
2
136
t
t
Example 11
You try! Raise your hand when you are done! First person done with the correct answer
will earn a math buck!$$$
yx
yx
xy 22
3
222222 yxyxyx
22
23
yx
yxyx
Assignment:
Page 448 (2-34) even
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