Download Lesson 6 - Adding and Subtracting Unlike Fractions

Lesson 2-6
Example 1 Subtract Unlike Fractions
3  1
Find      . Write in simplest form.
4  3

3  1
3 3  1 4
        
4  3
4 3  3 4
9  4
=    
12  12 
9
4
= 
12 12
94
=
12
5
=
12
The LCD is 2 ∙ 2 ∙ 3 or 12.
Rename each fraction using the LCD.
Subtract 
4
4
by adding its inverse,
.
12
12
Add the numerators.
Simplify.
Example 2 Add Mixed Numbers
5
1
Find  3  2 . Write in simplest form.
8
6
5
1
29 13
3 2   
8
6
8
6
29 3 13 4
  
=
8 3 6 4
87 52

=
24 24
 87  52
=
24
 35
11
or  1
=
24
24
Write the mixed numbers as fractions.
The LCD is 2 ∙ 2 ∙ 2 ∙ 3 or 24.
Rename each fraction using the LCD.
Add the numerators.
Simplify.
Example 3 Estimate the Sum of Mixed Numbers
1 8
1
MULTIPLE-CHOICE TEST ITEM Three books are 2 , 1 , and 2 inches thick. If
3 9
4
these books were stacked one on top of another, what is the total height of the books?
17
17
17
17
A 6
B 8
C 9
D 11
36
36
36
36
Read the Test Item You need to find the sum of three mixed numbers.
Solve the Test Item It would take some time to change each of the fractions to ones with a
common denominator. However, notice that all three of the numbers are about 2. Since 2  3 = 6,
the answer will be about 6. Notice that only one of the choices is close to 6. The answer is A.
Example 4 Evaluate Expressions
3
8
and y =  .
4
9
8
3
Replace x with and y with  .
9
4
ALGEBRA Find the value of x – y if x =
8  3
  
9  4
32  27 
  
=
36  36 
32  ( 27)
=
36
59
23
or 1
=
36
36
x–y =
Rename each fraction using the LCD, 36.
Subtract the numerators.
Simplify.