Download Lesson 3-6

Lesson 3-6
Example 1 Add Unlike Fractions
1
2
Find
+ .
4
5
2
1
2 4
1 5
+ =

+ 
Use 4  5 or 20 as the common denominator.
5
4
5 4
4 5
8
5
=
+
Rename each fraction with the common denominator.
20
20
13
=
Add the numerators.
20
Example 2 Add Fractions and Mixed Numbers
Find each sum. Write in simplest form.
5  3
1 1
a.
+ 
Estimate:
- =0
12  8 
2 2
5
5 2  3 3
 3
+   =

+   
The LCD of 12 and 8 is 24.
12  8  12 2  8  3
10
9
=
+
Rename each fraction with the LCD.

24  24 
1
=
Add. Compare to the estimate. Is the answer
24
reasonable?
3  1
+ 1 
Estimate: 3 - 1 = 2
4
 6
3  1  11  7 
2 + 1  =
+  
Write the mixed numbers as improper fractions.
4  6
4
 6
7
11 3  7  2
11
=
 +  
Rename
and 
using the LCD, 12.
6
4 3  6 2
4
33  14 
=
+  
Simplify.
12  12 
19
7
=
or 1 .
Add. Compared to the estimate, the answer is
12
12
b. 2
reasonable.
Example 3 Subtract Fractions and Mixed Numbers
Find each difference. Write in simplest form.
2 11
a.
9 18
2 11
2 2 11
= 
The LCD is 18.
9 18
9 2 18
4 11
=
Rename using the LCD.
18 18
7
=Subtract.
18
b. 5
3
1
-2
8
2
3
43
1
5 -2 =
8
8
2
43
=
8
43
=
8
23
=
8
5
2
5 4

2 4
20
8
7
or 2
8
-
Write as improper fractions.
Rename using the LCD.
Simplify.
Subtract.
Real-World EXAMPLE
Example 4 Use Fractions to Solve a Problem
7
5
3
HIKING
Peter hiked a total of 2 miles. If he hiked 1 miles east, mile south, how
8
8
4
many miles did he hike west?
Explore
You know distance of the total hike, 2
sections of the hike, 1
Plan
Solve
Check
7
miles, and the distance of two
8
5
3
and .
8
4
Add the known distances and subtract that sum from 2
7
.
8
Estimate your answer.
3 – (2 + 1) = 0
5
5
3
6
1 +
=1 +
Rename fractions with the LCD, 8.
8
8
4
8
3
11
=1
or 2
Simplify.
8
8
3
7
4
1
2 - 2 = or
Subtract and simplify.
8
8
8
2
1
Peter hiked miles west.
2
1
Since is close to 0, the answer is reasonable.
2