Transcript 4.6 – Complex Fractions Simplifying Complex Fractions Complex Fraction. Defn: A fraction whose numerator or denominator or both contain fractions. 710 7  11 15 2 3  5 8 x 62 7x6

4.6 – Complex Fractions
Simplifying Complex Fractions
Complex Fraction.
Defn: A fraction whose numerator or denominator or both
contain fractions.
5
7
3
10
9
7

11 15
2 3

5 8
x
6
4
2
3
7x
5
6
4.6 – Complex Fractions
Simplifying Complex Fractions
Simplify.
7y
10
1
5
7y 1

10 5
1
7y 5

10 1
2
7y
2
4.6 – Complex Fractions
Simplifying Complex Fractions
Simplify.
1 1

2 6
3 2

4 3
4 1

6 12
LCD: 6
LCD: 12
2
4 12

6 1
1
1 3 1
 
2 3 6
3 3 2 4
  
4 3 3 4
8
1
8
3 1

6 6
9
8

12 12
4
6
1
12
4.6 – Complex Fractions
Simplifying Complex Fractions
Simplify.
1 1

2 6
3 2

4 3
62
98
Alternate Method
1 1
12  
2 6
3 2
12  
4 3
LCD: 12
8
1
8
12 12

2
6
36 24

4
3
4.6 – Complex Fractions
Simplifying Complex Fractions
Simplify.
3
4
x
 1 LCD: 5
5
3 x 5

4
5
3
4
3
4
x
5
 1
5
5
x 5

5 5
3 5

4 x 5
15
4 x  5
3
4
x 5
5
4.6 – Complex Fractions
Order of Operations and Complex Fractions
Simplify.
2
2
  2
3
4 18

9 9
4
2
9
LCD: 9
14

9
4 2 9
 
9 1 9
4.6 – Complex Fractions
Order of Operations and Complex Fractions
Simplify.
 1 1  5 1 
     
 2 5  8 8 
LCD: 10
 1 5 1 2  6 
      
 2 5 5 2  8 
2  3 
 5
  

 10 10  4 
 3  3 
   
 10  4 
9

40
4.7 – Operations on Mixed Numbers
Multiplying and Dividing
1. Write any whole or mixed number as an improper fraction.
2. Use the multiplication and/or division rules of fraction
accordingly.
1
2
2 11
5 11
11
1 

1
9
3 15
3 15
9
3
5
1
1 3
10 11
55
9
3 2

6
3 4
3 4
6
2
4.7 – Operations on Mixed Numbers
Multiplying and Dividing
8
4
3
15
5
2
3
3 2
7
14
8 19

15 5
1
8 5

15 19
3
8
57
23 31

14
7
2
23 14

7 31
1
46
31
15
1
31
4.7 – Operations on Mixed Numbers
Adding and Subtracting
1. Add or subtract the fraction parts of the mixed numbers.
2. Add or subtract the whole numbers.
3. Simplify the answer.
5
1 5
1
1
2
2
2 
2
2 4
30
6 5
6
6
5
12
2 6
2 LCD: 30
4
4 
4
30
5 6
5
17
6
30
4.7 – Operations on Mixed Numbers
Adding and Subtracting
7
3
9
4
15
5
22
8
15
9
4
15
13
4
15
7
9
15
3 LCD: 15
4
5
7
9
15
3 3
4 
5 3
7
9
15
9
4
15
4.7 – Operations on Mixed Numbers
Adding and Subtracting
7
5
32  16
9
18
7
32
9
5 LCD: 18
 16
18
7 2
32 
9 2
5
 16
18
14
32
18
5
 16
18
9
16
18
1
16
2
4.7 – Operations on Mixed Numbers
Adding and Subtracting
6
1
12  3  2
7
5
12
6
3
7 LCD: 35
1
2
5
12
6 5
3 
7 5
1 7
2 
5 7
12
30
3
35
7
2
35
37
17
35
2
17  1
35
2
18
35
4.7 – Operations on Mixed Numbers
Adding and Subtracting
1
The girth of a beech tree is 23
4
feet.
5
The girth of a maple tree is 19
12
feet.
How much larger is the beech tree than the maple tree?
1
1 3
23
23 
4
4 3
LCD: 12
5
5
 19
 19
12
12
3
23
12
5
 19
12
15
22
12
5
 19
12
10
3
12
5
feet
3
6
4.7 – Operations on Mixed Numbers
Adding and Subtracting
1
A dress design requires 3 yards of material.
7
How many dresses could be made from a bolt of material that contains
44 yards?
1
44  3
7
44 22

1
7
2
44 7

1 22
1
14
1
14 dresses