Transcript Document

Chapters 4 and 5 Review
Fractions
a
b
Defn: Numbers that show the number of parts
existing compared to the number of parts in a
whole.
Numerator (a): the top number of a fraction that
describes the number of parts existing.
Denominator (b): the bottom number of the
fraction that describes the number of parts that
make a whole.
Fractions and Mixed Numbers
Write a fraction to represent the shaded portion of each figure.
2
5
5
8
7
12
Fractions and Mixed Numbers
Write a fraction to represent the shaded portion of each figure.
7
10
3
5
5
6
Fractions and Mixed Numbers
Draw and shade each fraction.
3
7
Fractions and Mixed Numbers
Proper Fractions
Defn: A fraction whose numerator is smaller than its
denominator.
Improper Fractions
Defn: A fraction whose numerator is larger than its
denominator.
Mixed Numbers
Defn: A number which is made up of an integer and a
fraction.
Fractions and Mixed Numbers
Classify each of the following fractions:
15
7
23
29
proper
47
33
improper
5
4
9
proper
27
7
mixed number
61
62
85
improper
mixed number
Fractions and Mixed Numbers
Converting Mixed Numbers to Improper Fractions
1. Multiply the denominator by the integer.
2. Add the numerator to the product of the
denominator and the integer.
3. Write the sum as the numerator over the
original denominator.
2  7  5  2  35  2  37
5
7
7
7
7
2  3  6  2  18  2
6
3
3
3
 20
3
Fractions and Mixed Numbers
Converting Mixed Numbers to Improper Fractions
7  10 10  7  100  7  107
10
10
10
10
10
11  12  8  11  96  11  107
8
12
12
12
12
Fractions and Mixed Numbers
Converting Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the integer of the mixed number.
3. The remainder is the numerator over the
original denominator.
9
5
1
 5 9
 5
4
4
 1
5
Fractions and Mixed Numbers
Converting Improper Fractions to Mixed Numbers
2
23
 9 23
9
 18
5
5
 2
9
4
62
 13 62
13
 52
10
10
 4
13
Factors and Simplest Form
Divisibility Tests
1. A whole number is divisible by 2 if the number is even.
354
968
140
2. A whole number is divisible by 3 if the sum of the digits
is divisible by 3.
126 1  2  6  9 (is divisible by 3)
24831  2  4  8  3  1  18 (is divisible by 3)
3. A whole number is divisible by 4 if the last 2 digits are
divisible by 4.
236 (36 is divisible by 4) 10,528(28 is divisible by 4)
Factors and Simplest Form
Divisibility Tests
4. A whole number is divisible by 5 if the number ends in a 0
or a 5.
140
1265
345
5. A whole number is divisible by 6 if it is divisible by both 2
and 3.
126 1  2  6  9 (is divisible by 2 and 3)
24834  2  4  8  3  4  21 (is divisible by 2 and 3)
6. A whole number is divisible by 9 if the sum of the digits is
divisible by 9.
936  9  3  6  18 (is divisible by 9)
Factors and Simplest Form
A Number as a Product of Prime Numbers
Factor Trees
24
24
2
3
12
2
2
6
2
8
3
3

2
3
2 2 23
4
2
2
3
2 2 23  2 3
Factors and Simplest Form
A Number as a Product of Prime Numbers
Factor Trees
72
2
210
36
2 105
2 18
2
21
5
9
3 3
3
2

2  2  2 33 2 3
3
7
2 35 7
Factors and Simplest Form
Simplest Form
Defn: A fraction is in simplest form when the numerator and
denominator have no other common factors other than 1.
30

45
15
2
3
2
2 35

3
335
45
30
5
5
9
3
3
Factors and Simplest Form
Simplest Form
Write in Simplest Form.
49

112
7
77
22227
112
49
7
56
2
28
2
14
2
2
7
7

16
Factors and Simplest Form
Simplest Form
Write in Simplest Form.
64

 common factor is 4
20
16
16
64


5
20
5
Factors and Simplest Form
Simplest Form
Write in Simplest Form.
7a 3
2

common
factor
is
7a
56a 2
a
7a 3
56a 2
8
a

8
Fractions and Simplest Form
Equivalent Fractions – Two Methods
7
21
Are and
equivalent ?
9
27
1. Simplify each fraction.
7
7 21

9 27
9

7 7

9 9
2. Cross Multiply.
7 21
 9  21  7  27

9 27
189  189
Fractions are equivalent.
Fractions and Simplest Form
Equivalent Fractions – Two Methods
6
34
Are
and
equivalent ?
15
85
1. Simplify each fraction.
2. Cross Multiply.
6
34
2  3 2 17



15 85
3  5 5 17
6
34
15  34  6  85

15 85
2 2

5 5
510  510
Fractions are equivalent.
Fractions and Simplest Form
Equivalent Fractions – Two Methods
12
10
Are
and
equivalent ?
39
36
1. Simplify each fraction.
12 10

39 36
12 10

39 36
2 23
25

3 13
2  2 33
5
4

18
13
2. Cross Multiply.
12  36  39 10
432  390
Fractions are not equivalent.
Multiplying and Dividing Fractions
Multiplying Fractions
1. Multiply the numerators.
2. Multiply the denominators.
3. The product of the numerators remains as the
numerator as the product of the denominators remains
as the denominator.
35 
15
3 5 

7  11
77
7 11
1 1 

3 9
1 1
39

1
27
Multiplying and Dividing Fractions
Multiplying Fractions
3
1
6 7  6  7  3 1

11  4
77  8
77 8
11 4
1
4 3  43 

27  8
27 8
9
2
1
1 1
92

3
44
1

18
Multiplying and Dividing Fractions
Multiplying Fractions
4 33
 
11 16
3
1
1 3
4

33

 
1 4
11 16
4
1
1 1
2 3y  2 3y 

3 2
3 2
1
1
1 1 y
1 1
3
 
4

y
Multiplying and Dividing Fractions
Multiplying Fractions
a3 b
 2
2
b a
3
 
4
a3 1
 a b 
b2  a2
a 1
b 1
3
3
3
   
4 4 4
33
43
b
3

a
b
1
27

64
Multiplying and Dividing Fractions
Multiplying Fractions
1 5
1 3 25  1  3  25  1 1  5 
 
6 10 16 2  2 16
6 10 16
2 2
5
64
Multiplying and Dividing Fractions
Dividing Fractions
1. Write the reciprocal of the second fraction (the
divisor).
2. Change the division operator to multiplication.
3. Work the problem as a multiplication problem.
4 2  8

9 1
9
4
8 5  45
8 2


7 1
7 2
7 5
1
4 1

9 2

20
7
Multiplying and Dividing Fractions
Dividing Fractions
5
10 9
10 2
59



 
 
4 2
4 9
4 1
1
45

4
1
3
1
3 1 1 
3y
3 3y
5y   3 
2
2
20
y
4 5y2 45 y
4
y
Multiplying and Dividing Fractions
Dividing Fractions
1
3
2
9
7
2 9 15


1

3

15
45

 
  

   
3 14 7
1 7  7
49
 3 14  15
1 7
3
9
Evaluate the expression x  y, if x   and y  .
4
2
1 1
1
1 1
3 2
3 9

     
6
23
4 9
4 2
2 3
Multiplying and Dividing Fractions
Dividing Fractions
9
9
Is  a solution of the equation 2 x   ? YES
8
4
1 2 9
1 9
9
9
9
 9

 
2         
1 4
4
1 8
4
4
 8
4
9
9
 
4
4
1
3
2
9
7
2 9 15


1

3

15
45

 
  

   
3 14 7
1 7  7
49
 3 14  15
1 7
Multiplying and Dividing Fractions
Dividing Fractions
Hershey Park is located in Pennsylvania. Of its sixty rides,
one-sixth of them are roller coasters. How many roller
coasters are in Hershey Park?
1
of 60
6
10
1 60
1 10
1


 60 
 10 roller coasters
6 1
1 1
6
1