Download Chapter 2 Review

Math 81 Activity
Your Name
Chapter 2 Review
Date ______
Your team: ______________________________ - ______________________________
______________________________
Chapter 2 - Concepts to know:
LCM & GCF:
LCM uses all factors and largest exponent from prime factorization of two or more
numbers. GCF uses COMMON factors and smallest exponent.
Fractions: parts of a whole.
Mixed numbers
Improper fractions,
Equivalent fractions.
Tip: ALWAYS leave fractions in simplest form.
Attach all work and put all answers on this worksheet. Turn in collaboration work
as well.
A. Practice: Basic Fractions:
Convert to a mixed number:
49
(1)
5
Convert to an improper fraction:
7
(3) 3
11
(2)
67
12
(4) 1
6
13
Find the value of the missing number:
(5)
45 15

?
7
(7) 3 =
(6)
5
?

13 52
9
Reduce to lowest terms using prime factorizations (hint: prime factor).
(8)
140
450
(9)
99
330
Perform the indicated operations. (remember… same denominator just add the
numerators. To add fractions with different denominators you must first find the LCD
and make equivalent fractions)
2
5
7
(10) 5  11  12
3
6
9
(13)
11 1

16 4
(11)
10
7 
  
15
 10 
(14)
8
9

21 35
(12)
5
1
  
8
6
B. Subtracting fraction with borrowing….
Tricks of the trade!
Note: for 15 thru 17, borrowing from the whole number is required.
First: Find the LCD and convert the fractions
THEN borrow from the whole number in the “language” (the denominator) the problem
is speaking… for example :
5
7
a )9  6 
8
8
7
 8 5
b)  8    6 
8
 8 8
13
7
c)8  6 
8
8
6
d )2 
8
3
e)2
4
(this problem is speaking the language of 8ths so in step “b”, 1 was taken from the
8
whole number nine as ’s , which equals 1) Don’t forget to simplify final answer!
8
(15) 8  2
4
5
(16) 5
1
2
3
4
3
(17) Find 11
5
11
decreasedby 2
12
16
B. (Collaboration!) Now… check your answers so far w/ team. Then, create a
subtraction of fractions problem where borrowing is required, solve it, then have
the person to your left try it (and of course get the same answer).
Your problem:
C. Multiplying Fractions and Mixed Numbers
(tip: prime factor and simplify first)
4 14
a.  
21 12
22 72
b.


73 223
2227
c.
 (two two’s and sevens are common factors and eliminated)
2  2 33 7
2
d.

33
2
e.
9
(18)
2
4

3
7
(21) 3
1
5

4
18
(19)
(22) 8
6 8

14 15
(20)
42
26

65
63
3
2
 9
10
5
D. Mixed Operations and Grouping Symbols
Simplify (reduce, when possible):
(23)
(24)
2
3 2 5
3  1 2 6 
 
4




   
8 3 3
4  3  5  5 
(25)
2 6  1
2
10    2   
7 42  50
3
D. Collaboration: Stump your partner! Write your own mixed operations problems. Use
at least three operations and try to stump your partner!
Your Problem:
E. Dividing Mixed Numbers and Fractions: (prime factor and eliminate common
factors)
Note:
a
c
ac


Recall, we can divide across if there is an even division:
b
d
bd
a
c
a d



If there is not an even division, then use:
b
d
b c
(29)
15
5

32
8
(31) 3
6
21

17
34
(30)
16
24

35
25
(32)
7 21

16 24
F. Finding the LCM & GCF
Find the LCM & GCF Steps: Prime factor, list by order w/ exponents, take
appropriate bases down for LCM & GCF. Take appropriate exponents,
multiply.
For example: 8 & 12
8 = 23
12 = 2 2  3
LCM = 23  3 =24 (ALL bases w/ greatest exponents)
GCF = 2 2
= 4 (only common bases w/ least exponents)
(33)
a. 9, 15 and 21
b. 125 & 100
c. 24, 36 and 50
9 =
15 =
21 =
LCM=
GCF =
125 =
100 =
24 =
36 =
50 =
LCM=
GCF =
=
=
LCM =
GCF =
=
=
TO FIND LEAST COMMON MULTIPLE!
Step One – Prime Factor
Step Two – Take ALL bases
Step Three- Take GREATEST exponents for each base.
Step Four – Multiply
TO FIND GREATEST COMMON FACTOR
Step One: Prime Factor
Step Two: Take COMMON Bases
Step Three: Take LEAST exponent for each base
=
=
Practice………
Prime factor…(be smart)
34. 550
7000
1100
420
10  2  5
Tricks of the trade:
100  2 2  5 2
Conversely; 2 4  54  10,000
1000  2 3  5 3
Note the pattern: exponent number = number of zeroes after “1”
So.. be smart! Ex: to prime factor 1500 factor out the 100 –
 15 100
 15  2 2  5 2
 3 5  22  52
 2 2  3  53
Last: If your LCM = 23  3  53  7 DON’T Multiply it all out!
Since 2 3  53  1,000
and 3  7  21
then, 2 3  3  53  7  21,000
Last….
35. Find the LCM and GCF of 1500 and 1400
(with “tricks of the trade” this is much easier!)