Download 1 Math 090 Exam 4 Review – Chapter 5 Remember that material

1
Math 090 Exam 4 Review – Chapter 5
Remember that material from earlier exams may be on this exam also – your exams will build on each other!
Section 5.1 Rational Numbers (Fractions)
Rational numbers: numbers that can be written in the form
are integers with b ≠ 0. a is the numerator
Remember:
a
is undefined
0
a
, where a and b
b
b is the denominator
0
0
any number
and
Proper fraction : the absolute value of the numerator is less than the absolute value of the denominator.
Ex.
3
5
3  3 and 5  5 3 < 5 so
3
is a proper fraction.
5
Improper fraction: the absolute value of the numerator is greater than or equal to the absolute
value of the denominator
Ex.
5 7
,
4 7
Mixed number is the sum of a whole number and a fraction
1. True or False:
5
0
0
Change the improper fractions to mixed numbers:
2.
58
5
3.

64
3
Change the mixed numbers to improper fractions:
4.
2
5
6
Ex. 2
3
4
2
5.
3
9
10
Section 5.2 Multiples, Factors, and Prime Factorization
Multiple - a multiple of a number is the product of that number and a natural number
Ex. a multiple of 5 is 2·5 = 10
Factor (divisor) – a number or a variable that is multiplied. Ex. 2 and 3 are factors of 6 since 2 3 = 6.
Some Common Divisibility Rules:
A number is divisible by the following numbers if:
2 If the last digit is even, the number is divisible by 2.
3 If the sum of the digits is divisible by 3, the number is divisible by 3.
5 If the last digit is a 5 or a 0, the number is divisible by 5.
6 If the number is divisible by both 2 and 3, it is also divisible by 6.
9 If the sum of the digits is divisible by 9, the number is divisible by 9.
10 If the number ends in 0, it is divisible by 10.
Prime number – a whole number, greater than 1, with exactly two different factors. These factors are 1 and
the number itself. Ex. 17 is a prime number since the only factors of 17 are 1 and 17
Composite number – a whole number with more than two different factors.
since it has more factors than 1 and 12. 2, 3, 4, and 6 are also factors of 12.
Ex. 12 is a composite number
Prime factorization – the number written as the product of prime factors. Ex. the prime factorization of 12
is 2 2  3
True or False:
6.
69 is a prime number
7. 16 is a composite number
8. 6 is a factor of 156
9. 124 is a multiple of 4
3
List all of the factors of:
10. 84
Write the prime factorization for:
11. 84
Section 5.3 Multiplying and Dividing Fractions
Equivalent fractions – fractions that are different names for the same number
Ex.
4
1
and
8
2
Simplifying a fraction – renaming the fraction by dividing both the numerator and denominator by a
common factor. A fraction is completely simplified when its numerator and denominator have no common
factors other than one. To simplify a fraction, look for common factors of the numerator and the
denominator. Ex.
4
1
can be simplified to by dividing both the numerator and denominator by 4.
8
2
Building a fraction – renaming the fraction by multiplying both the numerator and denominator by a
common factor. Ex.
2x
4x
can be built up to
by multiplying both the numerator and denominator by 2
3
6
Reciprocals – Two rational numbers are reciprocals if they have a product of 1. (To find the reciprocal of a
fraction, switch the numerator and denominator.) Ex. the reciprocal of 
Simplify:
12.
56a 2b
8ab
13.
64 x3 y 4 z 5
20 x 2 y 2 z 3
3
4

4
3
4
Build:
14.
14

7 28
15.
4d

3 12a
Multiply:
16. 
17.
4
26
 7    
13
 8 
 4 x3   15 z 3   2 z 


  5 
 5 z   16   x 
3 
5 
1
2
18. 3   4 
19. Distribute:
9
 2  6
 x x  
4
 3  7
5
Divide:
20.
6  14 
 
7  18 
21. 
4 x2
6x

7 y 21y 4
 6 x5   9 xy 
 
2 
 7 y   18 x 
22.  
23. Brad has a piece of copper wire that is 5
1
inches long. He wants 3 different students to be able to use
2
some of the wire for an experiment. If Brad divides the wire evenly into 3 pieces, how much wire will
each of the students receive?
24. If Loren uses 1
2
cup of water for each batch of chemical solution that he is mixing, how many cups of
3
water will he need to make 7 batches of solution?
Section 5.4 Conversion of Units Within a System
Convert using conversion factors:
25. 3 yards = _______ inches
6
26. 180 seconds = _________ hours
Section 5.5 Adding and Subtracting Rational Numbers (Fractions)
**Note that working with positive and negative signs when adding and subtracting fractions works the same
way as when adding and subtracting integers.
Common denominators – 2 or more fractions have common denominators when they have the same
denominator
Least Common Multiple (LCM) – the smallest natural number for which each number in the set is a divisor.
Least Common Denominator – the least common denominator of 2 or more fractions is the least common
multiple (LCM) of the denominators.
Like Fractions – have the same denominator
Unlike Fractions – have different denominators
Find the LCM:
27.
14, 8
28.
10, 15, 60
Compare (insert <, >, or = ):
29.
11
5
______
14
7
30. 
5
7
______ 
8
12
7
Simplify:
31.
5 1

8 6
32. 2
33. 9
5 3
1
6 8
2
7
5
3
12
34. Combine like terms:
1
5
7
x x x
4
6
8


5
6
35. Find the sum of the polynomials  3 x 
36. Subtract 
2 2
1
y from  y 2
3
3
37. Find the difference of 
2 2
1
y and  y 2
3
3
2 
1 
2
y  and  x  y 
3 
5 
3
8
3
8
38. Jill buys a board that is 18 feet long. She needs a board that is 15 feet long. How much will she need
to cut off the board that she bought?
Section 5.6 Evaluating Expressions and Average (Fractions)
Evaluate:
39. x 2 
x
5
5
for x  , y  
y
6
8
40. x  2 x  y  z  for x  
Find the average:
2
3
41. 3 , 2
42.
1
,
2
5
,
8
3
5
3
4
1
4
1
y=
z
2
5
3
9
Section 5.7 Solving Equations Involving Fractions
Solve:
43.
9
3 4 
x    x
10
4 5 
44.
3
6
3
x  2x   x 
8
4
2
10
Answers to Math 090 Exam 4
Review
1.
False
2. 11
3.
4.
5.
17. 

39
10
6. False, there are other
factors of 69 other than 1
and 69; for example, 3 and
23
7. True, there are factors of
16 other than 1 and 16; for
example, 2 and 8
34.
19.
4 2 3
x  x
7
2
35. 
54
49
21.
2xy 3
37. 
1 2
y
3
22.
12 x6
7 y2
38. 2
5
feet
8
36.
23. Each student would
receive a piece of wire
1
39.
23
36
40.
4
15
5
inches long.
6
2
3
24. He will need 11 cups of
water.
25.
41. 3
108 inches
26.
1
hour
20
2
11. 2  3  7
27.
56
12. 7a
28.
60
29.
>
30.
>
13.
16 xy 2 z 2
5
14.
14 56

7 28
31.
11
24
15.
4d 16ad

3
12a
32.
101
5
4
24
24
16. 7
1 2
y
3

42.
10. 1, 2, 3, 4, 6, 7, 12, 14, 21,
28, 42, 84
19
13
x y
6
15
20.
8. True, since 6  26 = 156
9. True, since 124  4 = 31
7
x
24
81
1
 16
5
5
1
3
17
6
49
1
4
12
12
33.
18.
3
5
21
3z 3
2 x2
2
15
5
8
43. x 
15
2
44. x  12
11