Download Unit 6 Study Guide - HCBE AC MATH 6

Name ________________________________________
Unit 3: Expressions Study Guide Answer Key
Vocabulary:
1. _Term______: A number, variable, product, or quotient in an expression. A term is not a sum or
difference.
2. __Numerical Expression_: A mathematical statement including numbers and operations.
3. __Algebraic Expression_: A group of numbers, symbols, and variables that express an operation or
a series of operations.
4. _Coefficient_: A numerical factor in a term of an algebraic expression.
5__distributive Property_: a × (b + c) = (a × b) + (a × c) and a × (b – c) = (a × b) – (a × c), where a, b, and
c stand for any real numbers.
6. _Exponent_: The number that tells how many equal factors there are.
7. __Expression: A variable or combination of variables, numbers, and symbols that represents a
mathematical relationship.
8. _Variable_: A quantity that changes or can have different values. A symbol, usually a letter, that
can stand for a variable quantity.
9. _Constant__: A number with a value that is always the same.
10. _Order of Operations_: Rules describing what sequence to use in evaluating expressions. (1)
Evaluate within grouping symbols. (2) Do powers or roots. (3) Multiply or divide left to right. (4) Add or
subtract left to right.
11._Like Terms_: Terms whose variables (and their exponents such as the 2 in x2) are the same.
12. __Communitive Property of Addition_: The sum stays the same when the order of the addends is
changed. a + b = b + a, where a and b are any real numbers.
13. Communtiative Property of Multiplication_: The product stays the same when the order of the
factors is changed. a x b = b x a, where a and b are any real numbers.
14. _Associative property of addition__: The sum stays the same when the grouping of addends is
changed. (a + b) + c = a + (b + c), where a, b, and c stand for any real numbers.
15. _Associative property of multiplication_: The product stays the same when the grouping of factors
is changed. (a x b) x c = a x (b x c), where a, b, and c stand for any real numbers.
16. _Evaluate_: To find the value of a mathematical expression.
17. _Substitution_: The replacement of the letters in an algebraic expression with known values.
Part A: Order of Operations/Computing with Negative and Positive
Fractions and Decimals
Simplify the following:
1 2
1
3
2
3
÷ = -5/16 19) 3 + (-2 ) + 1 + 2 = 4 1/2
8
5
6
4
6
4
21) -27.629 + 16.83 = -10.799
18)
22) -38.89 + (-52.521) =-91.411
23) -5.7 * -8.4 =47.88
25) 23.35 + (-11.05) +20 – 1.65 + 11.05 =41.7
27)
24
+ 16 – 12 ÷ 3 + (-3 - 5) 2 =84
3
20)
26) (
5
3
÷
= 25/36
12
5
24) 0.53 * -8.46 =-4.4838
3
3
 10
x
)x
=-3/7
7
10
3
28) 22 · 2÷4 + (-7- 3) 2 + 3(7 – 2) 2 =186
Name ________________________________________
Part B: Numerical Expressions
29. Is the value of 3 ·3 ·3· 3· 3· 3 the same as the value of 3 5 ? Explain No, it is to the 6th power not 5th
30. Explain the 2 different uses of the symbol “-“ in numerical expressions. One is a sign the other is
subtraction
31. Write using an exponent: 4 ·4 ·4 ·4· 4· 4· 4= 4 to the 7th power
32. Simplify the following:
a. 6 3 =-216
b. -12 4 = 20736
33. Write an expression to represent each problem. Then simplify it.
a. The bill for a dinner was $80.00, including tax and tip. One of the diners had a coupon for
$25.00 toward the dinner. The five diners then split the remaining bill equally. How much did
each diner have to pay? 11 each, 80-25/5
b. A piece of wood that is 9 feet long is cut in half lengthwise. Each half is then cut lengthwise
into six congruent pieces of wood. What is the length of each of the tweleve small pieces of
wood? ¾ or .75
Part C: Algebraic Expressions/Translating Expressions
34. Write an algebraic expression for the following situation:
There are x frogs and 2 lizards. What is the total? X + 2
35. There are 16 children on the bus. C of them got off the bus at the first stop. Write an algebraic
expression to represent the total number of children left on the bus. 16 - c
36. Johnny’s mother exercises on a stair-step machine. She exercises at the same rate for the entire
time. For every minute she exercises, she burns 9 calories. Write an expression to represent the
number of calories she burns after x minutes. 9x
37. Write an algebraic expression for the following.
a) nine less than g = g-9
b) k divided by five =k/5
c) twenty more than twice c= 2c + 20
d) The product of 5 and the sum of y and 2 = 5(y +2)
38. Write the expression in words for the following. Look at these!
e) 7z
f) n - 3
g) 36  m
h) 100 ÷ (6 + w)
i) 8k – 14
Name ________________________________________
Use the expression below to answer the following.
7x2 + 4xy + 10y + 3
39. How many terms are in the expression? 4
40. Name the terms. positive 7xsquared, positive 4xy, positive 10y, positive 3
41. Identify the constant.3
42. Identify the variable(s). xsquared, xy, y
43. Identify the exponent. xsquared
44. Identify the coefficient(s). 7, 4, 10
Evaluate the expression to find the missing values in the table.
45.
y
1
2
3
4
5
y2 + 3
4
7
12
19
28
Evaluate the following expressions.
46.
12
+ 7m for n = 6 and m = 4= 30
n
47. r2 + 15k for r = 15 and k = 5= 300
49. 32b – 3c – 5 for b = 0.5 and c = 1.5 = -34
50. 10w + 9x – 4 for w = 3
1
2
and x = = 37
2
3
51. Complete the table. Substitute the value on the left for the variable in the expression at
the top of each column. Then evaluate each expression.
t = 1.7
t = 2.04
t+2
3.7
4.04
2t - 1
2.4
3.08
2(t – 1)
1.4
2.08
2(2t)
6.8
8.16
52. In the algebraic expression 7÷ y, what is the coefficient of y? Explain: positive 1 any
variable with no number in front is positive 1
Name ________________________________________
Part D: Combining Like Terms
Identify the like terms in the following expressions.
53. 7x + 12x – 7 (7x, 12x)
54. 21 – 10t + 9 – 2t (-10t, -2t) and (21, 9)
55. –d + b + 2t – 4 (none)
56. -3 + x – 4x + 9 (-3, 9) and (x, -4x)
57. -6k + 10 – 4k (-6k, -4k)
Combine the like terms in the following expressions.
58. 2x 2 + 2x +1 + x 2 + 4x +5 = 3xsquared+6x+6
59. -3x 2 + x – 2x 2 + 4= -5xsquared+x+4
60. (x 2 - 3x – 2) – (4x 2 + 3x – 3)= -3xsquared-6x+1
Simplify the following expressions
61. 5x + 3(4- x)= 17x
62.
1
(8 + 3x) – x = 4 + 1/2x
2
63. 12(x + 3) + 4(2x – 5)= 20x+16
64. -7.6s – 1.5(8s – 20)= -19.6s+30
65.
13
1 1
3
x + - x + = 11/4 x+7/8
4
8 2
4
66. -7 (-v + 4)= 7v-28
67. -5( -w – 8)= 5w+40
68. Explain why you should perform the distributive property in the expression 4x + 3(2x + 1) before
simplifying it any other way. Then simplify. =10x+3
A. Rewrite each expression using the distributive property. B. Then simplify.
69. 4z + (-5z)= z(4 -5) = -z
Name ________________________________________
70. 5.8y – 7.2y + 8= 2(2.9y- 3.6y+4)= -1.4y+8
71. 40a – 24b=8(5a-3b)= cannot combine
72. -7c + (-2c)= c(-7-2)= -9c
73. 4 + 8m= 4(1+2m)= can not combine
Write an expression equivalent to each of the following.
74. 4a- 16a= 4a(1-4) or 2a(2-8)
75. y – 10y= y(1-10)
76.
1
(9g – 2)= 3g-2/3
3
77. Are these two expressions equivalent for each of the following? Explain your answer.
a. 4(x +8) and 4x +18 +14= no
b. 7(x + 2y) and 14x + 14y= no
c. 3c – 9d and 3(c – 3d)= yes
78. Use the GCF to write an equivalent expression for each expression.
a. 2y + 4= 2(y+2)
b. 10c – 15= 5(2c-3)
c. 24x – 40y= 8(3x-5y)
79. Prove that the two expressions in the table are equivalent using the given values of x.
Value of x
0
1
2
3
Value of expression 3(x +4)
12
15
18
21
Value of expression 3x + 12
12
15
18
21
Name ________________________________________