Chp 1 Flashcards
(105 cards)
0
Q
It changes
A
Variable
1
Q
A letter that represents various numbers
A
Variable
2
Q
A letter can stand for just one number
A
Constant
3
Q
There is no equal sign
A
An algebraic equation
4
Q
Consists of variables, constants, numerals, operations signs, and grouping symbols
A
Algebraic expression
5
Q
Replacing a variable with a number we say that’s is
A
Substituting
6
Q
When we replace all of the variables in an expression with numbers and carry out the operations in the expression.
A
Evaluating the expression
7
Q
Explain the steps of this problem:
Evaluate x + y when x = 37 and y = 29
A
- Substitute 37 for x
- Substitute 29 for y
- x + y = 37 + 29 = 66
8
Q
37 + 29 = 66 What number would be the value.
A
66 would be the value
9
Q
How would you evaluate 3y when y = 14
A
Substitute the y for 14
3y = 3 x 14
3 x 14 = 42
10
Q
What is the formula for area of a
rectangle
A
A = lw
11
Q
Find the area when l is 24.5 in. and w is 16 in.
A
- The formula is A = lw
- We substitute 24.5 in for l and 16 in for w
- 24.5 x 16 =
- 392 square inches
12
Q
What is the fraction bar
A
A symbol of division
13
Q
How would you evaluate a/b when a = 63 and b = 9.
A
- Substitute a for 63 and b for 9
- Divide
- 9 divided by 63
- 7
14
Q
How would you evaluate 12m/n when m = 8 and n = 16
A
- Substitute m for 8
- 12 x 8 = 96
- Then substitute n for 16
- 16 / 92 = 6
15
Q
Added to
A
Addition
16
Q
More than
A
Addition
17
Q
Increased by
A
Addition
18
Q
Sum
A
Addition
19
Q
Total
A
Addition
20
Q
Plus
A
Addition
21
Q
Subtract
A
subtraction
22
Q
Subtracted from
A
Subtraction
23
Q
Difference
A
Subtraction
24
Minus
Subtraction
25
Less than
Subtraction
26
Decreased by
Subtraction
27
Take away
Subtraction
28
Product
Multiplication
29
Times
Multiplication
30
Of
Multiplication
31
Divided by
Division
32
Divided by
Division
33
Quotient
Division
34
Translate
| Twice or two times some number
Y x 2, 2 x y, 2 times y or 2y
35
Thirty-eight percent of some number
38%• n, 0.38 x n, 0.38n
36
Seven less than some number
x - 7
| Remember less than some number so x goes first same as it were 10 less than 7
37
Eighteen more than a number
t + 18 or 18 + t
38
A number divided by 5
M/5, or
39
Five more than some number
N + 5, or 5 + n
40
Half of a number
1/2t, t/2,
41
Five more than three times some number
3p + 5 or 5 + 3p
42
The difference of two numbers
x - y
43
Six less than the product of two numbers
mn - 6
44
Seventy-six percent of some number
76%z or 0.76z
45
Four less than twice some number
2x - 4
46
Eight less than some number
x - 8
47
Eight more than some number
8 + n or n + 8
48
Four less than some number
n - 4
49
One-third of some number
1/3 • p or p/3
50
Six more than eight times some number
8x + 6, or 6 + 8x
51
The difference of two numbers
x - y
52
Fifty-nine percent of some number
59%n or 0.59n
53
Two hundred less than the product of two numbers
xy - 200
54
The sum of two number
z + y
55
A collection of objects
A set
56
One way to name a set uses what is called
Roster notation
57
Example of roster notation is
Numbers such as 0, 2, and 5 is {0,2,5}
58
Sets hat are part of other sets are called
Subsets
59
Name the two important subsets of the real numbers
Natural and whole numbers
60
{1, 2, 3, ....} these numbers are the numbers used for counting
Natural numbers
61
{0,1, 2, 3, .......} this is the set of natural numbers and 0.
Thee set of whole numbers
62
Represented on the right of zero on the number line
The natural numbers
63
The natural numbers and zero are
The whole numbers
64
Creating a new set of numbers by starting with the whole numbers 0, 1, 2, 3, and so on is called
Integers
65
Consist of these new numbers and whole numbers
Integers
66
{....,-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,....}
The set of integers
67
Integers to the left of the number line are called
Negative integers
68
Natural numbers are also called
Positive integers
69
Neither positive or negative
Zero
70
-1 and 1 are called
Opposites
71
Is its own opposite
Zero
72
Exy ended infinitely on the number line to the left and right
The integers
73
To create a large number system, we consider quotients of integers with nonzero division. This large number system is called
Rational numbers
74
2/3, 4, -3, 2.4 are
Rational numbers
75
= the set of numbers a/b, where a and b are integers and b is not equal to 0
Rational numbers
76
Means to find and marks its point on the number line
Graph
77
How do you convert to decimal notation
First find the decimal notation for the fraction. 5/8
Second divide
78
Some points on the number line where there is no rational number
Irrational numbers
79
What kinds of numbers are irrational numbers?
Pie and square root
80
Decimal notation for rational numbers
Either terminates or repeats
81
Decimal notation for irrational numbers
Neither terminate nor repeat
82
The rational and irrational numbers together correspond to all the points on the number line and make up what is called the
Real-number system
83
< means
Is less than
84
> means
Is greater than
85
a < b also has the meaning b > a
Order
86
Every true inequality yields?
Another true inequality when we interchange the numbers or the variables and reverse the direction of the inequality sign
87
A number is its distance from zero on the number line. We use the symbol
| x | to represent the absolute value of a number c
Absolute value
88
How do you find the absolute value
If a number is negative, it's absolute value is the opposite
If a number is positive or zero, it's absolute value is the same as the number
89
Explain addition on the number line
To do the addition a + b on he number line, start at 0, move to a, and the move according to b
1. If b is positive, move from a to the right
2. If b is negative, move from a to the left
3. If b is 0, stay at a
90
What are the rules for addition of real numbers
1. Positive numbers: add the same as arithmetic numbers. The answer is positive
2. Negative numbers: add absolute values. The answer is negative
3. A positive and a negative number:
- if the numbers have the same absolute value, the answer is 0
- if the numbers have different absolute values,subtract the smaller absolute value from the larger
- ---if the positive number has the greater absolute value, the answer is positive
- ---if the negative number has the greater absolute value, the answer is negative
4. One number is zero: the sum is the other number
91
For any real Number a. a + 0 = a
Identity property of 0
92
Suppose we wanted to add several numbers, some positive and some negative as follow how would you proceed.
15 + (-2) + 7 + 14 + (-5) + (-12) =
Change the grouping order when adding by grouping the positive numbers and the negative numbers and then add the separately.
Then add or subtract the results.
93
Say we add two numbers that are opposites, such as 6 and -6what is the result
0
94
When opposites are add the result is
Always 0
95
Another name for opposites is called
Additive inverses
96
True or false... Every real number has an opposite, or additive inverse
True
97
Two number whose sum is 0 is called ___________, of each other
Opposites or additive inverses
98
The symbol used for opposites
-
99
A number a can be changed to -a
The opposite of a, or the additive inverse of a
100
The opposite of an opposite is the
Is the number itself.. That is for any number a
-(-a)=a
101
How would you evaluate
-x and -(-x) when x = 16
If x is 16, then -x = -16
If x is 16, then -(-x) = -(-16) =
The opposite of 16 is -16
The opposite of 16 is 16.
102
For any real number a, the _______, or ________, of a denoted -a, is such that
a + (-a) = (-a) + a = 0
Opposite, or additive inverse
103
The difference between a-b is the number c for which a = b + c
Subtraction
104
How do you subtract by adding the opposite?
For any real number a and b
a - b = a + (-b).
To subtract, add the opposite additive inverse, of the number being subtracted.)
This tells us we can turn any subtraction problem into an addition problem
