Math Flashcards
1
Q
What is the fraction representation of 105/377?
A
105/377
This represents a ratio of two integers.
2
Q
How can 1025.0749 be expressed in sums of powers of tens?
A
1.0 × 10^3 + 0.0 × 10^2 + 2.0 × 10^1 + 5.0 × 10^0 + 0.7 × 10^-1 + 4.9 × 10^-2
This breaks down the number into its constituent parts based on decimal placement.
3
Q
What is the decimal form of 113,076/10,000?
A
11.3076
This result is obtained by moving the decimal point four places to the left.
4
Q
What is the decimal result of dividing 7 by 8?
A
0.875
This division results in a repeating decimal.
5
Q
What is the fraction form of 0.0053?
A
53/10,000
This fraction is simplified from the decimal by recognizing the place value.
6
Q
Convert 74% to a fraction.
A
74/100 Simplified = 3/50
This conversion involves expressing the percentage as a fraction out of 100 and simplifying.
7
Q
Convert 125% to decimal.
A
1.25
This conversion is done by dividing the percentage by 100.
8
Q
How do you convert 0.65 to a percentage?
A
Move decimal two places to the right and add percent symbol
This method converts a decimal to a percentage.
9
Q
What is the fraction form of 0.876?
A
7/8
This fraction represents the decimal value precisely.
10
Q
What is the prime factorization of 144?
A
2 x 2 x 2 x 2 x 3
The prime factorization indicates that 144 can be expressed as the product of prime numbers.
11
Q
What is the lowest prime number that divides 144 with zero remainder?
A
2
The factorization process starts with the lowest prime number, which in this case is 2.
12
Q
What do we call numbers that have factors other than one and itself?
A
Composite numbers
144 is classified as a composite number because it has multiple prime factors.
13
Q
What is the next prime number after 2 that divides 9?
A
3
9 is not divisible by 2, but it can be divided by 3.
14
Q
True or False: The prime factorization process can end with a prime number.
A
True
In this case, after dividing by 3, the quotient is 3, which is a prime number.
15
Q
Fill in the blank: 144 is a _______ number.
A
composite
This indicates that 144 has factors other than just 1 and itself.
16
Q
How do you multiply two fractions?
A
Multiply the numerators and multiply the denominators (multiply ‘straight across,’ top and bottom).
17
Q
What is the product of the numerators and denominators in the example 3/5 x 5/9?
A
15/45
18
Q
What is the simplified form of 15/45?
A
⅓
19
Q
What is the reciprocal of a nonzero fraction a/b?
A
b/a
20
Q
What is the product of a fraction and its reciprocal?
A
1
21
Q
Fill in the blank: The reciprocal of 3/5 is _______.
A
5/3
22
Q
True or False: The product of 3/5 and its reciprocal is 1.
A
True
23
Q
What is the reciprocal of ¾?
A
½
The product of a number and its reciprocal is always 1.
24
Q
What is the product of ¾ and its reciprocal?
A
1
The product is calculated as ¾ × ½ = 3 × 4 = 12.
25
Define the least common multiple (LCM).
The smallest number that is a multiple of both numbers
## Footnote
For example, the LCM of 2 and 3 is 6.
26
How do you find the LCM of two numbers?
Find the prime factorization of each number
## Footnote
The LCM will be a product of the different factors of both numbers, taking the greatest number of occurrences.
27
What is the LCM of 2 and 3?
6
## Footnote
6 is the smallest number that is a multiple of both 2 and 3.
28
Fill in the blank: The LCM will occur the ______ number of times it appears in either one of the factorizations.
greatest
## Footnote
This ensures that all factors are accounted for in the LCM.
29
What is the first step to add or subtract fractions with the same denominator?
Add or subtract their numerators
## Footnote
The denominator remains the same.
30
What must you find to add or subtract fractions with different denominators?
The least common denominator (LCD)
## Footnote
The least common denominator is the LCM of all the denominators.
31
To compute 4 + 1 - 7, what is the answer?
19 + 3 - 7 - 1 + 2 - 7 - 3
## Footnote
This illustrates the addition and subtraction of fractions.
32
Fill in the blank: The least common denominator is the _______ of all the denominators.
LCM
33
True or False: To add fractions with the same denominator, you must change the denominators.
False
## Footnote
The denominator remains the same when adding or subtracting fractions with the same denominator.
34
What is the process for adding or subtracting fractions with different denominators?
Find the least common denominator, change the fractions, then add or subtract
## Footnote
This ensures that the fractions are compatible for addition or subtraction.
35
What does LCM stand for in the context of adding fractions?
Least Common Multiple
36
What is the LCM of 15, 21, and 70?
210
## Footnote
The least common multiple (LCM) can be verified by multiplying factors: 15 × 14 = 210, 21 × 10 = 210, and 70 × 3 = 210.
37
Fill in the blank: The LCM of 15, 21, and 70 is _______.
210
38
What operation is used to find the LCM of a set of numbers?
Multiplication of their factors
39
True or False: The LCM of 15, 21, and 70 is a product of their least factors.
True
40
What does LCM stand for?
Least Common Multiple
41
What is the first step in performing arithmetic operations with rational numbers?
Identify the rational numbers involved
42
How can the task of adding a whole number and a fraction be simplified?
Multiply the whole number by the denominator and add the numerator
## Footnote
For example, to add 5 and 2/3, multiply 5 by 3 and then add 2.
43
What is the method to convert a fraction back to mixed-number form?
Divide the numerator by the denominator and write the quotient next to the remainder over the denominator
## Footnote
For example, converting 17/3 gives a quotient of 5 and a remainder of 2, resulting in 5 2/3.
44
What is the process for adding, subtracting, multiplying, and dividing mixed numbers?
Convert them to single improper fractions and then perform the operations as usual
45
Fill in the blank: To convert a mixed number to an improper fraction, you multiply the whole number by the _______ and add the numerator.
denominator
46
True or False: Mixed numbers can be added directly without conversion to improper fractions.
False
47
What is the additive inverse of a number?
The negative of a number
## Footnote
The additive inverse of a number is a value that, when added to the original number, results in zero.
48
What is the additive inverse of 7?
-7
## Footnote
The additive inverse of 7 is -7 because 7 + (-7) = 0.
49
What is the additive inverse of -7?
7
## Footnote
The additive inverse of -7 is 7 because -7 + 7 = 0.
50
What is the result of multiplying two negative integers, -3 and -5?
15
## Footnote
-3 × (-5) = -1 × 15 = 15
51
What happens when you multiply two negative numbers?
The result will always be positive
## Footnote
This is because multiplying or dividing two negative numbers involves their absolute values.
52
What is the result of dividing 27 by -3?
-9
## Footnote
27 ÷ (-3) = -9.
53
To multiply or divide two negative numbers, you multiply or divide their _______.
absolute values
## Footnote
The result will always be positive.
54
What is the result of multiplying -7 x (-8)?
56
## Footnote
The multiplication of two negative numbers yields a positive result.
55
True or False: The additive inverse of a number is always positive.
False
## Footnote
The additive inverse is the opposite of the number, which can be negative.
56
What is a fraction bar also known as?
Vinculum
57
What must be done before dividing in a fraction problem?
Perform all calculations above and below the fraction bar
58
In the example (36 - 6) / (12 + 3), what is the final answer?
2
59
What is often required when dealing with mixed numbers in arithmetic?
Convert to a fraction first
60
Fill in the blank: The TEAS preparation can be supported by searching the internet for _______.
order of operations practice
61
What is the result of the operation -3 x (2) + 2 x 8.23?
0.61
## Footnote
The calculation involves performing arithmetic operations with rational numbers.
62
Fill in the blank: The operation 0.75 - 6.6 + 1646 results in _______.
1640.15
63
What is the first step in solving the expression -3 x (2) + 2 x 8.23?
Perform multiplication operations first.
64
True or False: The expression -5.85 + 1646 can be simplified by adding the two numbers.
True
65
What is the final answer after performing all arithmetic operations in the expression 0.75 - 3 x 2 + 2 x 8.23?
0.61
66
List the arithmetic operations performed in the expression: -3 x (2) + 2 x 8.23.
* Multiplication
* Subtraction
* Addition
67
Fill in the blank: The expression 075 - 3 x 22 + 2 x 8.23 simplifies to _______.
-5.85 + 1646
68
What type of numbers are involved in the operation -3 x (2) + 2 x 8.23?
Rational numbers
69
What is the importance of performing arithmetic operations in the correct order?
It ensures accurate results.
70
What does the expression 0.75 - 6.6 + 1646 equal to?
1640.15
71
What is the arithmetic operation performed in the example 14.12 × (3.03 - 1.051) + 2.2 × (4.5 + 9.63)?
Perform arithmetic operations with rational numbers
## Footnote
The example illustrates the use of multiplication and addition involving rational numbers.
72
What is the first step in the calculation of 14.12 × (3.03 - 1.051)?
Calculate the expression inside the parentheses: 3.03 - 1.051
## Footnote
The result of this calculation is essential for the subsequent multiplication.
73
What is the result of the expression 3.03 - 1.051?
1.979
## Footnote
This value is used in the multiplication with 14.12.
74
What is the next calculation after finding 1.979 in the expression 14.12 × 1.979?
Multiply 14.12 by 1.979
## Footnote
This yields the first part of the overall expression.
75
What is the calculation performed in 2.2 × (4.5 + 9.63)?
Calculate the expression inside the parentheses: 4.5 + 9.63
## Footnote
This is followed by multiplying the result by 2.2.
76
What is the result of the expression 4.5 + 9.63?
14.13
## Footnote
This value is essential for the multiplication by 2.2.
77
What is the next step after calculating 14.13 in 2.2 × 14.13?
Multiply 2.2 by 14.13
## Footnote
This provides the second part of the overall expression.
78
What are the final calculations in the expression 14.12 × 1.979 + 2.2 × 14.13?
Add the results of the two multiplications
## Footnote
The final step combines both parts to yield the overall result.
79
What is the final result of the expression 14.12 × 1.979 + 2.2 × 14.13?
59.02948
## Footnote
This is the total after performing all calculations.
80
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82
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83
Answer:
84
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92
= 0.75 - 6.6 + 2 × 8.23
93
= 0.75 - 6.6 + 16.46
94
= -5.85 + 16.46
95
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117
What is the purpose of comparing and ordering rational numbers?
To understand the relative sizes of positive and negative numbers.
118
What are some examples of true inequalities?
0 < 5, 20 > -50, 12 < 13, 10 > 3, -4 < -2, 7 = 7
## Footnote
The last two inequalities are true because the inequality symbols used allow for equality.
119
Why is 7 < 7 or 7 > 7 not true?
Because both statements imply that 7 is not equal to itself.
120
How can you visualize the relationship between numbers?
By drawing a number line and noting the relative positions of the numbers.
121
What is a helpful way to remember the use of inequality symbols?
The large, open end of the symbol faces the larger number, and the small, pointed end points to the smaller number.
122
What is the main technique used to compare rational numbers?
We can use the techniques for multiplying by 1 to compare two or more rational numbers.
123
How do you determine which of two fractions is larger?
If the fractions have the same denominator, compare the numerators.
124
What is a common denominator?
A common denominator is a shared multiple of the denominators of two or more fractions.
125
How do you find the least common denominator?
List the multiples of each denominator and find the smallest number that appears in both lists.
126
What are the first few multiples of 7?
14, 21, 28, 35, 42, 49, 56, ...
127
What are the first few multiples of 8?
16, 24, 32, 40, 48, 56, 64, ...
128
What is the main technique used to compare rational numbers?
We can use the techniques for multiplying by 1 to compare two or more rational numbers.
129
How do you determine which of two fractions is larger?
If the fractions have the same denominator, compare the numerators.
130
What is a common denominator?
A common denominator is a shared multiple of the denominators of two or more fractions.
131
How do you find the least common denominator?
List the multiples of each denominator and find the smallest number that appears in both lists.
132
What are the first few multiples of 7?
14, 21, 28, 35, 42, 49, 56, ...
133
What are the first few multiples of 8?
16, 24, 32, 40, 48, 56, 64, ...
134
What is the focus of ATI TEAS SmartPrep 2.0?
Math
## Footnote
This includes comparing and ordering rational numbers.
135
What are the multiples of 8?
16, 24, 32, 40, 48, 56, 64, ...
## Footnote
These are examples of multiples of 8.
136
What is the least common denominator in the example given?
56
## Footnote
It is not necessary to find the least common multiple when comparing rational numbers.
137
What is the quickest way to compare rational numbers?
Multiply the denominators and use the result as a common denominator.
138
What can be concluded from 49/56 > 48/56?
718 > 61.
139
How can you compare three or more rational numbers?
Multiply all the denominators to get a common denominator.
140
Order the following from least to greatest: 2/3, 3/4, 5/8.
5/8, 2/3, 3/4.
141
What is the objective of M.1.3?
Compare and order rational numbers (including positive and negative numbers).
142
How can decimal numbers be ordered?
Write the numbers vertically, lining up the decimals.
143
What is the first step in analyzing decimal numbers for order?
Analyze the digit with the highest place value.
144
If two numbers start with the same digit in the ones place, what should you compare next?
Compare digits in the tenths place.
145
What is the decreasing order of the numbers 3.245, 3.524, and 0.3245?
3.524, 3.245, 0.3245.
146
What is the increasing order of the numbers 3.245, 3.524, and 0.3245?
0.3245, 3.245, 3.524.
147
How can inequalities be expressed for the numbers 0.3245 and 3.245?
0.3245 < 3.245 or 0.3245 ≤ 3.245.
148
What should you do if the numbers are not in decimal form?
Divide the fractions or fraction parts to convert them into decimal form.
149
How do you convert 5 ⅖ into decimal form?
Divide 2 by 7 to get approximately 0.285714.
150
What is the purpose of algebra?
Algebra allows us to deal with unknown quantities using variables, which stand for unknown numbers.
151
What symbol is commonly used for multiplication in algebra?
In algebra, multiplication is represented by a dot (•), parentheses, or by placing factors next to each other.
152
What symbols are used for division in algebra?
Standard symbols for division include the vinculum (/), either oblique or horizontal, and the obelus (÷).
153
What are the components of an algebraic equation?
An algebraic equation consists of terms and mathematical operations.
154
What is a term in algebra?
A term is a number, variable, or product of a number and variables, separated by addition and subtraction signs.
155
What is a coefficient?
A coefficient is the numeric part of a variable term that is being multiplied by the variable.
156
What is the coefficient of a variable written without a numerical part?
A variable written without a numerical part has a coefficient of one.
157
Identify the parts of the algebraic equation 8 - 10x + 2 = 11.
Variables: x; Coefficients: -10; Constants: 8, 2, 11.
158
What is a coefficient?
A coefficient is the numeric part of a variable term that is being multiplied by the variable.
159
What is the coefficient of x in the term -10x?
The coefficient of x in the term -10x is -10.
160
What is the coefficient of a variable that is written without a numerical part?
A variable written without a numerical part has a coefficient of one.
161
Identify the parts of the algebraic equation 8 - 10x + 2 = 11.
The variable terms are -10x, the coefficients are -10, and the constants are 8, 2, 11.
162
What is a solution in an algebraic equation?
A solution is any number(s) that can be substituted for the variable that makes the equation true.
163
What is the solution for the equation 5x = 20?
The solution is x = 4, because 5 • 4 = 20.
164
What are the variable term, coefficient, and constant in the equation 5x = 20?
The variable term is 5x, the coefficient is 5, and the constant is 20.
165
What is the addition principle in algebra?
The addition principle states that in a true equation where a = b, adding any number c to both sides results in a true equation: a + c = b + c.
166
What happens if c is less than 0 in the addition principle?
If c < 0, it is equivalent to subtracting c from both sides of the equation.
167
What are the inverse operations of addition?
The inverse operation of addition is subtraction.
168
How do you isolate a variable using the addition principle?
To isolate a variable, you can add or subtract the same number from both sides of the equation.
169
Solve the equation x + 10 = -4.
To isolate x, subtract 10 from both sides: x + 10 - 10 = -4 - 10, resulting in x = -14.
170
What is the goal of M.1.4 in ATI TEAS SmartPrep 2.0?
Solve equations with one variable.
171
What is the multiplication principle?
In a true equation where a = b, multiplying both sides by any number c results in a true equation: a * c = b * c. This also applies to division by a nonzero number.
## Footnote
Division by c is the same as multiplication by the reciprocal 1/c.
172
How can you solve the equation 2x = 8?
You can isolate x by either dividing both sides by 2 or multiplying both sides by the reciprocal of 2 (1/2).
