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Math Flashcards

1
Q

What is the fraction representation of 105/377?

A

105/377

This represents a ratio of two integers.

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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.

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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.

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4
Q

What is the decimal result of dividing 7 by 8?

A

0.875

This division results in a repeating decimal.

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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.

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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.

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7
Q

Convert 125% to decimal.

A

1.25

This conversion is done by dividing the percentage by 100.

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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.

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9
Q

What is the fraction form of 0.876?

A

7/8

This fraction represents the decimal value precisely.

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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.

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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.

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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.

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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.

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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.

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15
Q

Fill in the blank: 144 is a _______ number.

A

composite

This indicates that 144 has factors other than just 1 and itself.

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16
Q

How do you multiply two fractions?

A

Multiply the numerators and multiply the denominators (multiply ‘straight across,’ top and bottom).

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17
Q

What is the product of the numerators and denominators in the example 3/5 x 5/9?

A

15/45

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18
Q

What is the simplified form of 15/45?

A

⅓

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19
Q

What is the reciprocal of a nonzero fraction a/b?

A

b/a

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20
Q

What is the product of a fraction and its reciprocal?

A

1

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21
Q

Fill in the blank: The reciprocal of 3/5 is _______.

A

5/3

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22
Q

True or False: The product of 3/5 and its reciprocal is 1.

A

True

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23
Q

What is the reciprocal of ¾?

A

½

The product of a number and its reciprocal is always 1.

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24
Q

What is the product of ¾ and its reciprocal?

A

1

The product is calculated as ¾ × ½ = 3 × 4 = 12.

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25
Q

Define the least common multiple (LCM).

A

The smallest number that is a multiple of both numbers

For example, the LCM of 2 and 3 is 6.

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26
Q

How do you find the LCM of two numbers?

A

Find the prime factorization of each number

The LCM will be a product of the different factors of both numbers, taking the greatest number of occurrences.

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27
Q

What is the LCM of 2 and 3?

A

6

6 is the smallest number that is a multiple of both 2 and 3.

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28
Q

Fill in the blank: The LCM will occur the ______ number of times it appears in either one of the factorizations.

A

greatest

This ensures that all factors are accounted for in the LCM.

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29
Q

What is the first step to add or subtract fractions with the same denominator?

A

Add or subtract their numerators

The denominator remains the same.

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30
Q

What must you find to add or subtract fractions with different denominators?

A

The least common denominator (LCD)

The least common denominator is the LCM of all the denominators.

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31
Q

To compute 4 + 1 - 7, what is the answer?

A

19 + 3 - 7 - 1 + 2 - 7 - 3

This illustrates the addition and subtraction of fractions.

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32
Q

Fill in the blank: The least common denominator is the _______ of all the denominators.

A

LCM

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33
Q

True or False: To add fractions with the same denominator, you must change the denominators.

A

False

The denominator remains the same when adding or subtracting fractions with the same denominator.

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34
Q

What is the process for adding or subtracting fractions with different denominators?

A

Find the least common denominator, change the fractions, then add or subtract

This ensures that the fractions are compatible for addition or subtraction.

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35
Q

What does LCM stand for in the context of adding fractions?

A

Least Common Multiple

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36
Q

What is the LCM of 15, 21, and 70?

A

210

The least common multiple (LCM) can be verified by multiplying factors: 15 × 14 = 210, 21 × 10 = 210, and 70 × 3 = 210.

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37
Q

Fill in the blank: The LCM of 15, 21, and 70 is _______.

A

210

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38
Q

What operation is used to find the LCM of a set of numbers?

A

Multiplication of their factors

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39
Q

True or False: The LCM of 15, 21, and 70 is a product of their least factors.

A

True

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40
Q

What does LCM stand for?

A

Least Common Multiple

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41
Q

What is the first step in performing arithmetic operations with rational numbers?

A

Identify the rational numbers involved

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42
Q

How can the task of adding a whole number and a fraction be simplified?

A

Multiply the whole number by the denominator and add the numerator

For example, to add 5 and 2/3, multiply 5 by 3 and then add 2.

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43
Q

What is the method to convert a fraction back to mixed-number form?

A

Divide the numerator by the denominator and write the quotient next to the remainder over the denominator

For example, converting 17/3 gives a quotient of 5 and a remainder of 2, resulting in 5 2/3.

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44
Q

What is the process for adding, subtracting, multiplying, and dividing mixed numbers?

A

Convert them to single improper fractions and then perform the operations as usual

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45
Q

Fill in the blank: To convert a mixed number to an improper fraction, you multiply the whole number by the _______ and add the numerator.

A

denominator

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46
Q

True or False: Mixed numbers can be added directly without conversion to improper fractions.

A

False

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47
Q

What is the additive inverse of a number?

A

The negative of a number

The additive inverse of a number is a value that, when added to the original number, results in zero.

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48
Q

What is the additive inverse of 7?

A

-7

The additive inverse of 7 is -7 because 7 + (-7) = 0.

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49
Q

What is the additive inverse of -7?

A

7

The additive inverse of -7 is 7 because -7 + 7 = 0.

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50
Q

What is the result of multiplying two negative integers, -3 and -5?

A

15

-3 × (-5) = -1 × 15 = 15

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51
Q

What happens when you multiply two negative numbers?

A

The result will always be positive

This is because multiplying or dividing two negative numbers involves their absolute values.

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52
Q

What is the result of dividing 27 by -3?

A

-9

27 ÷ (-3) = -9.

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53
Q

To multiply or divide two negative numbers, you multiply or divide their _______.

A

absolute values

The result will always be positive.

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54
Q

What is the result of multiplying -7 x (-8)?

A

56

The multiplication of two negative numbers yields a positive result.

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55
Q

True or False: The additive inverse of a number is always positive.

A

False

The additive inverse is the opposite of the number, which can be negative.

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56
Q

What is a fraction bar also known as?

A

Vinculum

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57
Q

What must be done before dividing in a fraction problem?

A

Perform all calculations above and below the fraction bar

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58
Q

In the example (36 - 6) / (12 + 3), what is the final answer?

A

2

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59
Q

What is often required when dealing with mixed numbers in arithmetic?

A

Convert to a fraction first

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60
Q

Fill in the blank: The TEAS preparation can be supported by searching the internet for _______.

A

order of operations practice

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61
Q

What is the result of the operation -3 x (2) + 2 x 8.23?

A

0.61

The calculation involves performing arithmetic operations with rational numbers.

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62
Q

Fill in the blank: The operation 0.75 - 6.6 + 1646 results in _______.

A

1640.15

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63
Q

What is the first step in solving the expression -3 x (2) + 2 x 8.23?

A

Perform multiplication operations first.

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64
Q

True or False: The expression -5.85 + 1646 can be simplified by adding the two numbers.

A

True

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65
Q

What is the final answer after performing all arithmetic operations in the expression 0.75 - 3 x 2 + 2 x 8.23?

A

0.61

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66
Q

List the arithmetic operations performed in the expression: -3 x (2) + 2 x 8.23.

A
  • Multiplication
  • Subtraction
  • Addition
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67
Q

Fill in the blank: The expression 075 - 3 x 22 + 2 x 8.23 simplifies to _______.

A

-5.85 + 1646

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68
Q

What type of numbers are involved in the operation -3 x (2) + 2 x 8.23?

A

Rational numbers

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69
Q

What is the importance of performing arithmetic operations in the correct order?

A

It ensures accurate results.

70
Q

What does the expression 0.75 - 6.6 + 1646 equal to?

A

1640.15

71
Q

What is the arithmetic operation performed in the example 14.12 × (3.03 - 1.051) + 2.2 × (4.5 + 9.63)?

A

Perform arithmetic operations with rational numbers

The example illustrates the use of multiplication and addition involving rational numbers.

72
Q

What is the first step in the calculation of 14.12 × (3.03 - 1.051)?

A

Calculate the expression inside the parentheses: 3.03 - 1.051

The result of this calculation is essential for the subsequent multiplication.

73
Q

What is the result of the expression 3.03 - 1.051?

A

1.979

This value is used in the multiplication with 14.12.

74
Q

What is the next calculation after finding 1.979 in the expression 14.12 × 1.979?

A

Multiply 14.12 by 1.979

This yields the first part of the overall expression.

75
Q

What is the calculation performed in 2.2 × (4.5 + 9.63)?

A

Calculate the expression inside the parentheses: 4.5 + 9.63

This is followed by multiplying the result by 2.2.

76
Q

What is the result of the expression 4.5 + 9.63?

A

14.13

This value is essential for the multiplication by 2.2.

77
Q

What is the next step after calculating 14.13 in 2.2 × 14.13?

A

Multiply 2.2 by 14.13

This provides the second part of the overall expression.

78
Q

What are the final calculations in the expression 14.12 × 1.979 + 2.2 × 14.13?

A

Add the results of the two multiplications

The final step combines both parts to yield the overall result.

79
Q

What is the final result of the expression 14.12 × 1.979 + 2.2 × 14.13?

A

59.02948

This is the total after performing all calculations.

80
Q

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81
Q

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82
Q

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A
83
Q

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84
Q

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A
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91
Q

= 0.75 - 3 x22 +2 x 8.23

A
92
Q

= 0.75 - 6.6 + 2 × 8.23

A
93
Q

= 0.75 - 6.6 + 16.46

A
94
Q

= -5.85 + 16.46

A
95
Q

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117
Q

What is the purpose of comparing and ordering rational numbers?

A

To understand the relative sizes of positive and negative numbers.

118
Q

What are some examples of true inequalities?

A

0 < 5, 20 > -50, 12 < 13, 10 > 3, -4 < -2, 7 = 7

The last two inequalities are true because the inequality symbols used allow for equality.

119
Q

Why is 7 < 7 or 7 > 7 not true?

A

Because both statements imply that 7 is not equal to itself.

120
Q

How can you visualize the relationship between numbers?

A

By drawing a number line and noting the relative positions of the numbers.

121
Q

What is a helpful way to remember the use of inequality symbols?

A

The large, open end of the symbol faces the larger number, and the small, pointed end points to the smaller number.

122
Q

What is the main technique used to compare rational numbers?

A

We can use the techniques for multiplying by 1 to compare two or more rational numbers.

123
Q

How do you determine which of two fractions is larger?

A

If the fractions have the same denominator, compare the numerators.

124
Q

What is a common denominator?

A

A common denominator is a shared multiple of the denominators of two or more fractions.

125
Q

How do you find the least common denominator?

A

List the multiples of each denominator and find the smallest number that appears in both lists.

126
Q

What are the first few multiples of 7?

A

14, 21, 28, 35, 42, 49, 56, …

127
Q

What are the first few multiples of 8?

A

16, 24, 32, 40, 48, 56, 64, …

128
Q

What is the main technique used to compare rational numbers?

A

We can use the techniques for multiplying by 1 to compare two or more rational numbers.

129
Q

How do you determine which of two fractions is larger?

A

If the fractions have the same denominator, compare the numerators.

130
Q

What is a common denominator?

A

A common denominator is a shared multiple of the denominators of two or more fractions.

131
Q

How do you find the least common denominator?

A

List the multiples of each denominator and find the smallest number that appears in both lists.

132
Q

What are the first few multiples of 7?

A

14, 21, 28, 35, 42, 49, 56, …

133
Q

What are the first few multiples of 8?

A

16, 24, 32, 40, 48, 56, 64, …

134
Q

What is the focus of ATI TEAS SmartPrep 2.0?

A

Math

This includes comparing and ordering rational numbers.

135
Q

What are the multiples of 8?

A

16, 24, 32, 40, 48, 56, 64, …

These are examples of multiples of 8.

136
Q

What is the least common denominator in the example given?

A

56

It is not necessary to find the least common multiple when comparing rational numbers.

137
Q

What is the quickest way to compare rational numbers?

A

Multiply the denominators and use the result as a common denominator.

138
Q

What can be concluded from 49/56 > 48/56?

A

718 > 61.

139
Q

How can you compare three or more rational numbers?

A

Multiply all the denominators to get a common denominator.

140
Q

Order the following from least to greatest: 2/3, 3/4, 5/8.

A

5/8, 2/3, 3/4.

141
Q

What is the objective of M.1.3?

A

Compare and order rational numbers (including positive and negative numbers).

142
Q

How can decimal numbers be ordered?

A

Write the numbers vertically, lining up the decimals.

143
Q

What is the first step in analyzing decimal numbers for order?

A

Analyze the digit with the highest place value.

144
Q

If two numbers start with the same digit in the ones place, what should you compare next?

A

Compare digits in the tenths place.

145
Q

What is the decreasing order of the numbers 3.245, 3.524, and 0.3245?

A

3.524, 3.245, 0.3245.

146
Q

What is the increasing order of the numbers 3.245, 3.524, and 0.3245?

A

0.3245, 3.245, 3.524.

147
Q

How can inequalities be expressed for the numbers 0.3245 and 3.245?

A

0.3245 < 3.245 or 0.3245 ≤ 3.245.

148
Q

What should you do if the numbers are not in decimal form?

A

Divide the fractions or fraction parts to convert them into decimal form.

149
Q

How do you convert 5 ⅖ into decimal form?

A

Divide 2 by 7 to get approximately 0.285714.

150
Q

What is the purpose of algebra?

A

Algebra allows us to deal with unknown quantities using variables, which stand for unknown numbers.

151
Q

What symbol is commonly used for multiplication in algebra?

A

In algebra, multiplication is represented by a dot (•), parentheses, or by placing factors next to each other.

152
Q

What symbols are used for division in algebra?

A

Standard symbols for division include the vinculum (/), either oblique or horizontal, and the obelus (÷).

153
Q

What are the components of an algebraic equation?

A

An algebraic equation consists of terms and mathematical operations.

154
Q

What is a term in algebra?

A

A term is a number, variable, or product of a number and variables, separated by addition and subtraction signs.

155
Q

What is a coefficient?

A

A coefficient is the numeric part of a variable term that is being multiplied by the variable.

156
Q

What is the coefficient of a variable written without a numerical part?

A

A variable written without a numerical part has a coefficient of one.

157
Q

Identify the parts of the algebraic equation 8 - 10x + 2 = 11.

A

Variables: x; Coefficients: -10; Constants: 8, 2, 11.

158
Q

What is a coefficient?

A

A coefficient is the numeric part of a variable term that is being multiplied by the variable.

159
Q

What is the coefficient of x in the term -10x?

A

The coefficient of x in the term -10x is -10.

160
Q

What is the coefficient of a variable that is written without a numerical part?

A

A variable written without a numerical part has a coefficient of one.

161
Q

Identify the parts of the algebraic equation 8 - 10x + 2 = 11.

A

The variable terms are -10x, the coefficients are -10, and the constants are 8, 2, 11.

162
Q

What is a solution in an algebraic equation?

A

A solution is any number(s) that can be substituted for the variable that makes the equation true.

163
Q

What is the solution for the equation 5x = 20?

A

The solution is x = 4, because 5 • 4 = 20.

164
Q

What are the variable term, coefficient, and constant in the equation 5x = 20?

A

The variable term is 5x, the coefficient is 5, and the constant is 20.

165
Q

What is the addition principle in algebra?

A

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
Q

What happens if c is less than 0 in the addition principle?

A

If c < 0, it is equivalent to subtracting c from both sides of the equation.

167
Q

What are the inverse operations of addition?

A

The inverse operation of addition is subtraction.

168
Q

How do you isolate a variable using the addition principle?

A

To isolate a variable, you can add or subtract the same number from both sides of the equation.

169
Q

Solve the equation x + 10 = -4.

A

To isolate x, subtract 10 from both sides: x + 10 - 10 = -4 - 10, resulting in x = -14.

170
Q

What is the goal of M.1.4 in ATI TEAS SmartPrep 2.0?

A

Solve equations with one variable.

171
Q

What is the multiplication principle?

A

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.

Division by c is the same as multiplication by the reciprocal 1/c.

172
Q

How can you solve the equation 2x = 8?

A

You can isolate x by either dividing both sides by 2 or multiplying both sides by the reciprocal of 2 (1/2).

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