Master Real Numbers: Properties, Operations, and Absolute Value

Question 1

Which of the following properties does NOT apply to real numbers?

Accepted Answer

Inverse property of division

Answer

Commutative property of addition

Answer

Associative property of multiplication

Answer

Distributive property

Question 2

What is the absolute value of -5?

Accepted Answer

5

Answer

-5

Answer

10

Answer

0

Question 3

Simplify the expression: -2 + (-3) * 4 using the order of operations.

Accepted Answer

-14

Answer

-20

Answer

10

Answer

14

Question 4

Which of the following is a rational number?

Accepted Answer

1/3

Answer

π

Answer

√2

Answer

e

Question 5

Which of the following is NOT a real number?

Accepted Answer

√(-1)

Answer

0

Answer

π/2

Answer

1.234

Question 6

Which of the following statements is true about the sum of two real numbers?

Accepted Answer

The sum of any two real numbers is a real number.

Accepted Answer

The order of addition does not matter.

Accepted Answer

The sum of a real number and its additive inverse is always zero.

Answer

The sum of two positive real numbers is always positive.

Question 7

Evaluate: | -5 | + | 3 |

Accepted Answer

10

Answer

2

Answer

8

Answer

-8

Question 8

Translate the statement 'The distance between x and 5 is less than 3' into a mathematical inequality using absolute value.

Accepted Answer

|x - 5| < 3

Answer

|x - 5| > 3

Answer

|5 - x| > 3

Answer

|5 - x| < 3

Question 9

Simplify: (x² - 2x + 1) ÷ (x - 1)

Accepted Answer

x - 1

Answer

x + 1

Answer

x - 2

Answer

x + 2

Question 10

Which property of real numbers states that when two real numbers are added, the result is always a real number?

Accepted Answer

Closure under addition

Answer

Associativity of multiplication

Answer

Commutativity of subtraction

Answer

Distributivity of multiplication over addition

Question 11

Evaluate the absolute value of -5 and then add it to the absolute value of 3.

Accepted Answer

10

Answer

2

Answer

8

Answer

15

Question 12

Which of the following is equal to 1/8 in fractional form?

Accepted Answer

1/8

Answer

1/16

Answer

1/32

Answer

1/64

Question 13

Simplify the algebraic expression: (2x - 3)(x + 5)

Accepted Answer

2x^2 + 7x - 15

Answer

2x^2 - 11x - 15

Answer

x^2 + 17x - 15

Answer

x^2 - x - 15

Question 14

Which of the following symbols is **not** used to represent an inequality?

Accepted Answer

=

Answer

<

Answer

>

Answer

≤

Question 15

Which of the following numbers is a rational number?

Accepted Answer

0.123456...

Answer

π

Answer

√2

Answer

e

Question 16

Find the least common multiple (LCM) of 12 and 18.

Accepted Answer

72

Answer

6

Answer

12

Answer

36

Question 17

Which property states that the sum of any real number and 0 is equal to that real number?

Accepted Answer

Additive identity

Answer

Multiplicative identity

Answer

Additive inverse

Answer

Multiplicative inverse

Question 18

Which of the following is NOT a property of real numbers under the operations of addition and multiplication?

Accepted Answer

Closure under subtraction

Answer

Commutative property of addition

Answer

Associative property of multiplication

Answer

Distributive property

Question 19

Simplify the expression: |3 - (-5)|

Accepted Answer

2

Answer

8

Answer

|8|

Answer

|-2|

Question 20

Which of the following is the greatest lower bound of the set {2, 5, 7, 10} under the natural ordering?

Accepted Answer

2

Answer

0

Answer

5

Answer

10

Question 21

Find the value of x that satisfies the equation: 2x - 5 = 15

Accepted Answer

10

Answer

5

Answer

20

Answer

Cannot be determined

Question 22

Which of the following sets is a proper subset of the set of real numbers and contains only irrational numbers?

Accepted Answer

Irrational numbers

Answer

Integers

Answer

Rational numbers

Answer

Imaginary numbers

Question 23

Which of the following is the least common multiple of 6 and 12?

Accepted Answer

24

Answer

2

Answer

6

Answer

12

Question 24

Solve the inequality: 2x + 5 > 15

Accepted Answer

x > 5

Answer

x < 5

Answer

x > -5

Answer

x < -5

Question 25

Find the distance between the points (2, 3) and (-1, 5) using the Euclidean distance formula.

Accepted Answer

8

Answer

3

Answer

5

Answer

10

Question 26

Which of the following is a rational number?

Accepted Answer

5/7

Answer

√2

Answer

π

Answer

e

Question 27

Which property of real numbers states that grouping terms in an addition expression does not affect the value of the sum?

Accepted Answer

Associative property of addition

Answer

Commutative property of addition

Answer

Distributive property of multiplication over addition

Answer

Identity property of addition

Question 28

Which notation represents the set of all real numbers less than but not equal to 5?

Accepted Answer

(5, ∞)

Answer

[5, ∞)

Answer

(∞, 5]

Answer

[5, ∞]

Question 29

Find the least common multiple (LCM) of 12, 18, and 24:

Accepted Answer

72

Answer

6

Answer

12

Answer

36

Question 30

Which of the following is the correct order of the following real numbers from least to greatest: -2, 1.5, 0.5, and -1

Accepted Answer

-2, -1, 0.5, 1.5

Answer

-2, 0.5, -1, 1.5

Answer

-1, -2, 0.5, 1.5

Answer

0.5, -1, -2, 1.5

Question 31

Which of the following statements is NOT a defining property of real numbers?

Accepted Answer

They are closed under division by zero.

Answer

They include all rational and irrational numbers.

Answer

They possess a well-defined distance metric.

Answer

They can be ordered from least to greatest.

Question 32

Find the absolute value of the expression: |-9|

Accepted Answer

9

Answer

0

Answer

18

Answer

-9

Question 33

Identify the operation that is NOT closed under real numbers:

Accepted Answer

Division by zero

Answer

Addition

Answer

Multiplication

Answer

Subtraction

Question 34

Which of the following numbers is NOT rational?

Accepted Answer

π

Answer

0

Answer

√16

Answer

-7/3

Question 35

Which of the following is NOT a property of real numbers?

Accepted Answer

Non-associativity of multiplication

Answer

Distributive property of multiplication over addition

Answer

Closure under addition and multiplication

Answer

Commutativity of addition and multiplication

Question 36

What is the absolute value of 5 - 2?

Accepted Answer

3

Answer

-5

Answer

5

Answer

-3

Question 37

What is the additive identity for real numbers?

Accepted Answer

0

Answer

2

Answer

1

Answer

-1

Question 38

What is the greatest common divisor (GCD) of 12 and 18?

Accepted Answer

6

Answer

3

Answer

2

Answer

12

Question 39

What is the least common multiple (LCM) of 4 and 6?

Accepted Answer

12

Answer

6

Answer

2

Answer

24

Question 40

Which of the following is not a defining property of real numbers?

Accepted Answer

They are closed under multiplication.

Answer

They are ordered.

Answer

They are dense.

Question 41

What is the least upper bound (supremum) of the set of real numbers {2, 3, 4, 5, 6}?

Accepted Answer

6

Answer

4

Answer

5

Question 42

Which of the following is not a subset of the real numbers?

Accepted Answer

The set of imaginary numbers

Answer

The set of irrational numbers

Answer

The set of rational numbers

Answer

The set of integers

Question 43

Simplify the expression (3^2)^-1.

Accepted Answer

1/9

Answer

-9

Answer

9

Answer

3

Question 44

Which of the following is true about the set of real numbers?

Accepted Answer

It is an uncountable set.

Answer

It is a finite set.

Answer

It is a countable set.

Answer

It is an empty set.

Question 45

Find the greatest lower bound (infimum) of the set of real numbers {1, 2, 3, 4}.

Accepted Answer

1

Answer

2

Answer

3

Question 46

Solve the absolute value equation |x - 5| = 2.

Accepted Answer

x = 3 or x = 7

Answer

x = 5 or x = 7

Answer

x = 3 or x = -7

Answer

x = 5 or x = -7

Question 47

Which of the following sets accurately represents the real numbers?

Accepted Answer

The union of the sets of rational and irrational numbers

Answer

The set of rational numbers

Answer

The set of irrational numbers

Answer

The set of integers

Question 48

What is the absolute value of -5?

Accepted Answer

5

Answer

0

Answer

10

Answer

-5

Question 49

Which property of real numbers is illustrated by the equation (a + b) + c = a + (b + c)?

Accepted Answer

Associative Property of Addition

Answer

Distributive Property

Answer

Commutative Property of Addition

Answer

Identity Property of Addition

Question 50

Simplify the product of √2 and √8.

Accepted Answer

4

Answer

2√2

Answer

√10

Answer

√16

Question 51

Solve the absolute value equation |x - 3| = 5.

Accepted Answer

x = 8 or x = -2

Answer

x = 8

Answer

x = 3

Answer

x = -2

Question 52

Which of these is NOT a real number?

Accepted Answer

√-4

Answer

-10

Answer

0.5

Answer

π

Question 53

What is the decimal representation of 1/3?

Accepted Answer

0.333...

Answer

0.33

Answer

0.3

Answer

0.333

Question 54

Which of the following correctly defines a rational number?

Accepted Answer

A fraction p/q, where p and q are integers and q ≠ 0

Answer

Any number that can be written as a decimal

Answer

A number with a repeating decimal

Answer

A number with a terminating decimal

Question 55

What is the additive inverse of 7?

Accepted Answer

-7

Answer

7

Answer

1/7

Answer

0

Question 56

Which statement is TRUE about the set of real numbers?

Accepted Answer

Real numbers are ordered, meaning they can be compared using less than, greater than, or equal to.

Answer

All real numbers are integers.

Answer

Real numbers are all rational.

Answer

Real numbers cannot be negative.