Number Systems: Master the Basics of Numbers and Operations

Question 1

Which of the following is a characteristic that does NOT apply to real numbers?

Accepted Answer

The set of real numbers is finite.

Answer

Real numbers are closed under addition.

Answer

Real numbers are closed under multiplication.

Answer

Real numbers are dense.

Question 2

Which of the following best describes a real number?

Accepted Answer

A number that can be plotted on a number line.

Answer

A number that can be written as a fraction.

Answer

A number that cannot be written as a fraction.

Answer

A number that is always positive.

Question 3

Which of the following is NOT a subset of the real number system?

Accepted Answer

Complex numbers

Answer

Integers

Answer

Rational numbers

Answer

Irrational numbers

Question 4

Evaluate the quotient of -12 divided by 4.

Accepted Answer

-3

Answer

-4

Answer

3

Answer

4

Question 5

Which property is NOT applicable to integers?

Accepted Answer

Commutative under multiplication

Answer

Closed under addition

Answer

Additive inverse exists

Answer

Ordered

Question 6

Which number among these is a rational number?

Accepted Answer

-7/3

Answer

π

Answer

√2

Answer

0.1010010001...

Question 7

Which of the following is the absolute value of ||-3|?

Accepted Answer

3

Answer

-3

Answer

1/3

Answer

0

Question 8

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

Accepted Answer

Associative property of division

Answer

Closure under addition

Answer

Closure under multiplication

Answer

Commutative property of addition

Question 9

Find the greatest common factor (GCF) of 12 and 18

Accepted Answer

6

Answer

3

Answer

12

Answer

18

Question 10

What is the additive inverse of -10?

Accepted Answer

10

Answer

0

Answer

-10

Answer

20

Question 11

Convert the following fraction to a decimal: 3/8

Accepted Answer

0.375

Answer

0.625

Answer

0.75

Answer

0.875

Question 12

Which number system includes both rational and irrational numbers?

Accepted Answer

Real numbers

Answer

Integers

Answer

Rational numbers

Answer

Irrational numbers

Question 13

Which of the following is NOT a property of integers?

Accepted Answer

Contain fractions

Answer

Commutative under addition

Answer

Closed under multiplication

Answer

Ordered under the usual ordering

Question 14

Determine the greatest common factor (GCF) of 24 and 36:

Accepted Answer

6

Answer

2

Answer

12

Answer

24

Question 15

Simplify the fraction: (x^2 - 9)/(x + 3)

Accepted Answer

x - 3

Answer

x + 3

Answer

(x - 3)(x + 3)

Answer

(x - 3)/(x + 3)

Question 16

Identify the set of numbers that includes all rational and irrational numbers:

Accepted Answer

Real numbers

Answer

Integers

Answer

Natural numbers

Answer

Whole numbers

Question 17

Find the greatest common factor (GCF) and the least common multiple (LCM) of 24 and 36.

Accepted Answer

GCF: 12, LCM: 72

Answer

GCF: 6, LCM: 72

Answer

GCF: 12, LCM: 84

Answer

GCF: 8, LCM: 60

Question 18

Which of the following is the correct representation of the real number negative four?

Accepted Answer

-4

Answer

4i

Answer

-4i

Answer

4

Question 19

Which of the following is an example of an irrational number?

Accepted Answer

π

Answer

0

Answer

one-half

Answer

√16

Question 20

Simplify the expression: negative two cubed divided by negative two squared.

Accepted Answer

one

Answer

negative two

Answer

negative one

Answer

two

Question 21

Which set of numbers is closed under addition?

Accepted Answer

Rational numbers

Answer

Natural numbers

Answer

Integers

Answer

Irrational numbers

Question 22

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

Accepted Answer

-6

Answer

-10

Answer

-2

Answer

2

Question 23

Find the product of 0.5 and -2/3.

Accepted Answer

-1/6

Answer

-1/3

Answer

1/3

Answer

1/6

Question 24

Which of the following is the equation of a circle with center (0, 0) and radius 5?

Accepted Answer

x^2 + y^2 = 5

Answer

x^2 - y^2 = 5

Answer

x - y = 5

Answer

x + y = 5

Question 25

Which of the following best describes the relationship between rational and irrational numbers?

Accepted Answer

Rational and irrational numbers are disjoint sets.

Answer

Rational numbers are a subset of irrational numbers.

Answer

Irrational numbers are a subset of rational numbers.

Answer

The set of rational numbers is equal to the set of irrational numbers.

Question 26

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

Accepted Answer

Closure under division by zero

Answer

Associativity of multiplication

Answer

Commutativity of addition

Answer

Distributivity of multiplication over addition

Question 27

Which of the following is a non-terminating, non-repeating decimal?

Accepted Answer

√2

Answer

1.414...

Answer

1/2

Answer

0.333...

Question 28

Which of the following is a subset of rational numbers?

Accepted Answer

Integers

Answer

Real numbers

Answer

Irrational numbers

Answer

Imaginary numbers

Question 29

Which of the following is NOT a property of integers?

Accepted Answer

Commutativity of division

Answer

Closure under addition

Answer

Distributivity of multiplication over addition

Answer

Associativity of multiplication

Question 30

Which of the following is a hexadecimal number?

Accepted Answer

FF

Answer

111

Answer

1010

Answer

789

Question 31

Which of the following operations on integers always results in an even number?

Accepted Answer

Multiplying two even integers

Answer

Multiplying an even integer by an odd integer

Answer

Subtracting an even integer from an odd integer

Answer

Adding an even integer and an odd integer

Question 32

Which of the following is NOT a valid integer?

Accepted Answer

1.5

Answer

0

Answer

-10

Answer

100

Question 33

Which of the following is a rational number that can be expressed as a terminating decimal?

Accepted Answer

1/4

Answer

π

Answer

√2

Answer

e

Question 34

Which property is not characteristic of real numbers?

Accepted Answer

Discrete

Answer

Ordered

Answer

Dense

Question 35

Which number system consists of all numbers that can be expressed as a ratio of two integers?

Accepted Answer

Rational numbers

Answer

Real numbers

Answer

Irrational numbers

Answer

Integers

Question 36

Which operation is not closed on the set of rational numbers?

Accepted Answer

Division by zero

Answer

Subtraction

Answer

Multiplication

Answer

Addition

Question 37

Calculate the least common multiple of 12 and 18:

Accepted Answer

36

Answer

6

Answer

18

Answer

12

Question 38

Find the greatest common factor of 15 and 25:

Accepted Answer

5

Answer

3

Answer

1

Answer

15

Question 39

Which number qualifies as a prime number?

Accepted Answer

11

Answer

4

Answer

6

Answer

10

Question 40

Select the statement that accurately describes the number 0:

Accepted Answer

Neither positive nor negative

Answer

Positive

Answer

Negative

Question 41

Which of the following is the set of all real numbers that are greater than 0?

Accepted Answer

Positive real numbers

Answer

Irrational numbers

Answer

Negative real numbers

Answer

Natural numbers

Question 42

Which number is equivalent to 10 to the power of 100?

Accepted Answer

1 followed by 100 zeros

Answer

10 to the power of 10 followed by 10 zeros

Answer

10 to the power of 100 followed by 100 zeros

Answer

100 to the power of 10 followed by 10 zeros

Question 43

What is the smallest positive integer?

Accepted Answer

1

Answer

2

Answer

0

Answer

-1

Question 44

Which of the following is NOT a characteristic of rational numbers?

Accepted Answer

They cannot be expressed as a fraction

Answer

They are terminating or repeating decimals

Answer

They include integers

Answer

They can be expressed as a fraction

Question 45

Which number is irrational?

Accepted Answer

π

Answer

√16

Answer

1/2

Answer

0.75

Question 46

Simplify the numeric expression: (-3) + (+5)

Accepted Answer

2

Answer

-2

Answer

-8

Answer

8

Question 47

What is the value of 3³?

Accepted Answer

27

Answer

81

Answer

18

Answer

9

Question 48

Which of the following is a factor of 12?

Accepted Answer

3

Answer

7

Answer

11

Answer

5

Question 49

Which of the following numbers is classified as irrational?

Accepted Answer

√2

Answer

-7

Answer

5

Answer

1/3

Question 50

What is the decimal representation of the fraction 3/8?

Accepted Answer

0.375

Answer

0.333...

Answer

0.4

Answer

0.25

Question 51

Arrange the following numbers in ascending order: 1.5, -2, 0, -1, 3

Accepted Answer

-2, -1, 0, 1.5, 3

Answer

-1, -2, 0, 1.5, 3

Answer

0, -1, 1.5, -2, 3

Answer

3, 1.5, 0, -1, -2

Question 52

Calculate the product of (-5) and (-3).

Accepted Answer

15

Answer

-15

Answer

-8

Answer

8

Question 53

Which of the following numbers belongs to both the set of integers and the set of rational numbers?

Accepted Answer

-7

Answer

√3

Answer

π

Answer

2.5

Question 54

What is the result of 12 divided by 4?

Accepted Answer

3

Answer

16

Answer

48

Answer

0.333...

Question 55

A number is divisible by 4 if and only if which of the following conditions is true?

Accepted Answer

The last two digits of the number are divisible by 4.

Answer

The number is even.

Answer

The sum of its digits is divisible by 4.

Answer

The units digit of the number is 4.

Question 56

Determine the prime factorization of the number 36.

Accepted Answer

2² x 3²

Answer

3 x 12

Answer

2 x 3 x 6

Answer

6 x 6