### All Algebra II Resources

## Example Questions

### Example Question #11 : Types Of Numbers

What sets do the numbers have in common?

**Possible Answers:**

**Correct answer:**

Step 1: Define the different sets:

Rational: Any number that can be expressed as a fraction (improper/proper form) (example: )

Irrational: Any number whose decimal expansion cannot be written as a fraction. (example: )

Real numbers: The combination of all numbers that belong in the Rational and the Irrational set. (Example: )

Integers: All whole numbers from . (Example: )

Natural Numbers (AKA Counting numbers): All numbers greater than or equal to 1,

Step 2: Let's categorize the numbers given in the question to these sets above:

belongs to the set of rational numbers, natural numbers, and integers.

belongs to the set of rational numbers and integers.

belongs to the set of rational numbers.

Step 3: Analyze each number closely and pull out any sets where all three numbers belong..

All three numbers belong to the set of rational numbers.

In math, we symbolize rational numbers as .

So, all three numbers belong to the sets .

### Example Question #31 : Number Theory

Which of the following are natural numbers?

**Possible Answers:**

**Correct answer:**

The definition of natural numbers states that the number may not be negative, and must be countable where:

Decimal places and fractions are also not allowed.

The value of fifty percent equates to .

The only possible answer is:

### Example Question #13 : Types Of Numbers

Which of the following represents a natural number?

**Possible Answers:**

**Correct answer:**

Natural numbers are numbers can be countable. Natural numbers cannot be negative. They are whole numbers which include zero.

The fraction given is not a natural number.

Notice that the imaginary term can be reduced. Recall that , and . This means that .

The answer is:

### Example Question #11 : Types Of Numbers

Try without a calculator.

True or false:

The set includes only rational numbers.

**Possible Answers:**

True

False

**Correct answer:**

True

A rational number, by definition, is one that can be expressed as a quotient of integers. Each of the fractions in the set - - is such a number. The sole integer, 1, is also rational, since any integer can be expressed as the quotient of the integer itself and 1.

### Example Question #12 : Types Of Numbers

True or false: The set comprises only whole numbers.

**Possible Answers:**

True

False

**Correct answer:**

False

The whole numbers are defined to be 0 and the so-called counting numbers, or *natural* *numbers *1, 2, 3, and so forth. Negative integers and are not included in this set.

### Example Question #34 : Number Theory

Which of the following is a complex number?

**Possible Answers:**

**Correct answer:**

By definition, a complex number is a number with an imaginary term denoted as i.

A complex number is in the form,

where represents the real part of the number and represents the imaginary portion of the complex number.

Therefore, the complex number which is the solution is .

### Example Question #5092 : Algebra Ii

True or false:

The following set comprises only rational numbers:

**Possible Answers:**

False

True

**Correct answer:**

True

By the Quotient of Powers Property,

.

Therefore, each element, the square root of a fraction, can be seen to be the fraction of the square roots of the individual parts. Each numerator and denominator is a perfect square, so each square root is a fraction of integers:

By definition, any integer fraction, being a quotient of integers, is a rational number, so all elements in the set are rational.

### Example Question #13 : Types Of Numbers

True or false:

The following set comprises only imaginary numbers:

**Possible Answers:**

True

False

**Correct answer:**

False

To raise to the power of any positive integer, divide the integer by 4 and note the remainder. The correct power is given according to the table below.

Every element in the set is equal to raised to an even-numbered power, so when each exponent is divided by 4, the remainder will be either 0 or 2. Therefore, each element is equal to either 1 or . Consequently, the set includes *no *imaginary numbers.

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