### All Pre-Algebra Resources

## Example Questions

### Example Question #5 : The Number System

Of the following, which is an irrational number?

**Possible Answers:**

**Correct answer:**

The definition of an irrational number is a number which cannot be expressed in a simple fraction, or a number that is not rational.

Using the above definition, we see that is already expressed as a simple fraction.

any number and

. All of these options can be expressed as simple fractions, making them all rational numbers, and the incorrect answers.

cannot be expressed as a simple fraction and is equal to a non-terminating, non-repeating (ever-changing) decimal, begining with

This is an irrational number and our correct answer.

### Example Question #1 : Irrational Numbers

What do you get when you multiply two irrational numbers?

**Possible Answers:**

Always rational.

Imaginary numbers.

Always irrational.

Sometimes irrational, sometimes rational.

Integers.

**Correct answer:**

Sometimes irrational, sometimes rational.

Let's take two irrationals like and multiply them. The answer is which is rational.

But what if we took the product of and . We would get which doesn't have a definite value and can't be expressed as a fraction.

This makes it irrational and therefore, the answer is sometimes irrational, sometimes rational.

### Example Question #3 : Understand The Difference Between Rational And Irrational Numbers: Ccss.Math.Content.8.Ns.A.1

Which of the following is NOT an irrational number?

**Possible Answers:**

**Correct answer:**

Rational numbers are those which can be written as a ratio of two integers, or simply, as a fraction.

The solution of is , which can be written as . Each of the other answers would have a solution with an infinite number of decimal points, and therefore cannot be written as a simple ratio. They are irrational numbers.

### Example Question #6 : Understand The Difference Between Rational And Irrational Numbers: Ccss.Math.Content.8.Ns.A.1

Which of the following numbers is considered to be an irrational number?

**Possible Answers:**

**Correct answer:**

An irrational number cannot be represented as the quotient of two integers.

Irrational numbers do not terminate and are not repeat numbers.

Looking at the possible answers,

can be reduced to , therefore it is an integer.

by definition is a quotient of two integers and thus it is not an irrational number.

can be rewritten as and by definition is a quotient of two integers and thus it is not an irrational number.

is a terminated decimal and therefore can be written as a fraction. Thus it is not an irrational number.

is the number for and does not terminate, therefore it is irrational.

### Example Question #13 : Irrational Numbers

Add the following:

**Possible Answers:**

**Correct answer:**

To add the numerator, first multiply the denominator to find the least common denominator.

The common denominator is:

Rewrite the fractions.

### Example Question #11 : Irrational Numbers

Which of the following choices is irrational?

**Possible Answers:**

**Correct answer:**

The meaning of irrational states that numbers cannot be rewritten as a ratio of integers. Of the following that could be simplified, the only possible choice of irrational numbers is .

The answer is .

All other options are rational because they can be written as either a fraction of integers or just an integer.

### Example Question #11 : Irrational Numbers

Which of the following is an irrational number?

**Possible Answers:**

**Correct answer:**

A rational number can be put in the form , it can be a terminating decimal, or it can be a repeating decimal. is a continual number, therefore it is an irrational number.

### Example Question #11 : Irrational Numbers

Which of the following is an irrational number?

**Possible Answers:**

**Correct answer:**

An irrational number is any number that cannot be expressed as a ratio of integers.

Therefore, is considered irrational because it cannot be expressed as a ratio of integers.

### Example Question #12 : Irrational Numbers

Which of the following is an irrational number?

**Possible Answers:**

**Correct answer:**

An irrational number is a number that cannot be expressed as a ratio of integers and cannot be expressed as terminating or repeating decimals.

Therefore, the only answer that follows this definition is .

### Example Question #13 : Irrational Numbers

Which of the following is an irrational number?

**Possible Answers:**

**Correct answer:**

A rational number is any number that can be expressed as a fraction where both the numerator and denominator are integers. The denominator also cannot be equal to 0. In this set, the irrational number is because the There is no fraction that can be made, it's decimal goes on and on and does not repeat in a pattern. Using the fraction test, we can prove that the following numbers are rational: