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Pre-Algebra : Number Theory

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Example Questions

Example Question #6 : The Number System

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

Possible Answers:

$\sqrt{0.25}$

-1.235

3.14159265

$\sqrt{25}$

$\frac{2}{5}$

Correct answer:

3.14159265

Explanation:

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,

$\sqrt{25}$ can be reduced to $\sqrt{25}=\sqrt{5\cdot 5}=5$ , therefore it is an integer.

$\frac{2}{5}$ by definition is a quotient of two integers and thus it is not an irrational number.

$\sqrt{0.25}$ can be rewritten as $\sqrt{\frac{1}{4}}=\frac{1}{2}$ and by definition is a quotient of two integers and thus it is not an irrational number.

-1.235 is a terminated decimal and therefore can be written as a fraction. Thus it is not an irrational number.

3.14159265 is the number for $\pi$ and does not terminate, therefore it is irrational.

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Example Question #13 : Irrational Numbers

Add the following: $\frac{\pi}{e} + \frac{e}{\pi}$

Possible Answers:

$\frac{\pi+e}{e\pi}$

$\frac{\pi^2+e^2}{e\pi}$

$\frac{2\pi+2e}{e\pi}$

$\pi+e$

Correct answer:

$\frac{\pi^2+e^2}{e\pi}$

Explanation:

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

The common denominator is: $e\pi$

Rewrite the fractions.

$\frac{\pi}{e} + \frac{e}{\pi} = \frac{\pi(\pi)}{e(\pi)} + \frac{e(e)}{\pi(e)} = \frac{\pi^2+e^2}{e\pi}$

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Example Question #11 : Irrational Numbers

Which of the following choices is irrational?

Possible Answers:

3.14159

2.718

log(10)

$\sqrt{144}$

$2\pi$

Correct answer:

$2\pi$

Explanation:

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 $2\pi$ .

The answer is $2\pi$ .

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

log(10)=1

$3.14159=\frac{314159}{100000}$

$2.718=\frac{2718}{1000}$

$\sqrt{144}=\pm12$

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Example Question #71 : Number Theory

Which of the following is an irrational number?

Possible Answers:

$\pi$

2.35

$6.3\overline{3}$

$\frac{3}{4}$

Correct answer:

$\pi$

Explanation:

A rational number can be put in the form $\frac{a}{b}$ , it can be a terminating decimal, or it can be a repeating decimal. $\pi$ is a continual number, therefore it is an irrational number.

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Example Question #72 : Number Theory

Which of the following is an irrational number?

Possible Answers:

$\frac{5}{4}$

$\pi$

$10 \frac{4}{5}$

0.8521

$\frac{1}{3}$

Correct answer:

$\pi$

Explanation:

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

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

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Example Question #73 : Number Theory

Which of the following is an irrational number?

Possible Answers:

$\frac{5}{3}$

$\frac{1}{2}$

$\pi$

Correct answer:

$\pi$

Explanation:

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 $\pi$ .

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Example Question #74 : Number Theory

Which of the following is an irrational number?

Possible Answers:

$\sqrt4$

1.56

$\sqrt2$

Correct answer:

$\sqrt2$

Explanation:

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 $\sqrt2$ 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:

$\sqrt4=2=\frac{2}{1}$

$7=\frac{7}{1}$

$1.56=\frac{156}{100}=\frac{39}{25}$

$\sqrt2=1.414213562373095.....$

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Example Question #1 : Number Lines

Which of the following numbers is depicted by the point on the number line?

Number_2

Possible Answers:

$-\frac{3}{2}$

$\frac{3}{2}$

Correct answer:

$-\frac{3}{2}$

Explanation:

The point lies halfway between and , or at -1.5 .

$-1.5=-\frac{3}{2}$

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Example Question #1 : How To Plot Fractions On A Number Line

Plot the fraction $-\frac{7}{3}$ on the number line.

Possible Answers:

Question_11_incorrect_2

Question_11_incorrect_3

Question_11_incorrect_1

Question_11_correct

Correct answer:

Question_11_correct

Explanation:

The fraction $-\frac{7}{3}$ is less than and greater than , so it must fall between those points on the number line. Negative numbers are to the left of while positive numbers are to the right.

$-\frac{7}{3}=-2\frac{1}{3}$

Because $\frac{1}{3}$ is less than $\frac{1}{2}$ , the point must be closer to than .

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Example Question #2 : Number Theory

Find the distance between and on a number line.

Possible Answers:

7.5

10.25

Correct answer:

Explanation:

To find the distance on a number line:

$d=x_{2}-x{{_1}}$

d=11-(-4)

d=11+4

d=15

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Pre-Algebra : Number Theory

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #6 : The Number System

Example Question #13 : Irrational Numbers

Example Question #11 : Irrational Numbers

Example Question #71 : Number Theory

Example Question #72 : Number Theory

Example Question #73 : Number Theory

Example Question #74 : Number Theory

Example Question #1 : Number Lines

Example Question #1 : How To Plot Fractions On A Number Line

Example Question #2 : Number Theory

All Pre-Algebra Resources

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