Pre-Algebra : Pre-Algebra

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #961 : Pre Algebra

What happens when you multiply a positive integer with another positive integer?

Possible Answers:

Always a positive integer

Always a negative integer

Sometimes a positive integer

Zero

Sometimes a negative integer

Correct answer:

Always a positive integer

Explanation:

Positive integers start from one onward. No matter what number you multiply with, the answer is always positive and an integer. A positive integer multiplied by a positive integer is always a positive integer. 

Example Question #962 : Pre Algebra

What is a rational number?

Possible Answers:

Only positive and negative integers. 

All real numbers

Imaginary numbers

Any kind of fraction

Two integers that can be expressed in a fraction as long as the denominator is not zero.

Correct answer:

Two integers that can be expressed in a fraction as long as the denominator is not zero.

Explanation:

For a number to be rational, the numerator and denominator have to be integers. The exception is the denominator must not equal zero. It can be negative, positive, or zero. 

Example Question #963 : Pre Algebra

Which is an integer?

Possible Answers:

Correct answer:

Explanation:

Although all the choices have radicals and we know many radicals are irrational numbers, we can definitely simplify one of them.  is a perfect sqaure. The answer to that radical is  is an integer and is our answer. 

Example Question #964 : Pre Algebra

If we divide two rational numbers, what kind of answer do we get?

Possible Answers:

Always rational numbers

Integers

Imaginary numbers

Mostly rational numbers

Always irrational numbers

Correct answer:

Mostly rational numbers

Explanation:

It is true when we divide two rational numbers, we should get a rational number. The exception is when let's say we divide  and . If the denominator is , the answer is undefined. Undefined is a class of its own. This is the only exception so our answer is mostly rational numbers. 

Example Question #27 : Integers And Types Of Numbers

Which of these numbers is not a rational number?

Possible Answers:

Correct answer:

Explanation:

A number is rational if it is possible to express it as a fraction with integers as the numerator and denominator. 25 and -1 are integers, and could be written as fractions: . is already expressed as a fraction. At first glance,

 looks like an irrational number becasue it repeats forever. This is different from an irrational number because an irrational number will go on forever but without a repeating pattern.  could actually be expressed as the fraction . This leaves us with the correct answer of which goes on forever [is non-terminating] but without any clear pattern or repeating part.

Example Question #35 : Number Theory

What is the smallest composite number?

Possible Answers:

Correct answer:

Explanation:

Let's list all the counting numbers which start from 

 is neither prime nor composite. It is a unit; therefore, this answer isn't right. 

 are prime numbers.  A prime number only has factors of one and itself. Thus, these choices are not the correct answer.

 is a composite number. It has factors of . This is the smallest composite number and is our answer. 

 is not the correct answer because it is a composite number with factors of  and it is greater than the composite number . Thus, it cannot be the smallest composite number of the series.

Example Question #965 : Pre Algebra

Which of the following is an irrational number?

Possible Answers:

Correct answer:

Explanation:

Although all of the answers are radicals, many of them can be simplified as they are perfect squares. 

 is simplified to .

 is simplified to 

 is simplified to .

 is simplified to .

Only  is not a perfect square and is irrational. Therefore, it is the correct answer.

Example Question #966 : Pre Algebra

Which is a cubic number?

Possible Answers:

Correct answer:

Explanation:

Cubic number is a number raised to a third power. We should begin by listing the first few cubic numbers. The first few cubic numbers are  or . In doing so, we find that there is a match in our answer set which is 

Example Question #967 : Pre Algebra

What is a composite number?

Possible Answers:

A positive integer with at least one other factor besides one and itself

Negative integers

A positive integer with just factors of one and itself

Cubic numbers

Irrational numbers

Correct answer:

A positive integer with at least one other factor besides one and itself

Explanation:

Composite numbers have at least one factor other than one and itself. For example,  is a composite number. The factors are 

Example Question #968 : Pre Algebra

What do you get when you multiply an even number with an odd number?

Possible Answers:

Irrational number

Even number

Prime number

Imaginary number

Odd number

Correct answer:

Even number

Explanation:

For example, take an even number like  and an odd number like . Their product is  which is an even number. No matter what examples we use; we will find that the answer is always even. Furthermore, it can never be a square number because the multiplicand and multiplier will be two different numbers (one odd and one even).

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