### All Pre-Algebra Resources

## Example Questions

### Example Question #31 : Integers And Types Of Numbers

What is a composite number?

**Possible Answers:**

Cubic numbers

A positive integer with just factors of one and itself

Negative integers

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

Irrational numbers

**Correct answer:**

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

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

### Example Question #41 : Number Theory

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

**Possible Answers:**

Prime number

Irrational number

Imaginary number

Even number

Odd number

**Correct answer:**

Even number

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).

### Example Question #32 : Integers And Types Of Numbers

What kind of number is ?

**I. **rational

**II. **irrational

**III. **integer

**IV. **imaginary

**V. **composite

**Possible Answers:**

**I, III, V**

**III** and** V **only

**I ** and** III **only

**II **only

**II, IV**

**Correct answer:**

**I, III, V**

Even though it's a radical, we can simplify.

Check the answer.

The answer is .

is an integer and a composite number with factors of . Furthermore, it can be expressed a rational number .

Thus, the final answer is **I, III, V**.

### Example Question #43 : Number Theory

Which is a square number?

**Possible Answers:**

**Correct answer:**

Square numbers have one factor. If that factor is multiplied by itself, then the number becomes a perfect square. The only number in the selection that meets this requirement is . We can multiply twice to get the perfect square .

### Example Question #44 : Number Theory

What are odd numbers?

**Possible Answers:**

Integers that have a ones digit that ends in , , , , or

All the digits of the integer must have , , , , or

Integers that have a ones digit that ends in , , , , or

Integers that have a ones digit that ends in , , , , or

Integers that have a ones digit that ends in , , , , or

**Correct answer:**

Integers that have a ones digit that ends in , , , , or

In order to determine if a number is odd, we will check the ones digit. It must contain , , , , or . The answer is integers that have a ones digit that ends in , , , , or .

### Example Question #33 : Integers And Types Of Numbers

What number is found in the set of whole numbers but not in the set of natural numbers?

**Possible Answers:**

**Correct answer:**

Whole numbers start from and include all positive integers. On the other hand, natural numbers are all positive integers that we can count starting from . The only difference is that is found in whole numbers but not in the natural numbers series. Thus, is the correct answer.

### Example Question #34 : Integers And Types Of Numbers

Which of the following is an odd number?

**I. **

**II. **

**III. **

**IV. **

**V. **

**Possible Answers:**

**II, V**

**I, III, V**

**II, III, IV**

**I, III, IV**

**II, III, V**

**Correct answer:**

**II, III, V**

Odd numbers are integers that have a ones digit that ends in , , , , or . Choices **II, III, V **are odd numbers because they have a ones digit of , , and respectively.

### Example Question #31 : Integers And Types Of Numbers

What is the product of two nonidentical prime numbers?

**Possible Answers:**

Prime number

Square number

Cubic number

Composite number

Zero

**Correct answer:**

Composite number

When you take two prime numbers, you are creating a composite number. A compositie number has at least one more factor than one and itself. Since you multiply two prime numbers, you are increasing the factors of the new number.

### Example Question #47 : Number Theory

What do you get when you divide two negative integers?

**Possible Answers:**

Integers

Zero

Irrational number

One

Rational numbers

**Correct answer:**

Rational numbers

For example, we can take the negative integers and . When we divide , we get an answer of . This is an integer and a rational number. However, if we reverse it , we get an answer of . This is not an integer but it is a rational number. Integers can be rational numbers as they are expressed as any number over one. Futhermore, rational numbers are defined as the expression of any quotient or fraction possessing a non-zero denominator. Thus, our answer is rational numbers.

### Example Question #32 : Integers And Types Of Numbers

Given the following set of numbers:

Which numbers in the set are whole numbers?

**Possible Answers:**

**Correct answer:**

A whole number is any number without a fraction or decimal, but negative numbers are NOT whole numbers. Therefore, the only correct choices from this set are and , which are neither negative nor have decimals.

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