Pre-Algebra : Number Theory

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #41 : Number Theory

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

Possible Answers:

Imaginary number

Irrational number

Even number

Odd number

Prime number

Correct answer:

Even number

Explanation:

For example, take an even number like \displaystyle 2 and an odd number like \displaystyle 5. Their product is \displaystyle 10 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 #42 : Number Theory

What kind of number is \displaystyle \sqrt{16}?

I. rational

II. irrational

III. integer

IV. imaginary

V. composite

Possible Answers:

I, III, V

and III only

II, IV

II only

III and V only

Correct answer:

I, III, V

Explanation:

Even though it's a radical, we can simplify\displaystyle \sqrt{16}.

\displaystyle \sqrt{16}=4

Check the answer.

\displaystyle 4*4=16

The answer is \displaystyle 4

\displaystyle 4 is an integer and a composite number with factors of \displaystyle 1, 2, 4. Furthermore, it can be expressed a rational number \displaystyle (4=\frac{4}{1}).

Thus, the final answer is I, III, V.

Example Question #42 : Number Theory

Which is a square number?

Possible Answers:

\displaystyle 89

\displaystyle 35

\displaystyle 121

\displaystyle 99

\displaystyle 1234

Correct answer:

\displaystyle 121

Explanation:

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 \displaystyle 121. We can multiply \displaystyle 11 twice to get the perfect square \displaystyle 121

Example Question #43 : Number Theory

What are odd numbers?

Possible Answers:

Integers that have a ones digit that ends in \displaystyle 1\displaystyle 3\displaystyle 5\displaystyle 7, or \displaystyle 9

Integers that have a ones digit that ends in \displaystyle 0\displaystyle 2\displaystyle 4\displaystyle 6, or \displaystyle 8 

Integers that have a ones digit that ends in \displaystyle 1\displaystyle 2\displaystyle 5\displaystyle 8, or \displaystyle 9 

Integers that have a ones digit that ends in \displaystyle 1\displaystyle 5\displaystyle 6\displaystyle 8, or \displaystyle 9 

All the digits of the integer must have \displaystyle 1\displaystyle 3\displaystyle 5\displaystyle 7, or \displaystyle 9  

Correct answer:

Integers that have a ones digit that ends in \displaystyle 1\displaystyle 3\displaystyle 5\displaystyle 7, or \displaystyle 9

Explanation:

In order to determine if a number is odd, we will check the ones digit. It must contain \displaystyle 1\displaystyle 3\displaystyle 5\displaystyle 7, or \displaystyle 9. The answer is integers that have a ones digit that ends in \displaystyle 1\displaystyle 3\displaystyle 5\displaystyle 7, or \displaystyle 9

Example Question #44 : Number Theory

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

Possible Answers:

\displaystyle \pi

\displaystyle -1

\displaystyle 0

\displaystyle \frac{1}{2}

\displaystyle 1

Correct answer:

\displaystyle 0

Explanation:

Whole numbers start from \displaystyle 0 and include all positive integers. On the other hand, natural numbers are all positive integers that we can count starting from \displaystyle 1. The only difference is that \displaystyle 0 is found in whole numbers but not in the natural numbers series. Thus, \displaystyle 0 is the correct answer. 

Example Question #45 : Number Theory

Which of the following is an odd number?

I. \displaystyle 12

II. \displaystyle 33

III. \displaystyle 71

IV. \displaystyle 54

V. \displaystyle 89

Possible Answers:

I, III, IV

II, V

II, III, IV

I, III, V

II, III, V

Correct answer:

II, III, V

Explanation:

Odd numbers are integers that have a ones digit that ends in \displaystyle 1\displaystyle 3\displaystyle 5\displaystyle 7, or \displaystyle 9. Choices II, III, V  are odd numbers because they have a ones digit of \displaystyle 3\displaystyle 1, and \displaystyle 9 respectively. 

Example Question #43 : Number Theory

What is the product of two nonidentical prime numbers?

Possible Answers:

Cubic number

Prime number

Zero

Composite number

Square number

Correct answer:

Composite number

Explanation:

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 #44 : Number Theory

What do you get when you divide two negative integers?

Possible Answers:

Integers

Rational numbers

Irrational number

One

Zero

Correct answer:

Rational numbers

Explanation:

For example, we can take the negative integers \displaystyle -10 and \displaystyle -5. When we divide \displaystyle \frac{-10}{-5}, we get an answer of \displaystyle 2. This is an integer and a rational number. However, if we reverse it \displaystyle \frac{-5}{-10}, we get an answer of \displaystyle \frac{1}{2}. 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 #48 : Number Theory

Given the following set of numbers:

\displaystyle -4, -2, -0.5, 2, 15, 20.25

Which numbers in the set are whole numbers?

Possible Answers:

\displaystyle 2, 15, 20.25

\displaystyle 2, 15

\displaystyle -4, -2, 2, 15

\displaystyle -0.5, 20,25

\displaystyle 2

Correct answer:

\displaystyle 2, 15

Explanation:

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 \displaystyle 2 and \displaystyle 15, which are neither negative nor have decimals. 

Example Question #45 : Number Theory

\displaystyle -3 can correctly be considered all of the following types of number, EXCEPT:

Possible Answers:

Rational

Natural

Real

Integer

Negative

Correct answer:

Natural

Explanation:

Negative numbers are integers, they are real, and they are rational. Natural numbers, by definition, are whole and non-negative numbers. Therefore, \displaystyle -3 is NOT a natural number. 

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