1.1 Factors, products, and exponents

Elementary algebra Page 1 / 1

This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. This chapter contains many examples of arithmetic techniques that are used directly or indirectly in algebra. Since the chapter is intended as a review, the problem-solving techniques are presented without being developed. Therefore, no work space is provided, nor does the chapter contain all of the pedagogical features of the text. As a review, this chapter can be assigned at the discretion of the instructor and can also be a valuable reference tool for the student.

Overview

Factors
Exponential Notation

Factors

Let’s begin our review of arithmetic by recalling the meaning of multiplication for whole numbers (the counting numbers and zero).

Multiplication

Multiplication is a description of repeated addition.

In the addition

$7 + 7 + 7 + 7$

the number 7 is repeated as an addend* 4 times. Therefore, we say we have four times seven and describe it by writing

$4 \cdot 7$

The raised dot between the numbers 4 and 7 indicates multiplication. The dot directs us to multiply the two numbers that it separates. In algebra, the dot is preferred over the symbol $\times$ to denote multiplication because the letter $x$ is often used to represent a number. Thus,

$4 \cdot 7 = 7 + 7 + 7 + 7$

Factors and products

In a multiplication, the numbers being multiplied are called factors. The result of a multiplication is called the product. For example, in the multiplication

4 \cdot 7 = 28

the numbers 4 and 7 are factors, and the number 28 is the product. We say that 4 and 7 are factors of 28. (They are not the only factors of 28. Can you think of others?)

Now we know that

\begin{matrix} (factor) \cdot (factor) & = & product \end{matrix}

This indicates that a first number is a factor of a second number if the first number divides into the second number with no remainder. For example, since

4 \cdot 7 = 28

both 4 and 7 are factors of 28 since both 4 and 7 divide into 28 with no remainder.

Exponential notation

Quite often, a particular number will be repeated as a factor in a multiplication. For example, in the multiplication

$7 \cdot 7 \cdot 7 \cdot 7$

the number 7 is repeated as a factor 4 times. We describe this by writing $7^{4} .$ Thus,

$7 \cdot 7 \cdot 7 \cdot 7 = 7^{4}$

The repeated factor is the lower number (the base), and the number recording how many times the factor is repeated is the higher number (the superscript). The superscript number is called an exponent.

Exponent

An exponent is a number that records how many times the number to which it is attached occurs as a factor in a multiplication.

Sample set a

For Examples 1, 2, and 3, express each product using exponents.

$3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3.$ Since 3 occurs as a factor 6 times,

$3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 = 3^{6}$

	4 AP Key Terms 04 Tissue Level of Organization By OpenStax Start Key Terms
	NCE Ch 10 Professional Orientation By Anh Dao Start Quiz
	1 AP 01 Human Body Anatomy Physiology MCQ By OpenStax Start Quiz
	28 AP 28 Development Inheritance Essay By OpenStax Start Flashcards
	7 Neuroanatomy 07 The Visual System By Stephen Voron Start Quiz
©flickr: Dutch	Las Vegas Timeshare By Donyea Sweets Start Test
	Corporate Communication BUS210 By P. Wynn Norman Start Quiz
	Microbiology Practice Test By Sandhills MLT Start Test
	8 Psychology MCQ 2011 1 Exam By John Gabrieli Start Exam
	17 AP Key Terms 17 Endocrine System By OpenStax Start Key Terms

1.1 Factors, products, and exponents

Overview

Factors

Multiplication

Factors and products

Exponential notation

Exponent

Sample set a

Exercises

Questions & Answers

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!