9. Anything which has size or extent is called a magniFor example, the line AB, or the figure EFCD.

tude.

B

E

F

10. The result of measuring a magnitude is called a number or quantity. For example, if the line AB is measured and found to be 2.53 inches, this result, 2.53, which tells how many times the line AB contains another line one inch long, is called a number or quantity.

11. Any collection of symbols representing number is called an expression. For example, x+2y-3 is an expression.

12. The members of an expression connected by the signs plus or minus or both are called the terms. For

example, in the expression 3x+5y-z, the terms are 3x,

+5y, -2.

13. An expression consisting of one term is called a For example, 6 abc is a monomial.

monomial.

14. An expression consisting of more than one term is called a polynomial. For example, x2+5xy - 6 y2 is a polynomial.

15. A polynomial consisting of two terms is called a binomial. For example, 3x-2y is a binomial.

16. A polynomial of three terms is called a trinomial. For example, 4a+5b-8c is a trinomial.

17. The degree of a term with reference to a letter or letters is the exponent of the letter or the sum of the exponents of the letters in the term. For example, the degree of 9x2y3 is 5, that is, the sum of 2 and 3.

The degree of an algebraic expression is the highest degree of any of its terms. For example, in the expression 2+5x+9, the highest degree is 3, and hence this expression is of the third degree.

18. Terms whose literal factors are of the same degree are called like terms. For example, 9 x3, 5 x3, are like terms. 7 x2y, 4x2y, are also like terms. 4x2y and 5xy2 are not like terms, because the factors of these terms have not the same exponents.

19. The product obtained by multiplying a number by itself a number of times is called in arithmetic a power of that number. For example, 8 is the cube or third power of 2. 81 is the fourth power of 3. In algebra, power

means this much and something more which will be referred to later.

20. The number which multiplied by itself a number of times produces another number is called a root of that number. For example, 5 is the square root of 25, since 5x5=25. 6 is the cube root of 216, since 6 x 6 x6=216. 2 is the fifth root of 32, since 2 x 2 × 2 × 2 × 2 = 32. Square root of a number is indicated by . Cube root by. Fourth root by

CHAPTER II

THE FOUR SIMPLE RULES. FUNDAMENTAL LAWS

ADDITION

21. Addition is the process of combining numbers into a single number. The result in addition is called the sum.

22. To add two arithmetical numbers, count forward from the first number as many units as there are units in the second number. Thus, to add six and five, count forward from six as many units as there are in five. To add three arithmetical numbers, add the first two, and then add this result and the third number.

Example 1. What is the sum of +9 and +7?

The answer may be stated in symbols as follows:

+9+7+16.

The process may be represented graphically as follows:

A

요

1

=

Let AB+9, and CD +7. To add these two lines, place the beginning point of the second line at the end point of the first line. Then AE will be the sum. Next, count the marks from A to E. The result will be the sum.

This problem and result may be stated in symbols as follows:

or

− 6 + ( − 5) = − 11,

-6-5-11.

The solution may be represented graphically as follows: Let AB-6, and CD-5. To add AB and CD, place the beginning point of CD at the end point of AB, and then count the marks from A to E.

To add two positive numbers, add the numbers regardless of sign, and prefix the plus sign to the result.

To add two negative numbers, add the numbers regardless of sign, and prefix the minus sign to the result.

The value of a number, regardless of its sign, is called the absolute value of the number. Hence,

The sum of two numbers affected by the same sign equals the sum of the absolute values of the numbers with the common sign prefixed.

23. Addition of numbers with unlike signs.

Example 1. Suppose a man travels 100 miles north one day, and 80 miles south the next day, how far is he from his starting point?

This question may be expressed in symbols.

+100 miles + ( − 80 miles) = ?

+ 100 miles 80 miles = ?