Algebra (Page 27)

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10. A boy who earns b dollars a day spends x dollars a week. How much has
he at the end of 3 weeks?

11. A can perform a piece of work in x days, B in y days, and C in z days.
Express the part of the work that each can do in one day. Express what
part they can all do in one day.

12. How many square feet in a garden a feet on each side?

13. A money drawer contains a dollars, b dimes, and c quarters. Express the
whole amount in cents.

14. x is how many times y?

15. If m apples are worth n chestnuts, how many chestnuts is one apple worth?

16. Divide 30 apples between two boys so that the younger may have two-
thirds as many as the elder.

ALGEBRAIC EXPRESSIONS.

6. ILLUS. a, -c, b + 8, m – x + 2c2:

An algebraic expression is any representation of a number by algebraic
notation.

7. ILLUS. 1. -3a2b; 2x + a2z3 – 5d4:

-3a2b is called a term, 2x is a term, +a2z3 is a term, -5d4 is a term.

A term is an algebraic expression not connected with any other by the sign
plus or minus, or one of the parts of an algebraic expression with its own sign
plus or minus. If no sign is written, the plus sign is understood. By what signs
are terms separated?

ILLUS. 2. a2bc 3x2y3

-7a2bc -x2y3
5a2bc 1
2x2y3
The terms in these groups are said to be similar.

ILLUS. 3. x2y xy x2y

3a2b 3x2y 3ab

The terms of these groups are said to be dissimilar.
Similar terms are terms having the same letters a®ected by the same
exponents.

Dissimilar terms are terms which di®er in letters or exponents, or both.
How may similar terms di®er?

ILLUS. 4. abxy….fourth degree….7x2y2

x3…. third degree ….abc
3xy….second degree….a2
2a2bx3…. sixth degree ….4a5b

The degree of a term is the number of its literal factors. It can be found
by taking the sum of its exponents.

27

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