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 + 2c^{2}:

An algebraic expression is any representation of a number by algebraic

notation.

7. ILLUS. 1. -3a^{2}b; 2x + a^{2}z^{3} – 5d^{4}:

-3a^{2}b is called a term, 2x is a term, +a^{2}z^{3} is a term, -5d^{4} 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. a^{2}bc 3x^{2}y^{3}

-7a^{2}bc -x^{2}y^{3}

5a^{2}bc 1

2x^{2}y^{3}

The terms in these groups are said to be similar.

ILLUS. 3. x^{2}y xy x^{2}y

3a^{2}b 3x^{2}y 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….7x^{2}y^{2}

x^{3}…. third degree ….abc

3xy….second degree….a^{2}

2a^{2}bx^{3}…. sixth degree ….4a^{5}b

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

by taking the sum of its exponents.

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