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19. A man sold a cow for $80, and gained c dollars. What did the cow cost?

20. If the sum of two numbers is 60, how may the numbers be represented?

MULTIPLICATION

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4. ILLUS. 1. 4 * 5 * a * b * c, 7 x 6, x x y.

ILLUS. 2. abc, xy, amx.

ILLUS. 3. x * x = xx = x^{2}.

x * x * x = xxx = x^{3}.

These two are read “x second power,” or “x square,” and “x third power,”

or “x cube,” and are called powers of x.

A power is a product of like factors.

The 2 and the 3 are called the exponents of the power.

An exponent is a number expressed at the right and a little above another

number to show how many times it is taken as a factor.

Multiplication is expressed (1) by signs, i.e. the dot and the cross;

(2) by writing the factors successively; (3) by exponent.

The last two are the more common methods.

When use the exponent? When write the factors successively?

Exercise 12.

1. Express the double of x.

2. Express the product of x; y, and z.

3. How many cents in x dollars?

4. Write a times b times c.

5. What will a quarts of cherries cost at d cents a quart?

6. If a stage coach, goes b miles an hour, how far will it go in m hours?

7. In a cornfield there are x rows, and a hills in a row. How many hills in

the ¯eld?

8. Write the cube of x.

9. Express in a di®erent way a x a x a x a x a x a x a x a x a.

10. Express the product of a factors each equal to d.

11. Write the second power of a added to three times the cube of m.

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