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SIMPLE NUMBERS.

1. Any exact integral divisor of a number (except the number itself and 1) is called a factor of the number. The

factors of 6 are and . The factors of 10 are

and ——-.

2. A factor that is itself a prime number is called a prime factor. A factor that is itself a composite number is called a composite factor.

2 and 3 are factors of 24.

4 and 6 are ■ factors of 24.

3. Every composite number may be resolved into prime factors.

The prime factors of 12 are 2, 2, and 3.
The prime factors of 18 are 2, 3, and 3.

The prime factors of 15 are and .

The prime factors of 14 are and .

The prime factors of 30 are , —-, and .

4. From the above it will be seen that a number is equal to the product of its prime factors. 3 and 7 are the prime factors of ;2, 2, and 7, of ——.

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$11.22

NUMBER STORY.
Tf one acre of land is worth $-374,

1 hundredth of an acre of land is worth -—-.

3 hundredths of an acre of land are worth .

(b) Multiply $347 by .03. (c) $537 x .04. (d) Multiply $24.6 by .03. (e) $39.4 x .04. (f) At $875 an acre, how much will .04 of an' acre of land cost?

(g) (h) (i) (j) (k)

Add. Subtract. Multiply. Divide. Divide.

286.3 146f 356 $.04)$5.76f 4)$5.76j: 184£ 78.2 .05

* The pupil should understand that he multiplies $3.74 (not $374) by 3, and should be taught to write the decimal point in the product immediately after writing the tenths' figure of the product.

tThis means, find how many times i hundredths are contained in 576 hundredths.

X This means, find 1 fourth of $5.76.

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(a) At $5.20 a ton, how much will 4600 lb. of coal cost?

Explanation-
One ton costs $5.20.

1 tenth of a ton costs $.52.
3 tenths of a ton cost —.

2 tons cost .

Operation.
4600 lb. = 2.3 tons.

$5.20
2.3

$1,560 2.3 tons cost

$10.40
$11,960

Find the cost:
(b) 4800 lb. @ $5.40 per ton.
(d) 6200 lb. @ $5.35 per ton.
(f) 5600 lb. @ $5.70 per ton.

5. Three yd. are feet.

6. Three hr. are minutes.

7. Three min. are seconds.

8. Three bu. are quarts.

9. Three lb. are ounces.

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(h) Change 148 yd. to feet. (i) Change 15 yd. to inches,

(j) Change 24 hr. to min. (k) Change 24 hr. to seconds.

(1) Change 35 yr. to mo. (m) Change 52 wk. to days,

(n) Change 37 lb. to oz. (o) Change 49 gal. to quarts,

(p) Change 43 bu. to qts. (q) Change 56 pk. to pints.

(r) How many square inches in a 5-foot square?

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1. A rectangular solid has faces. Each face is a

rectangle.

2. Some or all of the faces of a rectangular solid may be squares.

3. If each face of a rectangular solid is a square, the solid is called a .

4. If some of the faces of a rectangular solid are oblongs, the solid is not a cube.

5. The area of a rectangular surface 3 inches by 4 inches is square inches.

6. The solid content of a rectangular solid 3 in. by 4 in. by 2 in. is cubic inches.

7. The area of a rectangular surface 3 inches by 5 inches is square inches.

8. The solid content of a rectangular solid 3 in. by 5 in. by 2 in. is cubic inches.

9. The area of a. rectangular surface 2 inches by 5 inches is . square inches.

10. The solid content of a rectangular solid 2 in. by 5 in. by 3 in. is cubic inches.

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