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REVIEW.

1. The prime factors of 63 are

and (a) What are the prime factors of 215 ? (b) Of 470 ? 2. Three, 3, 3, and 2 are the prime factors of (C) Of what number are 3, 5, 2, and 23 the prime factors ? 3. Add į and ģ. The l. c. m. of 8 and 3 is (d) Add , , and . The l. c. m. of 9, 12, and 3 is

(e) Divide by 1. The l. c. m. of 9 and 12 is
4. Multiply $324 by 1. This means
(f) Multiply $324 by .25.
5. One half of a rod is and

feet. (g) Twenty-six and one half rods are how many feet? 6. Three eighths of a mile are rods. (h) How many rods in 7 miles ? (i) In 4 miles ? 7. Two rods are yards. 3 rd. are yards. (j) How many yards in 42 rods ? (k) In 64 rods ? 8. When wheat is 70¢ a bushel, 240 lb. cost

(1) When wheat is 90¢ a bushel, how much will one ton of wheat cost?

9. A pile of wood 32 feet long, 4 feet wide, and 4 feet high contains cords.

(m) How many cu. ft. in a pile of wood 32 ft. by 4 ft. by 2 ft. ?

10. If 12 lb. of sugar are worth 454, at the same rate 8 lb. are worth cents.

(n) If 12 boxes of soap are worth $22.50, how much are 8 boxes worth at the same rate ?

MISCELLANEOUS PROBLEMS.

1. The perimeter of a rectangular surface 7 feet by 9 feet is feet.

(a) How many rods of fence are required to enclose a rectangular field 38 rods by 54 rods?

2. If the sun rises at 7 o'clock and sets at 4:30, from sunrise to sunset it is hours and minutes.

(b) If the sun rises at 7:14 and sets at 4:28, how long is it from sunrise to sunset ?

3. A man bought 16 dozen eggs at 10¢ a dozen; he lost 25 per cent of them by decay; he sold the remainder at 12¢ a dozen; he lost — cents.

(c) A man bought 360 dozen eggs at 94 a dozen; he lost 25% of them by decay; he sold the remainder at 11¢ a dozen. How much money did he lose?

4. From midnight Monday to midnight Wednesday it is hours.

(d) How many hours in a week? (e) In the month of January

5. At 45¢ each, 3 copies of “Robinson Crusoe” will cost dollar and cents; for $1.80 I can buy copies.

(f) How much will 7 copies of " Robinson Crusoe" cost?

(g) How many copies of “ Robinson Crusoe” can I buy for $10.35 ? (h) For $4.95 ?

(i) Add four thousand three hundred twenty-four and twenty-five thousandths, and seven hundred forty-six and thirty-four hundredths, and seventy-five and eight tenths.

(j) From forty-five hundred subtract forty-five hundredths.

SIMPLE NUMBERS.

1. Ten times 60 are
2. Ten times 46 are
3. Ten times 300 are

10 times 40 are
10 times 25 are
10 times 325 are

4. Ten times 2 times a number are

times the number.

(a) Multiply 347 by 20. Operation.

Explanation. 347

Two times 347 are 20

Ten times 694 are

Ten times 2 times (20 times) 347 are 6940

(b) Multiply 564 by 30. (d) Multiply 735 by 50.

(c) Multiply 468 by 40.
(e) Multiply 642 by 60.

times

5. One hundred times 2 times a number are the number.

(f) Multiply 86 by 200. (h) Multiply 75 by 400.

(8) Multiply 94 by 300.
(i) Multiply 48 by 700.

REVIEW.

6. The prime factors of 48 are and

(j) What are the prime factors of 290 ? (k) Of 430 ? Multiply. Divide.

Divide. (1) 317 by 70. (m) 8540 lb. by 70 lb.* (n) 1480 lb. by 20. (0) 575 by 70. (p) 9470 lb. by 70 lb. (9) 1350 lb. by 20.

* This means, find how many times 70 lb. are contained in 8510 lb. 70 lb. are contained in 8510 lb. - times. Story-In 8540 lb. of ear corn there are bushels. + This means, find 1 twentieth of 1480 lb. 1 twentieth of 1480 lb. is

Ib. Story - I wish to put 1480 lb. of wheat into 20 sacks; I must put lb. in each sack.

COMMON FRACTIONS.

1. Add b and 12. (a) 37510 + 25615
2. From 7} subtract 24.1 (b) 3467} -

12824

[blocks in formation]

(16)

(8)

(19)

9. Multiply 20¢ by 24.1 (i) 96 x 24 10. Multiply 20¢ by : (j) 124 x 11. Multiply $3 by 6. (k) 647 x 6. 12. Multiply $z by z. (1) $1 x 261 13. Multiply $17 by : (m) $274 x 1 14. Multiply $6 by 21.S (n) $864 x 23.

(13)

(13)

(22)

dollars; ja

15. At $4per ton, 2 tons of coal cost ton costs

; 2; tons cost 16. At $8 per ton, 2 tons of hay cost

* The pupil is expected to find by trial that the l. c. m. of 10 and 12 is + Take 1 from the 7, change it to fifths and add it to the .

In problems 9 to 13 inclusive, think of the number to be multiplied as the price per yard; this will suggest the following:

Problem 9, 27 yd. of ribbon at 20° a yard.
Problem 10, i yd. of ribbon at 204 a yard.
Problem 11, 6 yd. of ribbon at $3 a yard.
Problem 12, ļ yd. of ribbon at $1 a yard.

Problem 13, 4 yd. of ribbon at $12 a yard. ? This means, 2 times $6! plus ļ of $61. 2 times $6., are dollars. of dollars. $13 + $31 =

dollars. Story-At $64 a ton, 24 tons of coal will cost

| See note, page 6.

$6.1

, is

DECIMAL FRACTIONS.

(a) Multiply $546 by 3.24. This means, find 3 times $546, plus 2 tenths of $546, plus 4 hundredths of $546. Operation.

Explanation.
$546 One hundredth of $546 is
3.24

4 hundredths of $546 are

One tenth of $546 is $21.84

2 tenths of $546 are $109.2

3 times $546 are $1638

$21.84 + $109.2 + $1638 = $1769.04

NUMBER STORY.

If one acre of land is worth $546,

1 hundredth of an acre is worth
4 hundredths of an acre are worth
1 tenth of an acre is worth
2 tenths of an acre are worth
3 acres are worth
3.24 acres are worth

(b) Multiply $437 by 2.36; (c) $375 by 5.27. (d) Multiply $352 by 6.21; (e) $284 by 7.32.

(f) Multiply four hundred seventy-three dollars by four and thirty-five hundredths.

(g) When oil meal is $28 a ton, how much will 4680 lb. cost ? (4680 lb. tons.)

(h) Add. .886 .075

(i) Subtract. 8.744 .956

(j)
Multiply.

8.2*
.43

(k) Divide. $.5 $31

(1) Divide. 5 $31.

* One hundredth of 8.2 is .082. The pupil should write the decimal point in the first partial product immediately after writing the tenths' figure of the partial product.

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