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1. Ten times 6 times a number are times the number. 10 times 6 times 8 are 8 x 60 =

2. One hundred times 5 times a number are times the number. 9 multiplied by 500 =

(a) Multiply 78 by 80. (b) Multiply 96 by 700.

3. Divide 121 by 23. (Change to halves.) Story. (c) Divide 3453 by 2. (Change to --) Story. (d) Divide 345.6 by 2.4. This means,

Story. (e) Multiply $338 by 2.4. (f) Multiply $338 by 2.43.

(g) When land is $375 an acre, how much will 3.35 acres cost?

Find the value of the following: Commodity. Gross Weight (h) Straw. 4360 lb.

6240 lb.

Tare. 1780 lb. 1830 lb.

Price per Ton.

$4.25
$6.75

(i) Coal.

acres.

4. One acre is

square rods.

1 acre = 5. One mile is rods.

1 mile = 6. A piece of land of a mile long and 2 rods wide is

acres.

7. A piece of land 160 rods long and as wide as the schoolroom is about

(j) How many square rods in a rectangular piece of land 47 rods by 6 rods? Is this more or less than 1 acre ? Is it more or less than 2 acres ?

8. One cord is cubic feet. { cord =

(k) How many cubic feet of wood in a pile 7 feet by 5 feet by 6 feet ? Is this more or less than 1 cord ? Is it more or less than 2 cords?

MISCELLANEOUS PROBLEMS.

save

1. If a man can save $5 a month, in 3 years he can

dollars. (a) If a man can save $27 in a month, how much can he save in 9 years ?

2. Byron bought 2 doz. oranges for 40€; he sold them at 34 each; he gained cents.

(b) A merchant bought 35 barrels of apples for $85; he sold them at $2.75 a barrel. How much did he gain?

3. Henry had 25 chickens; a hawk caught 20% of them; he sold the remainder at 22¢ each; he received dollars and cents.

(c) Henry's father had 75 bushels of apples; he lost 20% of them by decay; he sold the remainder at 854 a bushel. How much did he receive for them ?

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4. If coffee costs $z a pound, for 1 dollar I can buy

pounds. 1 = (d) If tea costs $; a pound, how many pounds can I buy for $57? (Change $57 to fifth-dollars.)

5. The sum of two numbers is 34; one of the numbers is 12; the other number is

(e) The sum of two numbers is 346.2; one of the numbers is 75.36. What is the other number?

6. In a piece of slate 1 foot square and 1 inch thick there are

cubic inches. (f) How many cubic inches in a piece of slate 2 feet square and 2 inches thick ?

(g) If of a ton of coal is worth $4.20, how much is 1 ton worth?

SIMPLE NUMBERS.

1. One tenth of 6 is
2. One tenth of 46 is
3. One tenth of 300 is.

1 tenth of 40 is
1 tenth of 25 is
1 tenth of 325 is

.

-th of the

4. One half of 1 tenth of a number is one number. One third of 1 tenth of a number

(a) Divide 472 by 20.

Operation.
20)47'2

Explanation.
One tenth of 472 is
One half of 1 tenth (20) of 472 is

23.6

_th of

(b) Divide 741 by 30. (c) Divide 548 by 40. (d) Divide 735 by 50. (e) Divide 960 by 60.

5. One third of i hundredth of a number is one the number. One fourth of 1 hundredth of a number

(f) Divide 972 by 300. (8) Divide 972 by 400. (h) Divide 895 by 500. (i) Divide 976 by 800.

REVIEW.

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6. Common multiples of 15 and 6 are

etc. The least common multiple of 15 and 6 is 7. The prime factors of 63 are

and (j) What are the prime factors of 124 ? (k) Of 178 ?

8. 3, 3, and 5 are the prime factors of Forty-five is exactly divisible by 3; by 5; by (1)

(m) 128 cu. feet.)1536 cu. ft.

12)1584 cu. ft. (n)

(0) 160 sq. rd.)2400 sq. rd.

15)2445 sq. rd.

-; by

COMMON FRACTIONS.

5

30

30

16*

1. Add and 4. The l. c. m. of 15 and 6 is (a) Find the sum of 456 78, 3417, 245%, and 564. 2. From 935 subtract 43. 1146 (b) Find the difference of 4275 15 and 1328%. 3. Multiply by 9. This means 3* (c) Find the product of 453] multiplied by 9. 4. Multiply 2 by ž. This means 13* (d) Find the product of 458 multiplied by . 5. Multiply 17 by . This means 8* (e) Find the product of 741 multiplied by : 6. Multiply 17 by 2. This means (f) Find the product of 741 multiplied by 28 7. Multiply 16} by 24. This means 22* (g) Find the product of 732} multiplied by 24 8. Divide 8 by (4)* Change 8 to (h) Find the quotient of 97 divided by Story. 9. Divide 1 by (9)* Change to —ths. (i) Find the quotient of 311 divided by Story. 10. Divide 7} by 23. (14)* Change to

-ths. (j) Find the quotient of 55} divided by 23. Story. 11. Divide $17 (3) by 4. This means 15* (k) Find the quotient of 74 divided by 8.

Story.

-ths.

*

Add. 37513 2462

(n) Subtract. Multiply. 4352 3468

12

(0)
Divide.
3; ft.)232 ft.

Divide. 3)365 ft.

1821)

* These figures refer to notes on pages 6 and 7. See also foot-notes, page 62.

DECIMAL FRACTIONS.

1. One tenth of $6 is

.1 of $6.25 is

2. One hundredth of $6 is

.01 of $6.25 is $.0625. 3. Read each of the following in two ways: $.2436,* $.0532, $.6403, $.0042, $.0002, $.6042, $.8002.

(a) Multiply $6.25 by 4.23. This means, find 4 times $6.25 + 2 tenths of $6.25 +3 hundredths of $6.25. Operation.

Explanation. $6.25

One hundredth of $6.25 is 4.23

3 hundredths of $6.25 are $.18757

One tenth of $6.25 is

2 tenths of $6.25 are $1.250

4 times $6.25 are $25.00

$.1875 +$1.250 + $25 $26.4375

NUMBER STORY.

If one ton of coal is worth $6.25,

1 hundredth of a ton is worth
3 hundredths of a ton are worth
1 tenth of a ton is worth
2 tenths of a ton are worth
4 tons are worth
4.23 tons are worth

(b) Multiply $7.35 by 3.46; (c) $4.45 by 5.24.
* (1) 24¢, 3 m., and 6 tenths of a mill. (2) 2436 ten-thousandths of a dollar.

† TO THE TEACHER.—Read the foot-note on page 133; also, the first part of page 143. If the pupil finds difficulty in “pointing off," teach him to use a separatrix in the multiplicand as suggested on page 133. While multiplying 6.25 by 3 hundredths, it may appear

V06.25 on the slate thus:

4.23

Do not at this stage of the work allow the pupil to point off” by counting the decimal places in the multiplicand and multiplier. Rather, lead him to think the meaning of the problem. See foot-notes, page 53.

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