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19. What cost 37 tons of steel, at $63 per ton ?

20. What cost 372 yards of cloth, at $9 per yard? 21. What cost 568 acres of ground, at $175 per acre? 22. A railroad company bought 13 locomotives at $9500 apiece. What did they all cost? Ans. $123500. 23. An institution spends in advertising $565 per year; at this rate how much would it spend in 15 years?

Ans. $8475. 24. Multiply three hundred forty-one million six hundred four thousand five hundred one by twenty-three thousand six hundred eight. Ans. 8064599059608.

25. Find the product of seventy-five million three hundred sixty-seven thousand four hundred fifty-one by seven thousand twenty-one. Ans. 529154873471.

Written Exercises+

CASE III.

94. When either factor has one or more ciphers on the right.

EXAMPLE.-Multiply 325 by 10; by 100.

SOLUTION.

Multiplicand, 325

Multiplier,

Product,

10 3250

EXPLANATION.-Since 10 units of any order make 1 of the next higher order, the writing of a cipher on the right of a number, thus removing each of its figures one order to the left, must multiply it by 10. In like manner

the writing of two ciphers on the right of a number multiplies it by 100.

Hence, to 325 × 1, which is 325, we annex one cipher, and have 10 times the number; annex two ciphers and we have 100 times the number.

EXAMPLE.-Multiply 325 by 50; by 500.

SOLUTION. 325

50

16250

EXPLANATION.-Since 50 is 10 times 5, 50 times 325 must be 10 times 5 times 325.

5 times 325 is 1625, and 10 times as much, is 1625 with one cipher annexed, or 16250.

In like manner the annexing of two ciphers gives the product when 325 is multiplied by 500.

EXAMPLE.-Multiply 3250 by 50.

SOLUTION. 3250

50

162500

EXPLANATION.-5 times 3250 is 5 times 325 with a cipher annexed, or 16250, and 50 times 3250 is 16250 with one cipher annexed, or 162500, the required product.

95. RULE.-To the product of all the other figures annex as many ciphers as there are at the right of both factors.

PROBLEMS.

1. Multiply 375 by 100; by 420: 41900 by 9090. 2. Multiply 1450 by 3500; by 780: 3080 by 1450. 3. Multiply 6300 by 1700; by 4000: 7500 by 6300. 4. Multiply 245 by 36000; by 790: 1260 by 2450. 5. Multiply 375000 by 360; by 42: 1420 by 3750. 6. Multiply 5090 by 480; by 90: 6030 by 5090. 7. Multiply 6203 by 9300; by 200: 8. A barrel of flour weighs 196 pounds in 200 barrels ?

9. A barrel of fish weighs pounds in 150 barrels ?

10. A barrel of salt weighs pounds in 179 barrels ?

11. A barrel of lime weighs pounds in 56 barrels ?

4090 by 6200. pounds. How many Ans. 39200 pounds. How many

200 pounds.

Ans. 30000 pounds. 280 pounds. How many Ans. 50120 pounds.

240 pounds. How many Ans. 13440 pounds.

12. A bushel of coal weighs 76 pounds. How many Ans. 364800 pounds.

pounds in 4800 bushels ?

13. How much will 20 city lots cost, at $4100 each?

Ans. $82000. 14. How much will 16 acres of ground cost, at $170 per acre? Ans. $2720.

15. How much will 450 head of cattle cost, at $56 a head? Ans. $25200.

16. How much will 351 head of sheep cost, at $10 a head? Ans. $3510.

17. How much will 402 head of horses cost, at $230 a head? Ans. $92460. 18. In printing 5000 copies of a book, 24 sheets of paper were used for each book. How much paper was used?

Ans. 120000 sheets. 19. In building a line of telegraph 370 miles long, the cost was $1004 per mile. What was the entire cost?

Ans. $371480.

20. At a plow factory 108 plows were made each day for 50 days. How many plows were made? Ans. 5400 plows. 21. An agent travels 297 days at an average of 125 miles miles per day. How many miles does he travel in the year? Ans. 37125 miles.

22. How many days in 8 years of 365 days each?

Ans. 2920 days.

95'. A Parenthesis () is used to include such numbers as are to be considered together.

A Vinculum

has the same meaning.

Thus, 4 × (5 + 4), or 4 × 5 + 4 means that 4 is to be multiplied by 5+4 or 9. 4 multiplied by 9 36, Ans.

Without the parenthesis, or vinculum, 4×5+4 means 4 times 5 and 4 times 5 = 20; 20 + 4 = 24, Ans.

4 added.

+Written Exercises+

REVIEW PROBLEMS.

1. Multiply 325 — (15 × 15) by 47 × (1861 — 1814). Ans. 220900.

2. Multiply 801- - 169 + 533 by 624 25 × 21.

Ans. 9801.

3. Multiply (40 x 50) - 1850 by (91 x 19) - 1579. Ans. 22500. 4. Multiply (75 × 24) — 849 by (63 × 38) — 1393. Ans. 951951. 5. Multiply 42 + (13 × 43) by 1761 — (38 × 23). Ans. 533087. 6. 75 +8 × (25 +38) × (89 — 72) × 7-100= ?

Ans. 59951.

7. 20 × (16 × 5 — 14 × 3) + (42 — 18 x 2) — 700 =?

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9. 176491426 — 92190 + 111 = ?

10. What sum must be added to 271 x 300 to make the amount 131313?

11. What is the difference between 75011

and 463 × 201 86394 ?

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12. (463+537-901) × 990 = ?

Ans. 50013.

(671 × 102)

Ans. 98010.

13. 96+8x (35+40) by (56-40 × 8)-5=?

Ans. 85608.

14. A speculator bought 800 acres of land at $20 an acre; he sold at one time 350 acres at $25 an acre; at another time 250 acres at $30 an acre. At what price must he sell the remainder in order to gain on purchase $8250.

Ans. $8000.

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