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PROBLEMS.
1. Find the value of a single one if:

1. 144 eggs cost $2.88.
2. 20 francs $3.86.
3. 20 shillings = $4.8665.
4. 25 dress patterns = 102.50 yards.
5. 125 bushels of oats cost $36.50.
6. 100 acres of land cost $31563.
7. 72.50 C. cigars cost $84.10.
8. 1.440 M. bricks cost $10.44.
9. 22 days' work = $29.70.
10. .62 of a ton of hay cost $11.47.
11. 74 acres of land cost $70.125.
12. .71 yards of cloth cost $.73625.

13. 5 weeks' provisions cost $47.311. 2. Find the cost of 8.25 tons of hay when 2.2 tons cost $314.

3. Find the value of (6.25 = 31) = (33 — .275).

SHORT PROCESSES.

When the Multiplier approximates 100, 1000, etc.

1. How much less than 10 times a number is 9 times that number?

2. How much less than 100 times a number is 98 times that number?

3. Multiply 4965 by 99.

Explanation.

Process. 496,500

4965 491,535

496,500

4965 491,535

100 times 4965.

1 time 4965. 99 times 4965.

4. Multiply:

1. 4993 by 99. 6. 597,076 by 995.
2. 4967 by 98. 7. 575,854 by 98.
3. 59,678 by 999. 8. 954,367 by 96.
4. 98,849 by 98. 9. 697,547 by 996.

5. 457,836 by 997. 10. 5,064,367 by 97. 5. What cost 496 bushels of wheat at $.98 per bushel ? 6. Find the cost of 240 acres of land at $96 per acre ? 7. What is the value of .0755 X 997 ? 8. 2484 pounds of tea at $.96 = what ? 9. Find the value of 67.89 8 X 999

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.01 2 3 4 5

6 tens

When One Part of the Multiplier is an Exact Divisor of

Another Part. 1. 6 is how many times 3 ?

2. When you have taken a number 3 times, how many times that product will 6 times the number be?

3. Multiply 1728 by 63. Process.

Explanation. 1728

2 tens x 3. 1728 X 3 = 5184 units. 5184 x 63

2 tens 10,368 tens. Adding the two products we have 5184

108,864. 10368

NOTE.- Be careful in placing the first figure of each 108,864 partial product. 4. Multiply :

1. 4795 by 124 [12=4 X 3]. 9. 7495 by 735. 2. 4936 by 93 [9=3 X 3]. 10. 5349 by 927. 3. 7935 by 123.

11. 23,894 by 756. 4. 25,384 by 142.

12. 47,523 by 918. 5. 39,764 by 246.

13. 47,596 by 2505. 6. 79,546 by 328.

14. 39,864 by 8024. 7. 57,324 by 217.

15. 49,975 by 9045. 8. 4793 by 945 [45=5 X 9]. 16. 35,656 by 6+2.

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To Multiply or Divide when the Multiplier or Divisor is an

Aliquot Part of 10, 100, or 1000.

Process.

4) 189800

47450

1. Multiply 1898 by 25.

Explanation. Since 25 190, we multiply by 100 and divide the product by 4.

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Process.

1900

2. Divide 1900 by 25.

Explanation. 14° inverted Too; hence we multiply by 4 and point off two places to the right

4

76.00

Process.

3) 189900

63300

100

Process. 1728

3 51.84

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Process.

8) 569600

71200

3. Multiply 1899 by 331.

Explanation.
Since 33

13°, we multiply by 100 and divide the
product by 3.
4. Divide 1728 by 33.

Explanation.
19° inverted T&o; hence we multiply by and
point off two places to the right.
5. Multiply 5696 by 127.

Explanation.
Since 12

18%, we annex two ciphers and divide
the product by 8.
6. Divide 3.14156 by 121.

Explanation. 18° inverted T&v; hence we multiply by 8 and point off five plus two places to the right. 7. Multiply .7854 by 163.

Explanation.

100, we multiply by 100 and divide the product by 6.

Process. 3.14156

8 .2513248

Process.

6 ) 78.54

13.09

Since 16

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Process. 1492

6 89.52

8. Divide 1192 by 163

Explanation. 160 inverted Tod; hence we multiply by 6 and point off two places to the right.

25, 33}, 121, and 163 are aliquot parts of 100, i.e., they are such parts as exactly divide 100.

Other aliquot parts of 100 may be dealt with similarly ; also aliquot parts of 10 and 1000, etc.

EXERCISES. 1. Multiply :

1. 2556 by 25. 6. 40002 by 16%.
2. 7.36 by 50. 7. 205.59 by 1664.
3. 72.06 by 331. 8. 380.087 by 121.
4. 207.27 by 31.

9. 5908 by 144.
5. 9.087 by 333.

10. 390.8 by 27. 2. Divide : 1. 404 by 25.

6. 399099 by 3331. 2. 5005.09 by 27. 7. 7906.73 by 163. 3. 407.709 by 50. 8. 970008 by 1664. 4. 33659 by 331 9. 5227.38 by 121. 5. 9304.75 by 31. 10. 470058 by 144.

PROBLEMS.

Finding the Cost of Articles sold by the 100, 1000, and Ton.

1. If 100 articles cost a certain price, how many times that price will 500 articles cost?

2. If 1000 articles cost a certain price, how many times that price will 6000 articles cost ?

3. How many articles does C. represent? M., how many?

Process.

4. What will 2673 feet of timber cost at 26.73 $2.25 per C.? 2.25

Explanation. 13365

2673 feet 26.73 C. feet. Since C. feet cost $2.25, 5346

26.73 C. feet cost $2.25 X 26.73 = $60.1425. 5346 $60.1425

5. What is the value of 1262 fence pickets at $121

=

per M. ?

Suggestion : 1262 pickets = 1.262 M. pickets. 6. I sold 6000 cigars at $4.20 per C. Find the amount received therefor.

7. I paid $10.44 for 1440. What was the price per M. ? ? (1440 = 1.440 M.)

8. If the price of gas be $1.75 per M., find the amount of a man's bill when 12,240 cubic feet have been consumed.

9. What cost 23] M. feet of pine at $55 ? 10. What cost 43 M. brick at $8 ?

11. A contractor furnished the following materials for a house : 34,600 bricks at $9.60 per M., 7960 feet of lumber at $16 per M., 9050 feet of flooring at $22.50 per M., 7600 shingles at 40 cents per C. Find the total cost of the materials.

12. If 2000 pounds cost $10.00, what will 1000 pounds cost? 13. At $5.00 per M., what will 3200 pounds cost?

14. 2000 pounds = one ton. If one ton of iron costs $30, what will 1000 pounds cost? What will 4000 pounds cost ?

15. What must I pay for 7850 pounds of stone at $2.20 a ton ? Process.

Explanation. 2) $2.20

2000 lbs. cost $2.20.

1000 lbs. cost $1.10. 1.10

7850 lbs. = 7.850 M. 7.850

Since M. cost $1.10, 7.850 M. cost $1.10 X 7.850 = $8.63500 $8.63:

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