190. Illustrative problem. What is the quotient of 17.8 × 45.39 divided by .267?

Multiplying both dividend and divisor by 1000, to make the divisor integral, we have for the dividend 178×4539 (i.e. 10 times 17.8 and 100 times 45.39). Factoring and canceling, we have 2 x 1513=3026.

2 × 89

1513 178 × 4539

287

8 × 89

14. The product of 6.3, 1.4, and 5.7 is how many times as great as the product of 17.1, 0.06, and 7?

15. The product of 0.2, 0.21, and 7.5 is how many times. as great as the product of 0.14, 0.3, and 1.5?

16. How many times is the product of 1.6, 0.01, and 1.5 contained in the product of 0.032, 2.25, and 3?

17. The volume of a box whose interior dimensions are 2.4 in., 5 in., 1.7 in., is how many times as great as that of one whose interior dimensions are 3 in., 1.6 in., and .85 in.?

18. A block of marble 3.5 ft. by 41 ft. by 2.2 ft. weighs how many times as much as one that is 2 ft. by 7.7 ft. by 0.85 ft.?

.871

.50 .75 .8 .831 .371 .625

191. Common business fractions. The following are so commonly used that they should be remembered:

21. At 61 ct. a gallon, how much will 16 gal. of oil cost?

22. At 621 ct. a pound, how much will 8 lb. of tea cost?

23. At 87 ct. a pair, how much must a dealer pay for 80 pairs of overshoes?

HOW TO SOLVE PROBLEMS

192. Nature of the rest of arithmetic. Having learned how to work with integers and fractions, this work is hereafter to be applied chiefly to problems of life.

193. Step work. In solving a problem, or working an example as we also say, we should not only have the work in neat form on paper, but we should also have a brief statement of each operation, in numbered steps.

194. Illustrative problem. What is the value of a rectangular piece of land 20 rd. wide and 32 rd. long at $75 an acre?

= $300

160

3. 4 times $75 = $300.

Use x for times, following the custom

of the school as to writing 4 × $75, or $75 x 4.

Oral Analysis

Since a strip of land 32 rd. long and 1 rd. wide contains 32 sq. rd., a strip 20 times as wide contains 20 times 32 sq. rd., or 640 sq. rd.

Since 1 sq. rd. = rẻʊ A., 640 sq. rd. = 640 times ¦。 A. = 4 A. Since 1 A. is worth $75, 4 A. are worth 4 times $75 $300.

=

195. Teachers should not forget the value of each of these three phases of the work. To neglect the form of the actual computation is to place a premium upon slovenly work, always a temptation to inaccuracy; to neglect the step work is to tempt the pupil to looseness of thought as to the meaning of each operation; to neglect the analysis is to be uncertain as to the pupil's understanding of the work as a whole. The teacher's judgment must determine the emphasis to be placed at various times upon these respective phases.

CLOTHING OUR PEOPLE

GROWING THE COTTON

WRITTEN EXERCISE

1. This cotton field is 70 rd. long and 32 rd. wide. How many acres does it contain? What is it worth at $14.50

What to compress the bales for shipping, at 40 ct. a bale?

4. What did it cost to store it for 2 months in a warehouse, at 25 ct. a bale per month for storage and insurance? 5. The cotton was compressed in bales 5 ft. by 2 ft. by 1 ft. in size. How many cubic feet in each bale? How many cubic inches in each?

6. The 7 bales were sold by an agent. How much commission did he receive at 50 ct. a bale?

7. When cotton is worth 7 ct. a pound, what is the value of the crop produced on 14 acres averaging 245 lb. to the acre?

8. How long would it take a man to pick 3696 lb. of cotton if he averaged 154 lb. a day? It would take 4 men how long, at the same rate?

9. If this country produced 10,701,453 bales of cotton in a certain year, how many tons did it produce, estimating 500 lb. to a bale?

10. If Texas produced 2,438,555 bales in one year; Georgia, 1,345,699; Mississippi, 1,202,739; and Alabama, 1,005,313, what was the total for the four states?

11. If the Texas crop sold for $92,196,000, the Georgia crop for half as much, the Mississippi crop for ₫ as much, and the Alabama crop for as much, for how much did each sell?

8

12. If Texas pays $24,136,800 annually to have the cotton picked, and Georgia pays as much, and Alabama 0.9 as much as Georgia, how much does Alabama pay?

13. If there are 6,642,309 acres planted to cotton in Texas, in South Carolina as much as in Texas, and in Louisiana as much as in South Carolina, how many acres in each?

14. If our country raised $334,847,800 worth of cotton in a certain year, and paid of this amount for the labor of harvesting and marketing the crop, how much is left for the growers?

15. If we sold in one year to Great Britain $90,240,000 worth of cotton, as much to Germany, as much to France as to Germany, and † as much to Italy as to Great Britain, what is the value of the cotton sold to each?