11. 13 by 3 of 13.

12. 34 by 1 times 734.

13. (-) by (+1).

14. (1-12) by (1+1).

15. (31-21) by 31.

16. 111 by (18+11).

17. If the dividend is 6 and the quotient 1, find the divisor.

18. What must 103 be divided by to give as quotient 23 ?

19. If the dividend is 272 and the quotient 161, find the divisor.

20. Divide 43,560 by 2721.

PERCENTAGE

The result of taking a per cent of a quantity is percentage. A percentage of a number is simply a fraction of the number. The central fact in percentage is that 1% is Hence 100% is equivalent to 1. What per cent 100. is 18 equivalent to?

18 of 118 of 100% = 95%.

Example 1. Find 23% of 1789.

Example 2. Find 3.6 % of 2992.

3.6% is the same as 3.6100, or .036.

Therefore,

3.6% of 2992 is the same as .036 of 2992, which is 107.712.

24. Express each of the following decimals as a per cent : .04, .08, .12, .0165, .002, .006, .0024.

25. A piece of coal taken from the Texas and Pacific Coal Company's mine contains moisture, 5.46%; combustible matter, 35.66%; carbon, 49.17%; ash, 9.71%. Find the amount of each constituent in 2000 lb. of coal. Check your answer.

26. A specimen of lignite contains as follows: moisture, 29.07%; combustible matter, 28.96%; fixed carbon, 24.47%; ash, 17.50%. Find the amount of each constituent in a ton of lignite. Check.

27. Distilled water is composed of two gases, 111% by weight being hydrogen, and 888 % by weight being oxygen. Find the weight of each gas that can be obtained from 10 lb. of water.

28. A bookkeeper receives a salary of $1800 per annum. If he spends 62% of his salary, and saves the remainder, how much does he spend? How much does he save?

29. A gold-bearing ore contains .5% of gold. How many pounds Avoirdupois of gold would 2240 lb. of this ore yield?

30. A copper ore contains 51% of copper. Find the number of pounds of copper in 500 lb. of this ore.

31. A owns 163% of a boat valued at $12,300. What is the value of A's share of the boat?

32. The estimated value of the exports of the United States for 1899 was $1,275,000,000. The percentages of exports from United States ports for that year are given as follows: New York, 37.4%; Boston, 10.43%; Philadelphia, 5.05%; Baltimore, 8.9%; New Orleans, 6.4%; Galveston, 7.17%. Find the value of the exports from these cities.

To find what per cent one number is of another.
Example 1. What per cent of 12 is 5?

5 is 5 of 12.
12

12

= of 100% Example 2.

The value of the property of the Fort Worth and Denver City Railroad in Texas, as ascertained by the Railroad Commission of Texas, for the year 1906, was $5,771,600, and the income from its operation was $1,178,040. Find the rate per cent of income from operation.

To find what per cent one number is of another, find what fractional part the first number is of the second and multiply by 100%.

EXERCISE 78

1. What per cent of 15 is 12?

2. What per cent of 20 is 4? is 7? is 11? is 13? 3. What per cent of 40 is 2? is 8? is 12? is 17? 4. What per cent of 90 is 9? is 12? is 27? is 111? 5. What per cent of 120 is 15? is 18? is 45? is 80? 6. What per cent of 480 is 28.8? is 33.6? is 40? 7. What per cent of 1728 is 345.6? is 155.52? is 288? 8. What per cent of 231 is 21? is 77? is 34.65? 9. What per cent of 5280 is 88? is 440? is 330? 10. What per cent of a bushel is a quart? 11. What per cent of a mile is 8 rd.?

12. What per cent of an acre is a square rod? 13. What per cent of a chain is a yard?

14. What per cent of 1 sq. ch. is 1 sq. rd.?

15. What per cent of 1 gal. is 1 pt.?

16. What per cent of 1 sq. rd. is 7 sq. yd. 5 sq. ft. 9 sq. in.?

17. What per cent of a rod is 1 yd. 2 ft. 6 in.?

18. What per cent of 1 mi. is 1 knot?

19. What per cent of 1 mi. is an arc of 1' measured on the 40th parallel of latitude? (1′ = 4670 ft.)

20. What per cent of 1 mi. is 22 yd.? is 176 yd.?

21. What per cent of 1 sq. mi. is the S. W. of N.E. † of a section of land?

22. What per cent of a common year is 73 da.? is 219 da.? is 292 da.?

23. A meter is 39.37 in. What per cent of a meter is 1 yd.? What per cent of 1 yd. is 1 meter?

24. A kilometer is 1000 meters. mi. is 1 km.?

What per cent of 1

25. What per cent of 1 lb. Avoirdupois is 1 lb. Troy? 26. What per cent of 1 oz. Avoirdupois is 1 oz. Troy? 27. What per cent of the area of each of the following states consists of irrigated land?

28. Find the increase per cent in the population of each of the following cities for the ten years from 1900 to 1910: