APPROXIMATIONS.

Pupils should be drilled to take a broader view of their work, by estimating the probable result before taking a pencil. In this way many absurd answers might be avoided.

381. Give approximate answers at sight:

1. Find the interest of $150, at 4%, from Jan. 1, 1903, to Dec. 30, 1905. (Nearly 3 years.)

2. What is the weight, at 57 cake of ice 4 ft. by 2 ft. by 11 ft? feet.)

lb. per cubic feet, of a (Nearly 60 lb. per cubic

3. Find the amount of goods sold, the commission at 23% being $11.75. (About 3%.)

4. What % of 497 is 249?

5. What % of 315 is 1131?

6. Cost of 19,987 ft. boards at $ 30.05 per M?

7. How much will be paid for 4 barrels sugar, each containing 299 pounds, at 51 per pound?

8. 18.0327 ÷ 4.5026.

9. 8318-328.

10. 74 A. 155 sq. rd. land at $79 per acre?

11. 487 is what per cent of 960 ?

12. If 17 bu. 37 lb. of corn cost $8.75, what will 52 bushels cost?

13. About how many cords of wood in a pile 25 feet long, 4 feet wide, 5 feet high?

14. How many bushels (14 cu. ft.) can be placed in a bin 6 feet long, 5 feet wide, 4 feet high?

15. How many acres in a field 52 rods long, 30 rods wide? 16. About how many yards are there in the side of a square field containing 1 acre (4840 square yards)?

REVIEW OF SIMPLE NUMBERS.

47236 283416 2881396

382. Written Exercises.

6748

× 427

After multiplying by 7, the pupil multiplies this latter product by 6 tens, which gives him the product by 42 tens. In this way one line is saved.

3289 832 26312 105248 2736448

First multiply by 800, by placing the first figure of the product by 8 in the hundreds' place. Multiply this by 4, writing the first figure in the units' place.

2. Divide each of the following fractions by 6:

5 12 25 84

4, 13, 18, 103.

3. Reduce of of 5 of 24 to a simple fraction.

4. 385-2119. 403-187

5. What fraction of £1 18s. 9d. is 5s. 6d. ?

6. Multiply 241 by # of 3.

7. What is the greatest common divisor of 657 and 1168? the least common multiple of 12, 16, 20, 30?

8. What must be taken from 85 to leave 3?

9. Reduce 42 and 40% to their lowest terms.

10. Which is the greatest and which is the least, of, of, and 21 of?

11. What must be added to 34 to make 5?

12. Add 3 of a week, of an hour, of a minute.

13. How much is 9 times each of the following fractions?

16. What part of a 10-acre field is 4 A. 100 sq. rd. ?

17. What is the least number that will contain each of the numbers 6, 15, 18, and 20?

18. What must be multiplied by 41 to produce 161?

19. What is the value of 1⁄2 + 1⁄2

20. What quantity must be divided by 44 to produce 85 ? 21. Find the value of 24 ÷ 3

24. Add 3, 4, 51. Subtract 451⁄2 from the sum.

25. Multiply of 5 by 7. Divide the result by 14.

REVIEW OF DECIMALS.

387. Written Exercises.

57

1. Express as decimals 50, 1000, and 27.

2. .39586.7 + 209.0043 + .81 + 3.075 + 27.

3. Divide 34,020.072 by 5.309. 570÷.005 = ?

4. Multiply 80.037 by 10. Seventy-three hundred-thousandths by one hundred. .2054 × 1000 = ?

5. Subtract 48.8067 from 53.07. .0539 × 26.08

?

6. The smaller of two numbers is 8.5307, and their sum is 25.07. Find the larger number.

7. Express .39, 6.175, .00036, and 74.0005 as common fractions (or mixed numbers).

8. Divide .826 by 100; 543.71 by 10,000; and fifty-nine ten-thousandths by one thousand.

9. Find the difference between 9.84 and 38.005, and the continued product of 83.09, .734, and 5.007.

10. Reduce 6 shillings 9 pence to the decimal of a pound sterling.

11. Express as decimals seven hundredths, forty-three ten-thousandths, and ninety-one millionths.

12. Change, 8, 115, and 2 into decimals. Find their sum.

13. Express .42796 as a common fraction, and the sum of 10, 180, and 1873 as a decimal.

14. 3.009 x .07 x .0907.

15. Divide .0075 by .15, and .00044408 by .0112.

16. Divisor, 403.6; quotient, 2.709. Dividend?

17. What is the value of

.035 × .0056 ?

.00007

18. Change 69 rods to the decimal of a mile.

19. Change .4285 month (30 days) to days, hours, etc.