6. .356+1.275+32.0325.

11. 3.495+1.87 +3.25.

7. 15.815+17.21 + 31.41. 12. 38.835+8.9764 +1.385.

8. .2735+1.596 + 3.25.

9. 2.948 +3.7642 +85.035.

10. 46.2 +381.25 +2.985.

13. 1.8035 +3.00412 +31.025. 14. 62.589 + 3.875 + 1.3759. 15. 28.48 +17.578 +34.752.

16. What is the sum of 8 tenths, 12 hundredths, 75 thousandths, 69 ten-thousandths, 21 hundredths?

17. What is the sum of 312 ten-thousandths, 8 millionths, 65 thousandths, 413 ten-millionths, 9 tenths?

18. What is the sum of 82 hundredths, 510 thousandths, 6 tenths, 80 ten-thousandths?

19. What is the sum of 303 thousandths, 4108 millionths, 635 ten-thousandths, 803 ten-millionths?

20. A bicyclist traveled on his wheel 51.875 miles in one day, 45.75 the next, and 35.375 the next day. How far did he travel during these three days?

21. A ticket agent sold in one month tickets to the value of $18,756.75, in the next $17,983.25, in another $ 2001.875. How much were his sales during those three months?

SUBTRACTION OF DECIMALS.

219. 1. From take. From .18 take .13. take 15. From .035 take .026.

2. From

3. From 4 take. From 8 take .8.

WRITTEN EXERCISES.

220. 1. From 46.57 subtract 9.46325.

46.57000 = 46.57 9.46325 = 9.46325

37.10675

37.10675

EXPLANATION. - The numbers are written so that units stand under units, tenths under tenths, etc. The decimals may be made similar and then subtracted, care being taken to place the decimal point in the remainder directly under the decimal point in the numThe ciphers may be supposed to be annexed when we subtract, and consequently need not be written.

ber subtracted.

12. What is the difference between 6.325 and 1.0345 ? 13. What is the difference between 6.45 and 2.3375? 14. From 65 hundredths subtract 65 thousandths. 15. From 162 thousandths subtract 261 millionths. 16. Find the value of 23.2 − .0325+ 6.95 — 3.4876. 17. Find the value of 6.594 – 2.0341 — .70325 + 8.963.

18. Find the value of 81.8 +35.625 — 38.875 -2.0034. 19. Find the value of 4.6 +2.635.8925- .0359.

20. From a cistern that contained 30.5 barrels of water, 25.75 barrels were drawn off. How much water remains in the cistern?

21. A man bought a tub of butter for $35.75, paying $10 in cash and the rest in groceries. How much did he pay in groceries?

22. A man whose income was $10,000 spent in one year $7375.87. How much did he save that year?

MULTIPLICATION OF DECIMALS.

221. 1. What is the product of? Of .1 x .1? Of .5 x .5? How does the number of ciphers in the denominator of the product of these fractions compare with the number of ciphers in the denominators of the factors?

2. What is the product of X? Of 1 x .01 ? Of .5 x .05? How does the number of ciphers in the denominator of the product of these fractions compare with the number of ciphers in the denominators of the factors ?

3 How does the number of decimal places in a decimal fraction compare with the number of ciphers in its denominator?

4. How, then, does the number of decimal places in the product of two or more decimals compare with the number of places in the factors?

222. It is apparent, therefore, that:

The number of decimal places in the product of two or more decimals is equal to the number of decimal places in the factors.

WRITTEN EXERCISES.

223. 1. What is the product of .275 multiplied by .17?

.275

.17

1925 275 .04675

EXPLANATION. Since 275 and 17 are the numerators of the fractions, in multiplying the fractions, we must multiply 275 by 17, which gives 4675 for a new numerator.

Since thousandths. multiplied by hundredths produce hundred-thousandths, the product of the fractions is 4675 hundred-thousandths, or .04675.

Or the number of decimal places in the product will be five, the number of decimal places in both factors. Art. 222.

224. Hence, it is evident that:

To multiply decimals we multiply as if the numbers were integers, and from the right of the product point off as many figures for decimals as there are decimal places in both factors.

If the product does not contain a sufficient number of decimal places, the deficiency must be supplied by prefixing ciphers.

5.372 100 537.200

EXPLANATION. Since each removal of a figure one place to the left increases its value tenfold, the removal of the decimal point one place to the right multiplies by 10, and its removal two places to the right multiplies by 100; or, the process may be performed in the ordinary manner. 24. Multiply 27.65 by 10. 28. Multiply 6.8735 by 100. 25. Multiply 49.675 by 10. 29. Multiply .3768 by 1000. 26. Multiply 2.795 by 100. 30. Multiply 6.835 by 100. 27. Multiply 8.935 by 100. 31. Multiply .7634 by 1000.

32. Multiply 89.92 by 10. 33. Multiply 68.3025 by 100. By 1000. By 10,000. 34. Which is larger and how much, the product of .625 and .375, or their sum?

By 100. By 1000. By 10,000.

35. What will 52.75 bushels of oats cost at $.45 per bushel ?

36. A merchant sold 24.25 yards of muslin at $.125 a yard. How much did he receive for it?

37. A man bought 214 bags of barley. What did they cost him, if each bag held 2.5 bushels, and the price was $.96 a bushel?

38. A tailor bought 4.5 yards of cassimere at $2.25 a yard, and 6.25 yards of broadcloth at $6.50 a yard. How much more did the broadcloth cost than the cassimere?

39. How many acres are left in a farm of 563.27 acres, if 3 fields of 57.135 acres each are sold from it?

40. A steamship in crossing the Atlantic sailed at an average speed of 325.75 miles per day. If another steamer sailed from the same port at the same time at the rate of 395.35 miles per day, how far were they apart in 5.75 days?

DIVISION OF DECIMALS.

225. 1. When a number is divided by 3, what part of it

226. 1. 6)109.92 18.32

WRITTEN EXERCISES.

Find 1 sixth of 109.92, or divide 109.92 by 6. EXPLANATION. One sixth of 10 tens is 1 ten and 4 tens remaining; 1 sixth of 4 tens remaining and 9 units, or 49 units, is 8 units and 1 unit remaining; 1 sixth of 1 unit remaining and 9 tenths, or 19 tenths, is 3 tenths and 1 tenth remaining; 1 sixth of 1 tenth remaining and 2 hundredths, or 12 hundredths, is 2 hundredths. Therefore, one sixth of 109.92 is 18.32, or the quotient of 109.926 is 18.32.

2. What is 1 fifth of 86.4055?

3. What is 1 eighth of 94076.8?

= ?

5. $234.54÷9
6. $907.34÷7=?

4. What is 1 eleventh of 1086.415? 7. $324.784 ÷ 8 = ?

8. Find 1 eighth of 9675 acres.

8)9675.000

1209.375

This we

EXPLANATION. We divide as in simple division until we come to the remainder, 3 acres. change to 30 tenths and continue the division thus: 1 eighth of 30 tenths is 3 tenths and 6 tenths, or 60 hundredths, remainder. 1 eighth of 60 hundredths is 7 hundredths and 4 hundredths, or 40 thousandths, remainder; 1 eighth of 40 thousandths is 5 thousandths. Therefore, 1 eighth of 9675 acres is 1209.375 acres.

18. A man received $3278 for 5 acres of land. What

was the price per acre?

19. An estate valued at $35,267 was divided equally among 8 children. What was each child's share?