157

5 gr.

7. Subtract 4 fb, 93, 63, 29, 13 gr. from 9 H, 53, 19,

8. Subtract 7 fur. 3 rd. 4 yd. 2 ft. 8 in. from 1 m. 27 rd. 1 yd. 1 ft. 2 in.

9. Subtract 8 bu. 3 pk. 5 qt. from 17 bu. 2 pk. 3 qt. 10. Subtract 25 gal. 2 qt. 1 pt. from 37 gal. 2 qt. O pt.

0

NOTE. When in compound subtraction reductions are necessary, and the changed minuend is not written, it is usually easier to subtract from the value of the reduced unit and add the remainder to the minuend figure, or to subtract as many as possible from the written minuend figure and the rest from the value of the reduced unit, than to add first and subtract afterwards, as we have hitherto done.

Although this method is illustrated and explained in Section 7, Letter T, to which the pupil is referred, we insert a single example by way of review.

What is the value of 3 qr. 17 lb.

1 qr. 24 lb. ?

Explanation. On principles already explained, we take 1 qr. from the 3 qr. and reduce it to lb., which gives 28 lb. 28 lb. + 17 lb. 24 lb. = (28 lb. - 24 lb.) + 17 lb. 4 lb. + 17 lb.

=

21 lb.

=

Or we may subtract 17 of the 24 lb. from the 17 lb. of the minuend, and the remaining 7 lb. from 1 qr. or 28 lb., which leaves as before 21 lb.; then taking 1 qr. from 2 qr. we have 1 qr. left.

The answer is, therefore, 1 qr. 21 lb., which may be proved as before.

11. Bought 7 T. 14 cwt. 1 qr. 19 lb. of hay, from which I sold 3 T. 7 cwt. 3 qr. 26 lb. How much had I left?

12. A goldsmith bought 7 lb. 7 oz. of gold. How much will he have left after manufacturing and selling 3 lb. 5 gr. of it?

13. A trader sold 9 yd. 3 qr. 2 na. of cloth from a piece containing 27 yd. 1 qr. 1 na. How much was left in the piece? 14. A man set out on foot to travel from Boston to Springfield, the distance being 98 miles. 28 m. 7 fur. 19 rd., the second 24 m. 6 fur. 28 rd., the third The first day he travelled 29 m. 4 fur. 36 rd. How far from Springfield at the end of the first day? at the end of the second? at the end of the third?

15. Farmer Johnson raised 87 bu. 3 pk. of oats, 127 bu. 1 pk. of Indian corn, and 64 bu. 2 pk. 5 qt. of wheat. How much grain did he raise in all? How much more oats than wheat? How

14

much more Indian corn than wheat? than oats? If the oats weighed 2808 lb., the Indian corn 7238 lb., and the wheat 3879.375 lb., how much did the whole weigh? How much more did the Indian corn weigh than the oats? than the wheat? How much more did the wheat weigh than the oats?

16. Mr. Smith's farm contains 24 A. 3 R. 17 sq. rd. of pasturage, and 17 A. 2 R. 25 sq. rd. of tillage. How many more acres of pasturage does it contain than of tillage? It also contains 48 A. 1 R. 15 sq. rd. of woodland. How many more acres of woodland does it contain than of pasturage? than of tillage? How many more acres of woodland than of tillage and pasturage together? How many acres are there in his farm? If his pasturage is worth $1225.375, his tillage worth $1757.16, and his woodland worth $1520.875, how much is his farm worth? How much more is his woodland worth than his pasturage? How much more is his tillage worth than his woodland? than his pasturage? He sold 6 A. 2 R. 29 sq. rd. of pasturage, 8 A. 16 sq. rd. of tillage, and 17 A. 3 R. 37 sq. rd. of woodland. How many acres of each kind did he have left?

17. A man undertook to dig a ditch for a certain price per rod. On completing it he demanded payment for a ditch 37 rd. 0 ft. 3 in. long. His employer, doubting his honesty, measured it, and found it to be but 36 rd. 5 yd. 1 ft. 9 in. long. A dispute arising between them, they called in Mr. Jenks to settle it, agreeing to abide by his decision. He measured the ditch, and found its length to be 36 rd. 16 ft. 9 in. What was the difference in their measurements?

H. We can begin at the left to subtract as well as at the right, if we are only careful to reserve one for reduction from each denomination in the minuend when it is required by the lower denominations. This reduction will be necessary when the figures in the subtrahend at the right of the denomination considered, are greater than the corresponding ones of the minuend.

Example. How many are 508.935 249.748?

Explanation. Reserving 1 hundred from the 5 hundreds, we have, 2 hundreds from 4 hundreds = 2 hundreds. Reducing

the 1 hundred reserved, to tens, and reserving 1 ten for further reduction, we have, 4 tens from 9 tens = 5 tens. Reducing the 1 ten to units and adding 8 units, we have, 9 units from 18 units 9 units. Reserving 1 tenth, 7 tenths from 8 tenths = 1 tenth. Reducing the 1 tenth reserved to hundredths and adding 2 hundredths, (1 hundredth being reserved,) we have, 4 hundredths from 12 hundredths 8 hundredths. Reducing 1 hundredth to thousandths, and adding the 5 thousandths, we have, 8 thousandths from 15 thousandths 7 thousandths. answer is, therefore, 259.187.

=

The

Perform the following subtractions by beginning at the left.

NOTE. As soon as the process is sufficiently well understood to justify it, the explanations should be omitted, and the results only named. Thus, in the example explained above, the pupil should say, 2 hundreds, 5 tens, 9 units, 1 tenth, 8 hundredths, 7 thousandths. The answer is, therefore, 259.187.

It is also a good mental exercise to read the results at once by inspecting minuend and subtrahend. Having the numbers to be subtracted written thus,

perform the subtractions mentally, beginning at the left, and read at once 5916.78. Practice will make this very easy.

Subtract by the method last explained,

5. 473.81 from 2542.73; 81.425 from 6983.24. 6. 32.792 from 48.6; 430.062 from 621.05.

7. 314.378 from 617.83; 29.83 from 471.4263.

8. 197 A. 3 R. 27 sq. rd. 15 sq. yd. 5 sq. ft. 97 sq. in. from

231 A. 19 sq. rd.

9. 113°, 47', 25′′ from 127°, 18′, 14′′.

10. 213 T. 15 cwt. 23 lb. 11 oz. 6 dr. from 307 T. 8 cwt. 2 qr. 23 lb. 8 oz. 12 dr.

11. 431 yd. 2 qr. 3 na. 2 in. from 527 yd. 1 qr. 2 na. 1 in. 12. 784£, 7d.-327£, 14s. 8d. 3qr.

A good method of proceeding when several numbers are to be subtracted, is illustrated in the following example.

How many are 862 285938-56?

Arranging as below, we subtract the sum of each column of the subtrahend from the appropriate part of the minuend, reducing and changing denominations, as before explained. 862. Minuend.

Adding the units of the subtrahends, we have, 6, 14, 23, 31 units, which cannot be taken from 2 units. To obtain as many as 31 units, we must take 3 tens from the 6 tens. 3 tens = 30 units, which added to the 2 units equals 32 units; 31 from 32 leaves 1. Now it makes no difference whether we take 3 tens (on account of those we reduced to units) from the 6 tens, and afterwards take the tens in the tens' column of the subtrahend, or whether we take all together. Adopting the latter method, and adding the tens' column, we have 3, 8, 11, 16, 18 tens, which cannot be taken from 6 tens, but reducing 2 hundreds to tens and adding the 6 tens, we have 26 tens, from which 18 tens being taken there will remain 8 tens. 2 hundreds from 8 hundreds = 6 hundreds. The answer is, therefore, 681.

When the above is well understood, omit in practice a part of the explanation, as follows: 6, 14, 23, 31 from 32 leaves 1 unit; 3, 8, 11, 16, 18 tens from 26 tens = 8 tens; 2 hundreds from 8 hundreds = 6 hundreds.

The following form may also be taken: 6, 14, 23, 31, and 1 are 32 units; write one in the units' place; 3, 8, 11, 16, 18, and 8 are 26 tens; write 8 in the tens' place; 2 and 6 are 8 hundreds; write 6 in the hundreds' place.

Perform the operations indicated in the following examples, by the method explained above:

8. Subtract .87 + 4.73 + 826. + 42.71 + 9.854 +3.27 from 9012031.

9. Subtract 8837 +1429 +6372 +8406 +9785 +4203 from 9120301.

10. Subtract 8375.94 +276.483 +5427.98 +386.421 + 279.4381.679.4237 +4598.7 from 846271.3.

11. Mr. Ewell has in his possession $9478.63, but he owes $143.27 to Mr. Webster, $549.71 to Mr. May, $581.375 to Mr. Kingsbury, and $378.875 to Mr. Bryant. How much will he have left after paying his debts?

12. A cloth dealer bought 1497 yards of cotton cloth, 341.75 yd. of linen cloth, 247.875 yd. of broadcloth, 871.25 yd. of cassimere, and 647.38 yd. of satinet. How many yards did he buy? He sold to one man 327,75 yd. of cotton, and 87.27 yd. of linen; to another 236.84 yd. of cotton, 96.37 yd. of broadcloth, and 247.84 yd. of cassimere; and to another 468.49 yd. of cotton, 99 yd. of linen, 104.625 yd. of broadcloth, 439.75 yd. of cassimere, and 421.76 yd. of satinet. How many yards of cloth did he have left?

13. A man travelled 8725.67 miles in the following conveyances, viz. :— 1285.89 miles in rail-road cars, 876.81 miles in a canal-boat, 587.86 miles in a stage-coach, 725.18 miles on horse-back, 647.25 miles on foot, 3147.82 miles in a steamboat, and the rest in a ship. How many miles did he travel in a ship?

14. Messrs. Howes and Baker bought 27147 bushels of Indian corn. After selling, at private sale, 1438 bushels to one man, 2627 to another, 3781 to another, and 864 to another, they sold the rest at auction. How many bushels did they sell at auction? They received $719 for the first lot, $1313.50 for the second, $1890.50 for the third, $432 for the fourth, and enough to make up $13573.50 for what they sold at auction. How much did they receive for that which they sold at auction?